WORKING PAPER SERIES · 2005-01-31 · C22 ECONOMETRIC METHODS: Time Series Models C45 ECONOMETRIC AND STATISTICAL METHODS; Neural Networks ... CSFB/T Hedge Fund Index 0.879 2.569

College of Business Administration

University of Rhode Island

20042005 No 15

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Office of the DeanCollege of Business AdministrationBallentine Hall7 Lippitt RoadKingston RI 02881401-874-2337wwwcbauriedu

William A Orme

Gordon H Dash Jr Nina Kajiji and Christopher D Hunter

Hedge Fund Index Return Asymmetries Optimal Change-of-DirectionForecasting and Radial Basis Function Neural Networks

Hedge Fund Index Return Asymmetries Optimal Change-of-Direction

Forecasting and Radial Basis Function Neural Networks

By

Gordon H Dash Jr Associate Professor Finance and Insurance

Nina Kajiji Assistant Professor of Research Education

Christopher D Hunter Assistant Professor Civil Engineering

JEL CATEGORY

C22 ECONOMETRIC METHODS Time Series Models C45 ECONOMETRIC AND STATISTICAL METHODS Neural Networks C53 ECONOMETRIC MODELING Forecasting

Keywords Neural Networks radial basis function neural networks alternative investments financial engineering hedge funds return predictability

2002 By Gordon H Dash Jr Nina Kajiji and Christopher Hunter All rights reserved Explicit permission to quote is required for text quotes beyond two paragraphs In all cases full credit including notice is required

The research presented in this paper was completed under grants from The Office of Provost amp Vice President for Academic Affairs University of Rhode Island and The NKD Group Inc (wwwnkd-groupcom)

Acknowledgements The authors wish to recognize review comments provided by Professors Sean Reid Wentworth Boynton and Tong Yu Of course the authors are solely responsible for any remaining errors

Hedge Fund Asymmetries Optimal Forecasting -2- Dash amp Kajiji



Abstract

This paper provides evidence from hedge fund returns that the Kajiji-4 radial basis function (RBF) artificial neural network (ANN) dominates three alternative RBF networks when modeling one-period ahead change-of-direction and volatility forecasts ANN topologies are differentiated by both methodology and efficient implementation of the underlying algorithms Within the RBF topology and for the four methods under investigation in this research dominance is established by a focus on three defining characteristics First out-of-sample error minimization is addressed by a simulation experiment that is designed to improve the determination of network training size Second we reduce model dimensionality by invoking an orthogonal reduction of disparate and overlapping findings as presented in the extant literature on hedge fund return modeling Finally three objective measures of direction and profitability mapping are introduced to examine the performance of alternative networks in their ability to map both the magnitude and simultaneous directional change in return volatility The findings establish the computational and economic efficiency of the Kajiji-4 algorithm when applied to the problem of asset-return modeling




I Introduction

Investors have long sought to improve the efficiency of modeling financial returns

volatility as a means by which to maximize directional trading returns from identifiable trading

rules New and updated evidence from Barber et al (2001) more clearly establishes the link

between investors and their use of directional (or classification based) forecasting models

They document the ability of individual investors to earn abnormal returns from high frequency

directional trading by using the forecasts of informed security analyst At the institutional level

the role of forecasting gains an added dimension Not only are accurate forecasts needed to

support trading decisions but additionally Brown Goetzmann and Park (2001) find hedge fund

managers rely on historical and predicted peer benchmarks as performance guides In fact the

authors recognize the guides to be explanatory determinants of investor withdrawal activity

Amenc et al (2003) redirects the question to focus squarely on hedge fund return predictability

Althouth the authors stop short of providing and econometric estimation methodology they do

introduce a heuristic method to search for evidence of predictability in hedge fund returns within

a given tactical style They report strong evidence that significant predictability exists in hedge

fund index returns after adjusting for both tactical style and transaction costs

Despite the apparent investor need for efficient return-level forecasting methods the

extant literature has been less than clear in the production of stylized facts on the efficiency of

alternative modeling and prediction methods for alternative asset return levels For example in

a recent study on the predictability of three international capital market indices Leung et al

(2000) examined the contemporary view that investors have more confidence in return-level

prediction (magnitude) methodology than they do with classification (directional) alternatives

Leungs experiments found classification-based prediction dominated return-level methods in the

number of times a predicted observation was consistent with its actual outcome To support this


finding the authors also report the results of a threshold trading rule simulation that produced

greater wealth accumulation after the application of a classification prediction strategy The

normative probabilistic classification methods employed by Leung included linear discriminant

analysis logit- and probit-modeling along with a probabilistic neural network (PNN) By

contrast the comparative return-level forecasting methods included exponential smoothing

multivariate transfer function ARIMA vector autoregression with a Kalman filter and

multilayered feedforward neural network (MLFN) Within the return-level comparison the

artificial neural network architecture (MLFN) was found to produce superior forecasting and

trading performance

If classification methods do in fact dominate traditional return-level forecasting strategies

this would certainly provide an interesting challenge to some of the earliest and most influential

findings on predicting asset class returns as observed in the US and international markets (see

for example Keim and Stambaugh (1986) Campbell and Shiller (1989) Fama and French

(1989) Ferson and Harvey (1991) Barberis (2000) Harasty and Roulet (2000) and Lynch

(2000)) However before we accept the diminution of return-level modeling we note a serious

flaw in the Leung analysis as it pertains to the implementation of the reported ANN topology

The ANN normative results are derived from a software product (ThinkPro computer package)

for which there is neither active Internet site nor any other published academic evaluations The

absence of a comparative reference does not permit a required certification of the modeling

software nor does it permit a comparative analysis of algorithmic efficiency against more

established and recognized ANN applications1

The purpose of this study is to examine the applicability of RBF ANNs to efficiently

model and predict alternative asset returns To that end the study has a twofold purposes First

it is to reexamine and reconcile extant findings on asset return predictability Specifically we

seek to reconcile these findings as they may apply to alternative investment instruments like

hedge funds Hence we explicitly consider the asset-return findings under ANN modeling

provided by Leung et al (2000) on the one hand while considering Amencs report of style-

1 See Balci (2001) for an analytical framework for certifying modeling and simulation software applications Also for contemporary issues related to software compactness see Debray et al (2000) Fraser and Wendt (1986) Hanson (1983) Lindvall etal (2003) Dyba (2000) Sheldon and Greiner (1999) and Mayrand etal (2000)


based hedge fund returns predictability on the other Second it is to expedite the modeling of

monthly hedge fund index returns by applying the Kajiji-4 Bayesian information closed form

RBF ANN to the Credit Swiss First BostonTremont (CSFBT) family of hedge funds In earlier

studies the Kajiji-4 RBF ANN algorithm proved to be the more efficient method when applied

to both high-frequency (hourly) and daily financial data (see Dash et al (2003) and (2002) for

comparative details)

The paper proceeds as follows Section 2 of the paper presents a discussion on the

statistical properties that define hedge fund index returns This section also invokes a

multivariate statistical method to uncover the latent structure of overlapping hedge fund return

predictors Section 3 discusses the role of error measurement in ANN evaluation This section

also introduces enhanced methods to evaluate overall quality of directional forecasting Section

4 presents the results of the comparative modeling of hedge fund index returns Results of a

detailed prediction experiment are presented in section 5 The paper concludes with a summary

and conclusion in section 6

2 Hedge Fund Returns

The data for this analysis consists of 108 monthly return observations from January 1994

to December 2002 inclusive for the Credit Swiss First BostonTremont (CSFBT) family of

hedge funds (CSFBT)2 The tactical style of the 13 reported CSFBT hedge fund indices range

from high volatility (Dedicated Short Bias) to low volatility (Equity Market Neutral)

Throughout the manuscript we will refer to these two indices as the focus variables Detailed

descriptive characteristics of the CSFBT indexes are reported in Amenc (2003) Similarly

performance characteristics are provided by Lhabitant (July 2002) Because one of our

objectives here is to verify returns predictability by tactical style we augment the previously

published statistical findings on returns symmetry The added information is necessary to fully

isolate alternative ANN performance differences within the scope of the research objectives

2 httpwwwhedgeindexcom



The first part of this section presents a multivariate analysis of the returns time series

properties In addition to providing a graphical view of monthly returns we apply a linear

factor-analysis to uncover latent relationship among the thirteen indexes under study Figure 1

shows a cross-scatter chart of the monthly returns for the two focus hedge funds This display is

complemented by the descriptive statistics for the thirteen hedge funds as presented in table 1

The table corroborates but extends the evidence on returns behavior as reported by Amenc et

al (2003) Specifically we examine hedge fund returns asymmetries by reporting both skewness

and kurtosis characteristics Additionally table 1 also presents the results of applying the small

sample Shapiro-Wilks test for normality (W-Statistic)

Figure 1 Scatter Diagram of DED Short Bias vs Equity Market Neutral Fund

Scatter D iagramFeb 1994 - N ov 2002

DED Short Bias Equity Market Ntrl

1061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

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What are the latent dimensions that independently characterize the tactical style of the

CSFBT hedge fund returns We investigate this interesting question by implementing a

Varimax rotation on extracted principal components (PCA)3

3 As a purely linear projection method one that employs second-moment information it is well recognized that PCA may not be able to capture nonlinear relations among the data (see Demartines amp Herault (1997) for a curvilinear PCA that may be better able to model non-linearity in a multivariate distribution)


Table 1 Descriptive Statistics Mean STD Variance CV Skewness

Kurtosis WNormal

CSFBT Hedge Fund Index 0879 2569 6599 2924 0110 1238 0889 Convertible Arbitrage 0825 1405 1973 1704 -1602 3877 0826 Dedicated Short Bias 0203 5310 28201 26177 0825 1819 0802 Emerging Markets 0547 5361 28739 9795 -0477 2999 0895 Equity Market Neutral 0882 0922 0849 1045 0126 -0006 0919 Event Driven 0851 1813 3288 2132 -3272 20153 0773 Distressed 0983 2092 4375 2127 -2609 14281 0821 ED Multi Strategy 0783 1919 3684 2452 -2499 14522 0807 Risk Arbitrage 0680 1326 1758 1949 -1345 5775 0874 Fixed Income Arbitrage 0547 1184 1402 2165 -3155 14930 0734 Global Macro 1172 3668 13453 3129 -0018 1459 0907 Long Short 0973 3325 11055 3417 0236 2717 0859 Managed Funds 0571 3463 11993 6062 0042 0743 0913

Table 2 Varimax Analysis of Hedge Fund Index Returns Factor 1 Factor 2 Factor 3 Row

Dedicated Short Bias -08673 7669 LongShort 08322 7644 Event Driven 08234 04776 9151 Distressed 07814 7501 ED Multi-Strategy 07434 05511 8606 Emerging Markets 06906 5896 Risk Arbitrage 06886 6006 CSFBTremont Hedge Fund Index 06302 04651 -05537 9201 Equity Market Neutral 05278 3334 Convertible Arbitrage 07591 6977 Global Macro 05140 -07246 8555 Managed Funds -07710 7005 Fixed Income Arbitrage 08646 7642 Eigenvalue 51028 26988 17172 Cum Variance Explained 3925 6001 7322


The results of applying the Varimax rotation to the PCA eigenvalues are presented in

table 2 Three factors with eigenvalues of at least 10 are retained to account for just over 73

percent of the total variation in hedge fund returns For exposition purposes only factor loadings

greater than the absolute value of 040 are displayed Factor one is defined by indexes that

feature a short-trading investment style Factor two is defined by fixed income investing (and

multi-strategy funds) Factor three is defined by broad-based global investment strategies

Interestingly but as expected the CSFBTremont index loads across all three dominant factors

Taken together these first three factors account for just over 73 of the variation in the hedge

fund returns Despite the concerns raised by the observed non-linearity in hedge fund returns

the Varimax procedure was able to differentiate among the various trading styles In the next

section we examine the distributional properties of the hedge fund return vectors

In a manner that is consistent with prior findings we test the Gaussian properties of the

index returns (see Fung and Hsieh (1999) and Kat and Lu (2002) for detailed reviews on hedge

fund Gaussanity) As shown in table 1 the p-values extracted from the application of the

Shapiro-Wilks test support the conventional wisdom that hedge fund returns are not

characteristic of a normal distribution Additionally we find strong and significant evidence that

the CSFBT returns are leptokurtic (fat-tailed) Specifically we find only one fund (Equity

Market Neutral) with a kurtosis measure that is close to zero (-0006) The skewness measure for

this index is also very small and positive (we expected a negative value) This finding however

cannot be generalized to seven of the thirteen indexes For a subgroup of seven indexes the

kurtosis measure differs from zero and in some cases is quite high Within this group the

Emerging Markets index bounds the low range with a kurtosis measurement of 2999 The Event

Driven index produced the maximum kurtosis measure at 20153 The returns distributions for

this group of seven all display negative skewness coefficients These findings offer substantial

evidence that the distributions within this subgroup are asymmetrical The implication for the

risk-averse investor suggests a potential for extreme negative returns a finding that negates the

consideration of traditional mean-variance diversification methods as a risk reduction strategy


22 The Determinants of Hedge Fund Returns

We extend the calibration of hedge fund returns from economic determinants by

specifically addressing the current redundancy in variable specification that permeates the

literature Like Burgess (1995) and Refenes (1997) before us we invoke linear PCA for the

purpose of variance reduction to simple structure in a manner that is parsimoniously consistent

with the arbitrage pricing framework (see Han (2002) for an extensive literature review)4

221 Predictor Dimensions

One objective of this paper is to re-examine earlier modeling and prediction efforts directed at

hedge fund returns Table 3 provides a concatenated summary of the economic dimensions

examined by Leung et al (2000) on the one hand and Amenc (2003) on the other Pneumonic

identifiers are added separately We apply PCA with a corresponding Varimax rotation to

reduce the predictor variables to an uncorrelated latent structure Table 4 presents the latent

structure as eight factors with eigenvalues of at least 10 These factors explain slightly more

than 76 percent of the total variation in the predictor variables Table 5 provides an economic

summary of each dimension In the next section we present the methodology employed to create

proxy variables that represent the eight latent dimensions

4 Our reliance on monthly data rules out the ability to invoke the Bollerslev (1986) multivariate GARCH model or the multivariate stochastic volatility of Chib et al (2001)


Table 3 Contemporary Predictor Variables

Economic Dimension Pneumonic(s) Proxy-a Proxy-b Short Term Interest Rates

3TBYld 1D3TBYld Yield on the 3-month T-bill rate for the US

First difference of yield on 3-month US T-bill rate

Long Term Interest Rates

1D20TB First difference of the 20 year government bond rate for the US

Consumer Price Index (CPI)

1DCPI First difference US CPI

Industrial Production Level

1DIP First difference of US industrial production index

Dividend Yield SampPdivYld Dividend yield on the SampP stocks

Default Spread MBaaMAAA Difference between the yield on Moody s long term Baa bonds and the yield on Moody s long term AAA bonds

Term Spread 10TB-3TB Difference between the yield on 10-year T-bond and 3-month T-bill

Implicit Volatility VIX Change in the average intra-month values of the VIX

Market Volume NYSE Change in the market value on the NYSE

Events MLHBF MLHBFCC Merrill Lynch High Yield Bond Fund Log-differenced returns on the Merrill Lynch High Yield Bond Fund

Oil Price WTXOIL WTXOILlag

Average price of west Texas intermediate crude

Lag price of west Texas intermediate crude

US Equity Factor SampPlagCC SampPCC One period lag of the log-differenced returns of the SampP500 Index

Log-differenced returns of the SampP500 Index

World Equity Factor

MSCICC MSCIlagCC

MSCI EAFE World Index (excluding US) returns Europe Australia Far East

Log-differenced returns on the MSCI EAFE World Index (excluding US)

Currency Factor 1DCRB USDTW First difference in the Bridge Commodity Research Bureau Currencies Index

Trade-weighted Exchange Value of USD

Futures Index CRBF 1DCRBF CRB Futures Index First difference CRB Futures Index


Table 4 Varimax Rotated Factor Loading

Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 Factor 8 Row MLHBF -0946 949 SampPdivYld 0928 967 USDTW -0834 902 CRBF 0805 800 MBaaMAAA

-0466 0744 821

1D3TBYld -0660 630 3TBYld -0907 931 10TB-3TB 0886 887 WTXOILlag -0915 927 WTXOIL -0940 955 1DCRBF 0495 637 1DCRB 0522 545 MLHBFCC 0864 827 SampPCC 0936 923

VIX -0558 -0595 800 MSCIlagCC 0951 944 1DCPI 0804 822 1D20TB -0773 663 SampPlagCC 0833 789

NYSE 0745 773 1DIP 0837 755 Eigenvalue 3716 2600 2407 2345 2047 1501 1378 1251 Cumulative Variance

177 301 415 527 625 696 762 821


Table 5 Latent Factor Classification

Factor

Domain Characteristic

F1 Yields on Equity and Risky Bonds with Currency and Futures Effects F2 Default and Term Spread with Inverse 3-Tbill Effect F3 Continuously compounded returns on domestic and world Equity markets with

inverse effects of VIX F4 Oil F5 Continuously compounded returns on high yield bonds with lagged equity

returns and inverse VIX F6 First Differenced 20-year Tbond and 3-Tbill with inverse on differenced

currency effect F7 Effect of CPI and change in domestic market volume F8 Change in industrial production

222 Factor Scores

We follow the method of Thomson (1951) to create factor scores to represent the

independent factor domains Under the Thomson method if fr is the score of the rth factor

corresponding to a response of x then we estimate fr by a linear combination of the xi

r rf a x We choose ar such that 2

r rE f f is minimized In vector notation

1 kf f f and the solution is estimated by

F x (1)

where is the factor loading matrix the covariance matrix and x the original data matrix

From each set of responses x we obtain the vector of factor scores f The computed factor

scores serve as orthogonal determinants for the modeling of hedge fund index returns


3 Efficient ANN Modeling of Hedge Fund Returns

In this section we define a methodology for the efficient modeling of hedge fund returns

by ANN methods using the proxy variables obtained from the orthogonal latent dimensions

Specifically for any specific hedge fund let rt = (rit rpt) represent a vector of p returns

observed at time t t = 1 T Additionally let Ft = (F1t Fkt) specify k latent factors that are

sampled by maximum validity factor scores denoted as Spt for the p = 1 k latent factors across

t periods The modeling of returns for any individual hedge fund (HFIm) is achieved by

estimating

HFImt = (S1t Skt) (2)

for m = 1 M the13 published indexes

31 Measurement Errors in Return Level Prediction

Comparative evaluation relies upon the computed residuals for the training out-of-

sample validation and fitness (entire sample) data subsets Specifically model errors are

computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)

where MSEtraining is local to the training sub-set (Tt) and the MSEvalidation measure captures the

out-of-sample error component (Tt+1Tv) The MSEfitness measure is computed over all (T)

observations For purposes of this paper all algorithmic comparisons rely solely on the direct

evaluation of the computed MSEfitness


32 Measurement Errors - Classification Prediction

Neural network classification topology generally relies upon an output function of

probabilities to assign group membership (Leung tested this approach) In this study we invoke a

direction and mondified direction term to minimize the chance of misclassifying the error

functions produced by the use of alternative neural network architectures Each is defined

below

321 Direction Measure

Direction is defined as the number of times the prediction observation followed the up

and down movement of the known target variable The initial calculations were presented by

Harvey et al (2002) and later modified by Castiglione (2001) as shown below

1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where

Pi+1 = Indexi+1 Indexi is the percentage return on the index at time step i+1 T

Gi+1 = the forecast percentage return on the index at time step i+1 T

T = the number of days in the validation period

HS = a modified Heavyside function where HS(x)=1 for xgt0 and 0 otherwise

322 Modified Direction Measure

A more robust method of direction called modified direction was presented by Merton

(1981) as follows

Modified Direction = (( of correct up predictions of times index up) +

( of correct down predictions times index down)) 1 (7)


323 Time Dependent Directional Profit

To capture the simultaneous effects of time and (simulated) profit in the forecast variable

we introduce the Yao (Access Year 2003) time dependent directional profit measurement error

(TDDP) measure Under this method incorrectly predicted directional moves (classification

errors) are penalized more heavily than are correct predictions The weights are then adjusted

based on the amount of change from one forecast point to the next In essence a large

adjustment to the weights is made given a wrong directional forecast which is accompanied by a

large change in the underlying values Conversely a small adjustment to the weights is signaled

by a correct directional forecast for a correspondingly large change in the underlying The

TDDP error measure is defined as

2

1

1( )( )

2

N

TDP TDP p ppE f p t o

N

(8)

where ( ) ( )TDP DPf f p w p and the vectors t and o capture the target-prediction and observed

values over the p prediction periods Changes in the underlying and direction as described above

are determined by 1(| | ( ))DP p p p pf F t t sign t o At prediction point p the directional

profit adjustment factor is determined according to

1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)

where is the standard deviation of the target variable over all N observations (training and

validations observations) Simulation results for the monthly time scale lead us to the following

parameter values 1 05a 2 08a 3 12a and 4 15a We caution however that there is

insufficient evidence to recommend the extrapolation of these settings to other time scales such

as daily or higher frequencies


40 RBF ANN Modeling

This section identifies the four RBF ANN algorithms that will be compared for overall

model efficiency in target variable mapping We proceed by presenting modeling results for the

Kajiji-4 SPSS Statsoft and Matlab methods In section 41 the Kajiji-4 modeling results are

preceded by a presentation of the algorithm and resolution on efficient Kajiji-4 RBF training

Sections 42 43 and 44 present the results generated by solving the SPSS (2001) StatSoft

(2001) and Matlab algorithms respectively

41 The Kajiji-4 Closed Form Regularization Enhanced RBF ANN

The Kajiji-4 RBF ANN is an enhanced Bayesian neural network constructed with a

closed-form regularization parameter5 The optimal weighting values used within the Kajiji-4

RBF ANN are extracted by applying a supervised least-squares method to the training set The

supervised learning function is stated as

( )y f x

(10)

where y the output vector is a function of x the input vector with n number of inputs

Alternatively the supervised learning function can be restated as the following linear model

1

( ) ( )m

j jij

f x xw h (11)

where m is the number of basis functions (centers) h is the hidden units w is the weight vectors

and i = 1k output vectors (target variables) The flexibility of f(x) and its ability to model many

different functions is inherited from the freedom to choose different values for the weights Then

applying the least-squares principle is similar to minimizing the sum of squared errors as

represented by

2

1

( )p

i ii

SSE y f x

(12)

5 The Kajiji-4 algorithm is one of several application methods hosted within version 21752 of the WinORSfx

software system produced by The NKD-Group Inc (wwwnkd-groupcom)


Kajiji (2001) presents the RBF mapping function as a modified Tikhonov regularization

equation (1977) Tikhonov regularization adds a weight decay parameter to the error function to

penalize mappings that are not smooth If a weight penalty term is added to the SSE the SSE

can be restated as the following cost function

2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)

where kj are regularization parameters or weight decay parameters Under this specification the

function to minimize is

2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)

Iterative techniques are commonly employed to compute the weight decay parameter k

or a vector of parameters k But since the introduction of weight decay methods by Hoerl and

Kennard (1970) and Hemmerle (1975) it is generally understood that iterative techniques are

computationally burdensome and lack specificity [see Orr (1996 1997)] Further

computational experience has established that iteration often leads to local minima or in the case

where the weight decay approaches infinity inflated residual sums of squares By contrast the

Kajiji-4 RBF algorithm is a Bayesian regularization algorithm that derives a globally optimized

regularization parameter based on a cross-population of recent extensions in optimal ridge

regression parameter estimation by Crouse (1995) The design of the Kajiji-4 algorithm directly

attacks the twin evils that deter efficient ANN modeling the curse of dimensionality

(multicollinearity or over-parameterization) and inflated residual sum of squares (inefficient

weight decay)

411 Efficient RBF Training

RBF ANN algorithms are trained to predict the target variable by supervising the use of

an increasing number of cases (observations) on the input variables up to the point where

modeling improvements becomes redundant Overfitting or redundancy occurs at the point

where the ANN ceases to learn about the underlying process but instead it begins to memorize

the peculiarities of the training cases Mehta etal (2003) was able to demonstrate this effect in


a financial trading model In this case the overfit network effectively obscured important short-

term patterns of profitable trading ANN researchers agree that prior to initiating the economic

modeling process it is important to determine the efficient number of cases over which to train

the network In this research we accomplish this by introducing a step minimization of the cost

function (equation 14)

min maxQ

iiC

where C is defined in equation 14 and maxQ is the maximum number of cases in the training set

For the comparative modeling process invoked in this paper we step the network over maxQ

vectors to find i the vector associated with a global minimization of the cost function ( C )

Figure 2 shows the results of the training simulation applied to the Kajiji-4 RBF Because the

problem of overfitting a network is common to each of the four RBF methods considered here

we apply i at 78 vectors to the training phase of each method

Figure 2 Training Simulation S im u la tio n R e s u lts

F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1

T ra in in g S izeTra in in g S ize

7 57 06 56 05 55 04 54 03 53 02 52 01 51 0


412 Kajiji-4 Model Solutions

The analysis begins with a review of the computed fitness MSE for the two focus

indexes Table 6 shows a fitness error of 0369 and 0016 for the Dedicated Short Bias and

Equity Market Neutral hedge fund indexes While these measure appear relatively low the

fitness errors are even lower for four other hedge fund indexes CSFBTremont Risk Arbitrage

Global Macro and LongShort When the effects of skewness and kurtosis are considered we

note that the risk arbitrage hedge fund index produced a near immeasurable fitness error (000)

with a skewness coefficient of -1345 and the fifth highest kurtosis measure (5775) among the

CSFBT hedge fund index group Examining this effect across the study group the Kajiji-4

method appears to resolve an effective mapping of the target variable even as third- and fourth-

moment distributional characteristics increase in their characterization of the data distribution

However there is a dissipation in the modeling accuracy as absolute skewness and kurtosis

measures increase This effect is best exemplified by the Event Driven index With an absolute

skewness coefficient of -3272 and a kurtosis measure of 20153 the modeling process produced

a measureably higher fitness error (0088) When other indexes with high skewness and kurtosis

values are considered again we observe that high skewness and kurtosis measures are more

clearly associated with deteriorating modeling accuracy as measured by the neural network

fitness MSE A graphical display of modeling efficiency between the actual and predicted cases

is displayed in figures 3 and 4 for the two target indexes

The application of the Kajiji-4 algorithm produced a consistent reporting of directional

change across all indexes The Direction measure attained a high value of 0982 and a low value

of 0963 Similar results are found for the modified direction measure It ranges from a high of

1000 to a low of 0986 We need to note that a modified direction measurement of 10 does not

necessarily imply a perfect model A more conservative interpretation would suggest that the

Kajiji-4 algorithm correctly models the target variables change in direction but that does not

mean that it always captures the full extent of the peaks and troughs found in the observed

dataset Taken together the two direction measures provide strong evidence that when applied

to the monthly returns data of alternative assets the Kajiji-4 algorithm exhibits near perfect

results in the modeling of directional change These results are supported by the correspondingly

strong performance measures reported by the profit-enhanced TDDP dimension For this

measure a low value is preferred to a higher one


Table 6 Kajiji-4 Model Results

Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

Validation Error 0027 0076 1327 0086 0059 0317 0684 0127 0001 0173 0032 0044 1530

Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425

Performance Measures

Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833

Model Characteristics

Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722

Transformation None None None None None None None None None None None None None

MinMaxSD na na na na na na na na na na na na na

Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000


Figure 3 Actual and Predicted Using Kajiji-4 RBF on Dedicated Short Bias Fund

DED Short BiasActual and Predicted (Feb 1994 - Feb 2002)

Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

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Figure 4 Actual and Predicted Using Kajiji-4 RBF on Equity Market Neutral Fund

Equity Market NatrlActual and Predicted (Feb 1994 - Feb 2002)

Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

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42 SPSS Neural Connection Model Solutions

The SPSS RBF modeling results differ markedly from those produced by the Kajiji-4

algorithm Referring to table 7 the SPSS RBF modeling experiment achieves the lowest error

value when modeling the Equity Market Neutral index This is one of the two focus indices

However at 1370 the reported fitness error is more than one thousand times larger than that

produced by application of the Kajiji-4 RBF ANN For the other focus index Dedicated Short

Bias the SPSS fitness MSE not only is the reported error more than 1975 times higher than that

produced by the Kajiji-4 counterpart but it is also the largest MSE reported for all SPSS

modeling solutions Returning to our examination of RBF modeling performance under

conditions of distributional asymmetry we note that except for the Fixed Income Arbitrage index

the SPSS algorithm generates a consistent performance for hedge fund indices with absolute

skewness levels above 300 and kurtosis measures greater than 140 Within the subgroup

defined by the Event Driven Distressed and ED Multi-Strategy indices the reported fitness

MSE measures ranged from 3172 to 3643 By comparison the Kajiji-4 algorithm also

performed consistently across this same subgroup but the reported MSE measures were

decidedly lower (0425 to 0111) In summary the SPSS RBF algorithm demonstrated the

ability to produce consistent performance across monthly return indices with high absolute

skewness and high kurtosis measures Unfortunately and setting asymmetry issues aside it is

clear that the performance of the SPSS algorithm dissipates as the level of relative variation (CV)

increaseS A graphical display of the two focus indexes is provided in figures 5 and 6

respectively


Table 7 SPSS Model Results

SFB Tremont Hedge Fund

Convertible Arbitrage

Dedicated Short Bias

Emerging Markets

Equity Market Neutral

Event Driven

Distressed ED Multi-Strategy

Risk Arbitrage

Fixed Income Arbitrage

Global Macro

Long Short

Managed Funds

Return-level Error Measures Training Error 1074746 0998806 1018551 1073490 0948484 098785 0464553 091175 0860569 0522714 070402 101266 0939322 Validation Error 0279682 0827859 0868138 0503276 0544275 075957 0899311 063094 0671334 0788974 022464 033472 1210085 Fitness Error 6999264 2468697 27655226 28473214 1370447 364267 3127028 349122 1698769 0767644 1093985 1094859 1205949 Classification Error Measure Direction 05046 06697 04404 05138 05780 05596 05688 05963 06055 06514 06789 05229 05413 M Direction 03425 03080 01521 02103 03271 02917 05255 03644 02735 04862 04496 03112 -00137 TDDP 16879 08222 78533 53780 02697 08478 06223 10244 04540 01597 17682 34983 35241


Figure 5 Actual and Predicted Using SPSS RBF on the Dedicated Short Bias Fund

Dedicated Short BiasActual and Predicted

Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

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-2

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-8

Figure 6 Actual and Predicted Using SPSS on Equity Market Neutral Fund

Equity Market Neutral FundActual and Predicted

Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

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43 StatSoft Statistica Model Solutions

On balance the results produced by StatSoft RBF algorithm fall between those produced

by SPSS and Kajiji-4 Before discussing the details as provided in table 8 it is important to note

that the user interface of the StatSoft algorithm differs considerably from what is presented by

either the Kajiji-4 or SPSS methods For the StatSoft-based experiment where possible optional

parameter settings were set to levels specified as default levels under the Kajiji-4 method We

then undertook a manual optimization process with the goal of identifying parameter settings that

would produce best (if not optimal) solution results for the sample data Stated differently while

we were able to apply default settings without modification under the Kajiji-4 and SPSS

experiments that was not possible in the application of the StatSoft method

As with the prior applications the StatSoft method achieved the lowest fitness MSE for

the Equity Market Neutral index model but we note that the reported MSE is over 1000 times

larger than that produced by the Kajiji-4 network For the other focus index Dedicated Short

Bias at 23051 the fitness MSE is the highest recorded across all RBF applications and their test

results The fitness MSE here is more than 57 times that achieved for the same index under the

Kajiji-4 method Figure 7 and 8 provide a graphical view of the algorithms predictive ability for

the Dedicated Short Bias and Equity Neutral fund returns It is clear from this view that the

target variable achieves reasonable directional performance but falls short in its ability to

replicate the magnitude of the changes We observe that the StatSoft method performs best when

modeling monthly hedge fund returns with relatively low coefficients of variation The

algorithms predictive ability dissipates noticeably as relative variation as measured by the

coefficient of variation (CV) increases How if at all this deterioration is impacted by

distributional asymmetry is not immediately clear from the results generated by this experiment


Table 8 Staistica-4 Model Results




Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds

Return-level Error Measures Training Error 03647 05030 01663 01280 09018 04456 03509 04142 06886 06328 01994 02182 02826 Validation Error 04937 05097 01747 01227 05999 05693 04590 04475 06107 06829 02747 01314 04146 Fitness Error 50695 10008 230509 160618 07297 32304 32736 34262 14754 11334 150169 71130 108056 Classification Error Measure Direction 06330 08532 06055 06422 07523 07431 06422 06055 07248 06881 05963 05596 05229 M Direction 01901 05861 03245 05216 00556 05211 04792 02315 02890 00415 00659 04142 02421 TDDP 10963 03143 64969 30278 01067 11203 08245 11080 04369 03822 43435 21328 30088


Figure 7 Actual and Predicted Using the StatSoft ANN on Dedicated Short Bias Fund

Dedicated Short Bias Fund Actual and Predicted

Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

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Figure 8 Actual and Predicted Using the StatSoft ANN on Equity Market Neutral Fund

Emerging Markets Neutral FundActual and Predicted

Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

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44 Matlab Model Solutions

On first review the Matlab RBF algorithm appeared to be outstanding during the training phase of the analysis Reported

training error values were negligible (0000) at the formatted table accuracy Unfortunately overall model fitness errors did not

follow this trend Matlab followed the other method by reporting the lowest fitness MSE for the Equity Market Neutral index model

In the case of the Dedicated Short Bias index Matlab reports the fitness MSE at 8430 a value that is almost 23 times higher than that

reported by the Kajiji-4 RBF application This result is directly attributable to overfitting during the training phase of the analysis

Figure XX and XX provide a graphical view of the algorithms predictive ability for the Dedicated Short Bias The graph clearly

shows a near perfect mapping of the predicted variable to the target variable over the 78 training vectors However over the

remaining test phase the Matlab RBF predicted target fails to reproduce the volatility of the target index Clearly the Matlab RBF

trained to learn the peculiarities of the training vectors rather than learning the intricacies of the volatility exhibited by the Dedicated

Short Bias hedge fund index

Table xx Matlab Model Results

CSFB Tremont Hedge Fund



Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds




Actual and Predicted (Jan 1994 - Dec 2002)

Actual Predicted

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46 RBF Comparative Analytics

A comparative analysis of the results achieved by application of the three RBF

algorithms clearly points to the role of CV and distributional asymmetry as factors that impact

modeling accuracy Table 9 provides a concentrated view of the underlying statistical properties

by algorithm We focus our view on the role of third- and fourth-moment characteristics as

factors that influence the behavioral characteristics of the models with the lowest fitness MSE

In this context it becomes apparent that model solutions produced by the SPSS and StatSoft

algorithms choose the indices with the thirteenth ranked CV and the thirteenth ranked kurtosis

These indices also exhibit low skewness (tenth ranked) From these results it is apparent that the

SPSS and StatSoft algorithms perform best under conditions where the time series of returns is

least disturbed by third- and fourth-moment asymmetries By contrast the Kajiji-4 algorithm

was at its best whenever relative dispersion was at its highest Although the Kajiji-4 algorithm

was the dominant modeling method under the presence of moderate levels of skewness and

kurtosis it too performed more accurately as asymmetry measures diminished But it is

interesting to observe that the highest MSE produced by the Kajiji-4 method occurred only when

the index exhibited high(est) skewness and kurtosis measures Under SPSS and StatSoft the

highest MSE recording was not necessarily associated with a particular level of returns

asymmetry


Table 9 Relative Dispersion Comparison

Kajiji-4 SPSS StatSoft Matlab Lowest Validation MSE

Dedicated Short Bias [179] and Global Macro [51310]

Equity Market Neutral [131013]



Highest Validation MSE

Event Driven [911]

Dedicated Short Bias [179]



Rankings for CV Skewness and Kurtosis are in parentheses

431 Direction and Modified Direction Efficiency

Table 10 provides a comparison of the Direction and Modified Direction measures The

performance achieved by the Matlab algorithm points to an important use of these measures

Under Matlab Modified Direction is perfect at 1000 while Direction achieves a high level of

0988 As previously noted the Matlab method suffers from over-fitting It is obvious that a

correct and comparative use of both measures can only be assured when reasonable volatility

mapping over both the training and test vectors occurs Because fitness volatility mapping did

take place for the other three RBF algorithms the two directional measures offer a measure of

comparative efficiency Tables 10 and 11 present a ranked view of the two directional

measures What is most obvious is the lack of a ranking consistency Except for a weak

argument in the case of the Managed Funds index there is no overlap in the rankings achieved

across the test algorithms Again the Matlab results are suspect owing to the problem of over-

fitting Despite the observed lack of consistency the Kajiji-4 algorithm performs best while the

StatSoft algorithm appears to maintain an edge over the SPSS algorithm in directional accuracy

Table 10 Summary of Direction and Modified Direction Kajiji-4 SPSS StatSoft Matlab

Min Direction 3-tied (0963) Dedicated Short Bias (0440367)

Managed Funds (0522936)

ALL (0988)

Max Direction 10-tied (0982) Global Macro (0678899)

Convertible Arbitrage (0853211)

ALL (1000)

Min Modified Direction

2-tied (0986) Managed Funds (-0013723)

Fixed Income Arbitrage (0041528)

ALL (1000)

Max Modified 11-tied (1000) Distressed Convertible ALL (1000)


Direction (0525463) Arbitrage

(0586124) Computed values in parentheses


Table 11 Comparative Rankings of the SPSS and StatSoft Direction Measures

Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1

Long Short 2 2 10 8 12 5 1 1 Emerging Markets

1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1


432 Directional Profit Efficiency

The TDDP measure employs a correction weight that is designed to compensate for

incorrect directional movements by the overall magnitude of the movement The correction

weight at time t is applied to future predicted values over the generated forecasting values at time

t+1 T The smaller the weight the more accurate the training phase of the model By

definition large weights are indicative of a missed direction an incorrect magnitude of

adjustment or some combination of the two Table 12 presents the TDDP measures for each of

networks under study

The TDDP results confirm the relative efficiency of the Kajiji-4 RBF ANN The TDDP

measure summarizes the accuracy of the predicted variable to meet the target variables inflection

points (classification) and the magnitude (level) of movement associated with any particular

inflection A comparative TDDP performance ratio is computed for each of the alternative

networks such that low (high) values indicate similar (dissimilar) performance Again the ratios

for the Matlab experiment are deemed unreliable In all cases the Kajiji-4 method is more

efficient at modeling returns However we do note some dissipation in performance as the

return distributions report increasing levels of asymmetric and leptokurtic behavior

45 3 The Informational Content of Model Residuals

In this section we first apply a PCA with Varimax rotation to the residual returns

extracted from the application of equation [7] above for all Kajiji-4 models Specifically we

subject to the PCA procedure where 1( )mt mt t ktHFI f S S The section continues by

reformulating [7] to incorporate the latent information uncovered in the first step The results of

this reformulation are designed to account for the impact of skewness in an effort to improve the

forecasting properties of the method


Table 12 Relative TDDP Measures with Asymmetry Identification

Kajiji-4

SPSS StatSoft Matlab SPSSKajiji-4 StatSoftKajiji-4

MatlabKajiji-4

Asymmetrical

Risk Arbitrage 1 3 4 7 Na Na Na A Global Macro 2 9 12 1 884100 2171750 0050

CSFBT Hedge Fund

3 8 6 4 843950 548150 2700

Long Short 4 10 9 5 874575 533200 2175 Convertible Arbitrage

5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A

Event Driven 10 6 8 10 28620 37343 2393 A Distressed 11 4 5 12 9574 12685 2114 A


12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546


The results of this application are presented in table 13 As with the earlier use of the

factor analytic method we replace factor loadings below the absolute value of 040 with a

period Additionally only those factors with eigenvalues of 10 or higher are retained for display

purposes Two significant factors are reported Factor 2 is differentiated from factor 1 by the

asymmetry characteristics of the hedge fund indices For the skewness dimension only the

Emerging Markets index has a negative skewness above -30 Similarly for the kurtosis

dimension (with the same exception for the Emerging Markets index) each index that loads on

factor 2 has a kurtosis measure that exceeds 140 The factor analytic results provide additional

support for the MSE directional analysis that produced observed differences in model efficiency

based on the existence of asymmetry in the observed hedge fund returns

Table 13 Varimax Results After Model Residuals Fund Name Factor 1 Factor 2 Row Global Macro 09625 9673 Managed Funds 09509 9438 SFTTremont Hedge Fund 09197 8871 Distressed 08138 6795 Dedicated Short Bias 08037 6797 Equity Market Neutral -07893 6369 LongShort -07252 5355 Risk Arbitrage -06540 4539 Fixed Income Arbitrage -05113 -05972 6181 Emerging Markets 07347 6848 Event Driven -09171 9340 ED Multi-Strategy 08562 7847 Convertible Arbitrage 06195 3870 Eigenvalue 61157 30765 Percent of Variance Explained 4704 7071

5 One-Period Ahead Forecast of Hedge Fund Index Returns

The one-period ahead forecast is achieved by embedding a delay between the observed

time series (hedge fund return) and the model that is capable of generating it The model

specification is promulgated from the PCA results as presented above Specifically the

economic forecasting model proxies each orthogonal dimension as a predictor variable by

including the time series with the highest factor loading The result of this process produces

equation (15)


HFIt = f MLHBFt-k 3TBYld t-k MSCIlagCC t-k WTXOIL t-k MLHBFCC t-k 1D20TB t-k 1DCPI t-k 1DIP t-k (15)

In this model statement the lag parameter k is set to 1 The one period ahead forecasts from the

application of equation (15) to each of the 13 indexes are presented in table 14

Table 14 One-Period Ahead Forecast of Hedge Fund Returns Name of Fund Actual Value Predicted

Value Incorrect Direction

CSFBT Hedge Fund Index 128 0994 Convertible Arbitrage 302 1311 Dedicated Short Bias -273 2438 Emerging Markets -045 -0188 Equity Market Neutral 031 0848 Event Driven 227 0864 Distressed 312 0987 ED Multi Strategy 198 0835 Risk Arbitrage -039 0653 Fixed Income Arbitrage 126 0632 Global Macro 203 0921 LongShort -007 0850 Managed Fund 607 3486

The Kajiji-4 RBF correctly predicted the directional level for ten of the thirteen models

For two of the three models where the directional classification forecast was incorrect the

indices in question are known to incorporate a strong commitment to a short-position investment

trading philosophy Since one of the primary objectives of this research is to produce accurate

one-period ahead forecasts we propose three alternate models for the three erroneous results

Replacing the economic variable with the highest factor loading with one that more

adequately captured either short-term or direct capital market activity produces the re-formulated

models The results of solving equations (16) to (18) are presented in table 15 These models

produced directional returns level forecast that matched the overall findings from applying

equation (15)

Risk Arbitrage Indext = f(3TBYld t-k WTXOIL t-k MLHBFCC t-k 1DCPI t-k MSCICC t-k 1D3TBYld t-k (16)

LongShortt = fMLHBF t-k 3TBYld t-k WTXOIL t-k MLHBFCC t-k 1DCPI t-k MSCICC t-k 1D3TBYld t-k (17)

Ded Short Biast = fMLHBF t-k 3TBYld t-kWTXOIL t-k MLHBFCC t-k 1DCPI t-k 1D3TBYld t-k SampPCC t-k (18)


Table 15 Results of Solving the Reformulated One-Period Ahead Forecast Models

Name of Fund Actual Value Predicted Value

Dedicated Short Bias -273 -3797 Risk Arbitrage -039 -0248 LongShort -007 -1012

6 Summary and Conclusions

The objective of this research was two-fold The initial phase of the research re-

examined hedge fund asymmetries and developed an efficient set of hedge fund index

determinants For six of thirteen hedge funds managed by CSFBTremont we find that in

addition to relative volatility (coefficient of variation) both skewness and kurtosis play a

significant role in the fitness measure of performance for each of the tested RBF methods

Again the Kajiji-4 method surfaced as the most computationally efficient when confronted with

high relative volatility skewness and peaked return distributions When using the efficient

determinants as derived from a factor-analytic application the comparative performance of three

alternative RBF algorithms provided additional evidence of the dominance enjoyed by the Kajiji-

4 RBF when compared to the RBF algorithms from SPSS and StatSoft The evidence on the

relatively short duration monthly time series also proved to be strikingly similar to previously

reported findings on longer duration series covering a more dense time scale For this initial

objective and most importantly the research findings presented here offer an expanded view of

the conclusions proffered by Leung Unlike Leung we do not find a reason to differentiate

classification and return-level forecasts Under the Kajiji-4 method it is possible to achieve

efficient classification of future returns volatility as well as an efficient point estimate of the

forecasted return level

Finally this paper established the characteristics under which the Kajiji-4 method is able

to generate accurate one-step ahead volatility and level forecast For the thirteen indexes under

investigation the Kajiji-4 method predicted the correct direction of the next period return for ten

of the indexes The three incorrect forecasts are each characterized by behavior that relies upon

short-investment positions This observation leads us to conclude that in its current

specification the Kajiji-4 forecasting model is not yet capable of forecasting one-period ahead


monthly returns for hedge funds that follow short-investment based philosophies By relaxing

the generality of the economic model correct directional and level forecast were possible for

these three indexes as well In summary the Kajiji-4 method appears to be a reliable method for

forecasting direction and level of hedge fund index returns for funds that do not incorporate a

short-position commitment


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Tikhonov A and Arsenin V 1977 Solutions of Ill-Posed Problems Wiley New York

Yao J amp Tan C L Access Year 2003 A Study on Training Criteria for Financial Time Series Forecasting JTYaomasseyacnz Palmerston North New Zealand

Typically a MLP begins training with a poor fit to the data (due to its random weight initialization) As training progresses the neural networks fit to the data improves At some point however the neural network begins to overfit the data meaning that its performance on the training data continues to improve but only because it is beginning to memorize the peculiarities of the training cases not because it is learning more about the underlying process Remember the object is to have the neural network generalize usefully to new cases not memorize the training cases

Our responsibility is to provide strong academic programs that instill excellenceconfidence and strong leadership skills in our graduates Our aim is to (1)promote critical and independent thinking (2) foster personal responsibility and(3) develop students whose performance and commitment mark them as leaderscontributing to the business community and society The College will serve as acenter for business scholarship creative research and outreach activities to thecitizens and institutions of the State of Rhode Island as well as the regionalnational and international communities

Mission

The creation of this working paper serieshas been funded by an endowmentestablished by William A Orme URICollege of Business AdministrationClass of 1949 and former head of theGeneral Electric Foundation This workingpaper series is intended to permit facultymembers to obtain feedback on researchactivities before the research is submitted toacademic and professional journals andprofessional associations for presentations

An award is presented annually for the mostoutstanding paper submitted

Founded in 1892 the University of Rhode Island is one of eight land urban and sea grantuniversities in the United States The 1200-acre rural campus is lessthan ten miles from Narragansett Bay and highlights its traditions ofnatural resource marine and urban related research There are over14000 undergraduate and graduate students enrolled in seven degree-granting colleges representing 48 states and the District of ColumbiaMore than 500 international students represent 59 different countriesEighteen percent of the freshman class graduated in the top ten percentof their high school classes The teaching and research faculty numbersover 600 and the University offers 101 undergraduate programs and 86advanced degree programs URI students have received Rhodes

Fulbright Truman Goldwater and Udall scholarships There are over 80000 active alumnae

The University of Rhode Island started to offer undergraduate businessadministration courses in 1923 In 1962 the MBA program was introduced and the PhDprogram began in the mid 1980s The College of Business Administration is accredited byThe AACSB International - The Association to Advance Collegiate Schools of Business in1969 The College of Business enrolls over 1400 undergraduate students and more than 300graduate students

Ballentine HallQuadrangle

Univ of Rhode IslandKingston Rhode Island



By

Gordon H Dash Jr Associate Professor Finance and Insurance

Nina Kajiji Assistant Professor of Research Education

Christopher D Hunter Assistant Professor Civil Engineering

JEL CATEGORY

C22 ECONOMETRIC METHODS Time Series Models C45 ECONOMETRIC AND STATISTICAL METHODS Neural Networks C53 ECONOMETRIC MODELING Forecasting

Keywords Neural Networks radial basis function neural networks alternative investments financial engineering hedge funds return predictability

2002 By Gordon H Dash Jr Nina Kajiji and Christopher Hunter All rights reserved Explicit permission to quote is required for text quotes beyond two paragraphs In all cases full credit including notice is required

The research presented in this paper was completed under grants from The Office of Provost amp Vice President for Academic Affairs University of Rhode Island and The NKD Group Inc (wwwnkd-groupcom)

Acknowledgements The authors wish to recognize review comments provided by Professors Sean Reid Wentworth Boynton and Tong Yu Of course the authors are solely responsible for any remaining errors




Abstract





I Introduction

































trading performance





























































1061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9







Kurtosis WNormal








































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission











Abstract





I Introduction

































trading performance





























































1061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9







Kurtosis WNormal








































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission











I Introduction

































trading performance





























































1061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9







Kurtosis WNormal








































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission

















trading performance





























































1061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9







Kurtosis WNormal








































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission

















































1061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9







Kurtosis WNormal








































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission






















1061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9







Kurtosis WNormal








































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission










Kurtosis WNormal








































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission












































































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission
















































World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission






























World Equity Factor

MSCICC MSCIlagCC









-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission











-0466 0744 821




177 301 415 527 625 696 762 821



Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission










Factor






222 Factor Scores







F x (1)












estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission
















estimating






computed as

2

1

t

training i ii

MSE y y t

(3)

2

1

v

validation i ii

MSE y y v

(4)

2

1

T

fitness i ii

MSE y y T

(5)











below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission














below





1 1 1 11

11i i i i

i T

HS P G HS P GT

(6)

where







(1981) as follows














2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission



















2

1

1( )( )

2

N


N

(8)





1

2

3

4

0 | |

0 | |( )

0 | |

0 | |

p p p

p p p

DPp p p

p p p

a if t o and t

a if t o and tf p

a if t o and t

a if t o and t

(9)







40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission









40 RBF ANN Modeling












( )y f x

(10)



1

( ) ( )m

j jij

f x xw h (11)





represented by

2

1

( )p

i ii

SSE y f x

(12)








2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission













2 2

1 1

( )p m

i i j ji j

C y f x k w

(13)



2 2

1 1

argmin( ( | ))

p m

i i j ji j

C y f x k k wk

(14)












weight decay)













min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission














min maxQ

iiC








F itn e s s E rro r

M in H e a d ro o m

5 04 94 84 74 64 54 44 34 24 1 4 03 9 3 8 3 73 6 3 5 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1 1 1 0

Fitn

ess

Err

or

1


7 57 06 56 05 55 04 54 03 53 02 52 01 51 0



































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission










































Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission










Target CSFB

Tremont

Hedge

Fund

Convertible

Arbitrage

Dedicated

Short Bias

Emerging

Markets

Equity

Market

Neutral

Event

Driven

Distressed ED

Multi-

Strategy

Risk

Arbitrage

Fixed

Income

Arbitrage

Global

Macro

Long

Short

Managed

Funds

Computed Measures

Lambda 1901 1359 1300 2644 1311 0651 0558 1166 16254 0647 3489 2101 1306

Training Error 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000


Fitness Error 0007 0021 0369 0024 0016 0088 0190 0035 0000 0048 0009 0012 0425


Direction 0963 0982 0982 0982 0982 0982 0963 0982 0982 0982 0982 0963 0982

Mod Direction 0986 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 0986 1000

TDPM 0002 0005 0132 0006 0005 0030 0065 0012 0000 0017 0002 0004 0147

R-Square 9994 9947 9936 9996 9909 9867 9784 9953 9999 9827 9997 9994 9833


Training (N) 78 78 78 78 78 78 78 78 78 78 78 78 78

Training () 722 722 722 722 722 722 722 722 722 722 722 722 722



Radius 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000




Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission











Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

9897969594939291908988878685848382818079787776757473727170696867666564636261605958575655545352515049484746454443424140393837363534333231302928272625242322212019181716151413121110987654321

3

2

1

0

-1






















respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission





























respectively






Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission













Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission











Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1






























Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission





































Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission













Emerging Markets


Event Driven

Dis-tressed

ED Multi-Strategy

Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission











Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9



Actual Predicted

1081061041021009896949290888684828078767472706866646260585654525048464442403836343230282624222018161412108642

3

2

1

0

-1

-2

















Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission
























Emerging Markets


Event Driven


Risk Arbitrage


Global Macro

Long Short

Managed Funds





Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission











Actual Predicted

110108106104102100989694929088868482807876747270686664626058565452504846444240383634323028262422201816141210864

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

-9


















asymmetry









Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission
















Event Driven [911]






















ALL (0988)



ALL (1000)




ALL (1000)







Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission













Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission










Kajiji-4

SPSS StatSoft

Matlab

Hedge Fund Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

Direction

Rank

Modified Direction

Rank

DirectionRank

Modified Direction

Global Macro

1 1 1 3 11 11 1 1


1 1 2 6 1 1 1 1


1 1 3 2 5 13 1 1

Risk Arbitrage

1 1 4 10 4 7 1 1

ED Multi-Strategy

1 1 5 4 10 9 1 1


1 1 6 7 2 12 1 1

Distressed 2 1 7 1 6 4 1 1

Event Driven

1 1 8 9 3 3 1 1

Managed Funds

1 1 9 13 13 8 1 1


1 1 11 11 7 2 1 1

CSFBT Hedge Fund

2 2 12 5 8 10 1 1


1 1 13 12 9 6 1 1



























Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission


































Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission










Kajiji-4


MatlabKajiji-4

Asymmetrical


CSFBT Hedge Fund

3 8 6 4 843950 548150 2700


5 5 2 3 164440 62860 1040 A


6 2 1 2 53940 21340 0020

Emerging Markets

7 12 11 6 896333 504633 1900 A

ED Multi-Strategy

8 7 7 9 85367 92333 3008 A


9 1 3 8 9394 22482 1812 A



12 13 13 13 59495 49219 1074

Managed Funds

13 11 10 11 23973 20468 0546



















equation (15)

















equation (15)







































REFERENCES





















































Mission


























equation (15)

















equation (15)







































REFERENCES





















































Mission
























equation (15)







































REFERENCES





















































Mission











































REFERENCES





















































Mission















REFERENCES





















































Mission









REFERENCES





















































Mission















































Mission






























Mission















Mission









Mission








Documents

WORKING PAPER SERIES · 2005-01-31 · C22 ECONOMETRIC METHODS: Time Series Models C45 ECONOMETRIC AND STATISTICAL METHODS; Neural Networks ... CSFB/T Hedge Fund Index 0.879 2.569