Capm Condiz October09 MS

8/6/2019 Capm Condiz October09 MS

1/39

A Conditional CAPM Model with Local Covariates forDetecting and Evaluating Active Management

September 28, 2009

Abstract

The intercept of the standard CAPM and Conditional CAPM model, the alpha,

is used to evaluate the long-run performance of managed portfolios. However,

this measure is not always appropriate for detecting the presence and impact

of active management strategies. In this paper, we introduce a Conditional

CAPM model where the time-varying alpha and beta parameters depend only

on the past history of the underlying portfolio returns and of the benchmark

returns. The dynamics of the parameters has two components: the rst de-

scribes the long-term behavior of the alpha and beta, whereas the second isassociated with the short-term performance of the underlying portfolio. The

interpretation of parameters allows the identication of portfolio managers who

implement active management strategies. We provide an empirical application

based on a large set of U.S. mutual funds showing how widespread active man-

agement approaches are, even if only a minor fraction persistently beats the

benchmark. We also show that the recent nancial crisis has had negative ef-

fects on mutual fund performances.

Keywords : Conditional CAPM, time-varying parameters, local covariates,

mutual funds.

1


2/39

1 Introduction

One of the main purposes of portfolio managers is to beat the benchmark, mak-

ing their nancial products attractive for private and institutional investors. Extra-

performances over the reference index could be produced, for instance, by imple-

menting active management strategies such as security selection programs and tacti-

cal asset allocation (TAA) choices. The nancial literature often uses style analysis

and conditional factor models to study ex-post the performances of managed prod-

ucts. These methods give some insight into the effectiveness of portfolio manage-

ment, but generally say very little about the type of active strategies implemented

(i.e., security selection, TAA, timing, static or dynamic strategies) and on their spe-

cic contribution to the overall return, apart from the particular case in which the

portfolio composition is known and available over the sample period. This last piece

of information is generally not accessible to private investors or to all institutional

investors which, in any case, are interested in knowing the presence and the results

of active management over a number of given portfolios.

In this paper we contribute to this branch of the literature and propose a model

that tries to solve some critical aspects of the actual approaches. We introduce

a modication of standard Conditional CAPM models that allows verication of the existence of active management strategies and their effectiveness. Overall, this

contribution provides four methodological and empirical contributions.

In the available Conditional CAPM models, the dynamics of the parameters

has two components: the rst is a constant, while the second is dynamic and re-

lated to one or more economic and nancial covariates. However, the identication

of the appropriate covariates is fundamental to avoid omitted variable problems

and to correctly detect active management presence and effectiveness. In addition,

non-fundamental strategies are not identied through quantitative covariates, an

additional critical aspect of Conditional CAPM approaches.

The rst contribution of this paper is given by a methodology for building con-

ditioning variables. Our covariates are based on local estimates of the standard

static CAPM model and, thus, are extracted from historical data. As a result, we

2


3/39

overcome many criticisms and problems associated with the selection and relevance

of covariates.

Covariates are difficult to identify and may vary across managers. As a result,

the parameter interpretation cannot be easily associated with active managementapproaches. Differently from standard conditional CAPM models and thanks to

the introduction of the previous methodology, the second contribution of this work

is associated with a direct interpretation of model parameters. The time-varying

alpha and beta of our conditional CAPM model still have two components (con-

stant and dynamic), but with a proper meaning: the intercept describes the long-

term behavior of alpha and beta, whereas the second component is associated with

the short-term performances of the underlying portfolio. Furthermore, by analyz-

ing parameter signicance, we are able to study portfolio performances, and, more

interestingly, to identify portfolio managers who implement effective TAA or se-

curity selection strategies. Finally, the intercept of the time-varying alpha is also

interpretable as an overall measure of returns persistence. Building on parame-

ter interpretation, we also provide a classication of mutual funds focusing on the

management approaches.

Using the previous results, the Conditional CAPM model we propose has some

advantages compared to the traditional approaches. In addition to the solution to

problems associated with the covariates, this model enables investors to check the

correspondence between portfolio objectives and performances: beating the bench-

mark and using active management strategies. The model can also be considered as

an advanced tool in the selection of investment products for both private investors

and fund of funds investment managers.

To show the potential of our modeling approach, we present two empirical ap-

plications based on a database containing 1823 U.S.-based mutual funds quoted inthe range January 2003 to May 2009.

In the rst analysis, using data up to December 2007, we show how dynamic

active management strategies are widespread across managed products, and that

only a fraction of managers is able to persistently beat the benchmark. At this stage,

3


4/39

our model is used to detect active management and to classify funds according to

the scheme proposed in the paper.

Later, we move a step forward and, by contrasting the model estimates obtained

in the previous analysis with those found using data up to May 2009, we highlight thenegative impact of the 2008 nancial crisis on the investment management industry.

We found evidence that the crisis leads to a reduction of effective active management

strategies, the deterioration of the overall performances level, and a reduction in the

number of funds outperforming the benchmark.

The remainder of the paper is organized as follows: Section 2 reviews Condi-

tional CAPM models, highlights their connections with the analysis of portfolio

performances and demonstrates some critical aspects; in Section 3, we introduce

our Conditional CAPM model with local covariates and discuss its components;

Section 4 is devoted to the matching of parameter signicance and active manage-

ment presence; Section 5 presents the estimation results on a database of 1823 U.S.

mutual funds highlighting the effects of the recent nancial crisis; nally, Section 6

concludes.

2 Conditional CAPM models

When addressing the problem of performance evaluation and comparison across

different portfolios, the nancial literature generally assumes the existence of an

efficient capital market, and uses a parametric equilibrium asset pricing model. A

general form of this model is

r p,t r f,t = L +k

i =1

L,i F i,t + t , (1)

where r p,t is the portfolio return at time t , r f,t is the risk-free return, F i are the

risk factors that determine the expected return of the portfolio, and t is an error

term, often assumed to be Gaussian and i.i.d. The L subscripts denote long-run

coefficients to distinguish them from the time-varying coefficients introduced in the

following. Model 1 nests the APT of Ross (1976), and the three-factor model of

4


5/39


6/39

from that of the reference index, for example, over-weighting some portfolio compo-

nents with respect to the benchmark composition. As a result, investment policies

could inuence the long-run exposure of a portfolio to the benchmark risk, inducing

L = 1.A second element inuencing the long-run beta is the market timing, the ability

of managers to anticipate the future direction of the market (Treynor and Mazuy,

1966; Merton and Henriksson, 1981; Henriksson, 1984). Timing strategies induce

deviations of beta from 1. Third, beta values different from 1 can also be the outcome

of investment strategies based on aggressive/defensive portfolios with respect to the

benchmark.

In the short run, the benchmark exposure may vary and deviate from the long-

run value due to TAA choices of the management. These strategies are implemented

by modifying the exposure of the overall portfolio to some specic risk factors, and

are aimed at exploiting local trends or extra-performances of specic assets or of

components of the market (or benchmark). This causes a deviation of the portfolio

from the reference investment mix, and thus modies L . Summarizing, the long-

run beta may deviate from 1 for long-run or static active management choices. In

addition, the beta also changes in the short-run due to the short-run changes in the

portfolio composition, as we previously noted, and that we associate with dynamic

active management choices.

Thus, the ability to identify ex-post the implementation by mutual fund man-

agers of protable investment strategies, TAA choices, timing and selectivity skills,

and static and dynamic strategies, has a relevant value in the comparison of alter-

native investment products. The possibility of detecting selection abilities is also

important both for investment managers of funds of funds, and for private investors.

However, a constant parameter model is generally unsuitable for identifying all of these elements. In fact, a time-varying exposure of a portfolio to risk factors usually

causes a time-varying behavior of model parameters. Thus, more advanced CAPM-

and APT-like models have been introduced to track investment choices and possible

time-varying risk factors exposure. In particular, the previous arguments lead to

6


7/39

the consideration of conditional performance evaluation, by introducing multifactor

models with time-varying parameters. These models are represented as follows:

r p,t r f,t = t +k

i =1 i,t F i,t + t (3)

t = 0 + 1 Z t 1 (4)

i,t = 0 + 1 Z t 1 , (5)

where 0 and 0 are scalars, 1 and 1 are m 1 vector parameters, and Z t is a

m 1 vector of covariates or conditioning variables. For this reason, models fol-

lowing (3)-(5) are called conditional models (see for instance, Ferson and Schadt,

1996, among others). Model (3)-(5) tries to capture the dynamics of portfolio risk

exposure, allowing the parameters to vary depending on Z t 1 . The conditioning

variables set includes indicators inuencing or driving the timing and selectivity

strategies implemented by the portfolio manager. For example, if we consider a

manager who follows a low-frequency fundamental top-down approach, Z t may in-

clude macroeconomic variables such as the Industrial Production Index, the Gross

Domestic Product, the exchange rate, and a set of interest rates for different maturi-

ties. Differently, for a bottom-up fundamental manager, relevant variables tracking

his selectivity and timing could include indices monitoring value-growth styles andvariables such as rms size, book-to-market and earnings-to-price ratios, and mo-

mentum, among others (Fama and French, 1994). For examples of the use of model

(3) in nancial analysis, see Chen and Knez (1996), Cochrane (1996), Ferson and

Schadt (1996), Jagannathan and Wang (1998), and Avramov and Chordia (2006),

among others.

In conditional models, parameters interpretation is similar to that of the static

CAPM: 0 represents the long-run extra-performances (similarly to L ) while the

vector 1 tracks the changes in the performances due to the covariates; 0 is the

long-run exposure to the benchmark (similarly to L ) risk or factor risks while 1

represents the impact of covariate risks on the long-run exposure to the benchmark

or to risk factors. Since the coefficients 1 and 1 track the variables used by fun-

damental portfolio managers either in the stock selection or in the exposure to risk

7


8/39

factors, their signicance is associated with the selectivity skill of managers and

with the introduction of TAA strategies. In the previous model, market timing can

easily be accounted for by appropriately designing the risk factors, for instance, by

setting F 1 ,t = r m,t and F 2 ,t = r m,t I (r m,t > 0) (Treynor and Mazuy, 1996).Related models are those proposed by Zivot et al. (2004), and Ang and Chen

(2007), which generalize model (3)-(5) by introducing a parameter-specic inno-

vation in equations (4) and (5), and the model of Avramov and Wermers (2006),

with time-varying covariates and benchmarks. We do not follow these approaches

because they require computational intensive estimation methods while the coeffi-

cients of model (3)-(5) could be estimated by least squares or maximum likelihood

techniques.

Conditional models may present several kinds of dynamics for parameters, mainly

depending on the choice of conditioning variables, the type of dependence between

the conditioning variables and the portfolio returns, and the presence of shocks af-

fecting the dynamic evolution of parameters. The models of Ferson and Schadt

(1996), Avramov and Chordia (2007), among others, and their generalizations, de-

scribe tactical choices, timing, and selection skills, allowing parameters to vary

depending on variables associated with fundamental management. However, this

approach may lead to a number of problems. First, the identication of the ap-

propriate covariates is not simple given the managers heterogeneity and the fact

that they may use different indicators to implement similar investment strategies.

Portfolio managers could use different conditioning variables because the portfolios

include stocks of different economic sectors (for instance, consumer cyclical and non-

cyclical stocks may be associated with different covariates), or because the managers

follow different allocation strategies (they may focus on company-specic covariates

rather than on macroeconomic indicators). Therefore, studies using the same set of covariates on a large number of managed portfolios may incur in an omitted vari-

able problem. A possible solution is the use of a large set of covariates. However,

inferential procedures are again not optimal since we are including unnecessary re-

gressors for many funds. Alternatively, we could dene portfolio specic covariates,

8


9/39

increasing the computational complexity of analysis performed on a large number

of portfolios. In addition, this last approach is open to criticism. In fact, managers

may follow different investment strategies over time, also making the covariates set

time varying. From a different point of view, the manager of a specic portfolio mayalso change over time, creating a structural break that could inuence the outcomes

of a Conditional CAPM model.

Furthermore, Conditional CAPM models may not be well designed to track

the portfolios of managers following non-fundamental approaches, such as technical

analysis. Finally, Conditional CAPM models, independently of the conditioning

variables included, cannot appropriately monitor the returns of portfolio managers

following qualitative investment strategies (as opposed to quantitative approaches).

In addition to the optimal number of risk factors and the evaluation of their

time-varying impact, additional issues concerning the inference on parameters in

(4)-(5) have been emphasized in the literature; see Silli (2006), Barras et al. (2005),

Otten e Bams (2004), Ferson et al. (2008), among others. For example, to obtain

accurate parameter estimates, the length of the considered time series should not

be too short, but when analyzing only long time series, problems of survivorship

bias can occur (see Brown et al., 1992). Moreover, signicance test and condence

intervals are usually based on Gaussianity and homoscedasticity assumptions, which

are not always satised.

Usually, CAPM analyzes are conducted on monthly data. However, for our pur-

poses, this frequency may not be optimal, a further distinctive element with respect

to the large part of the Conditional CAPM literature. The estimation of CAPM

models is generally based on monthly data because, historically, managed portfolios

were monitored and adjusted on a low frequency base, monthly or even quarterly.

In addition, covariates of general Conditional CAPM specications include macroe-conomic variables that are not available at higher frequencies. Modern portfolio

management approaches could maintain, in many cases, a monthly horizon for pe-

riodic revisions and assessments of the portfolio. However, the monitoring of single

positions with respect to their gains and losses, the risk evaluation of the portfo-

9


10/39

lio with respect to risk factors (or covariates) and the liquidity management, may

be implemented at higher frequencies. It is not unusual that active portfolio man-

agers modify portfolio holdings, at least partially, on a weekly basis, and even daily,

if needed. Some examples are the liquidation of positions with large losses/gains(stop-loss or take-prots technical rules) and the adjustment of holdings to control

market risk or to prot from specic investment opportunities. Moreover, portfolio

managers may apply high-frequency (daily or weekly) allocation programs, rotating

(even partially) their portfolios in the short-term. In these cases, the portfolio ex-

posure to the benchmark may signicantly vary within a month. As a result, the

portfolio alpha and beta will also vary in the short-run, while in the long-run they

can be assumed to be xed. These long-run quantities measure the association of

portfolio returns with the benchmark (the long-run beta) and the expected extra-

performance with respect to the benchmark (the long-run alpha). The long-run beta

monitors the investment policies and the strategic allocation choices of the portfolio

managers, while long-run alphas are interpreted as the overall extra-performance

measures. In this framework, active managers are characterized by changing alphas

and betas with a relevant impact of the short-term deviations around the long-term

values. On the contrary, passive managers and active managers with static or long-

run strategies are characterized by static (long-run only) parameters. For all these

reasons, we propose and estimate our model on daily data to appropriately capture

active management.

3 A Conditional CAPM model with local covariates

We noted that a number of critical aspects characterize both CAPM and Condi-

tional CAPM models when the purpose of the analysis is the evaluation of activelymanaged portfolios. To mitigate these drawbacks, we introduce a modication of

the Conditional CAPM model. In particular, we propose a model where the dy-

namics of parameters is based on two conditioning variables extracted from the past

history of the portfolio returns and of the benchmark returns. Our approach may

10


11/39

resemble the model proposed by Zivot et al. (2004). However, the dynamics we

suggest for the alpha and beta parameters is not stochastic, and the estimation

is simple and requires linear regression and quasi maximum likelihood techniques.

These are computationally simpler than the use of approaches based on the Kalmanlter, as that adopted in Zivot et al. (2004). In addition, the parameters have an

interpretation associated with the presence and effectiveness of active management

strategies.

As in standard Conditional CAPM models, specic dynamic equations describe

the parameters evolution:

(r t r f,t ) = t + t (r m,t r f,t ) + t (6)

t = 0 + 1 ( t 1 0 ) (7)

t = 0 + 1 ( t 1 0 ), (8)

where 0 , 1 , 0 , 1 are scalar parameters, while t and t represent local estimates

of t 1 and t 1 , and t is an innovation process. The local estimates are obtained

by tting model (2) over a sample including only the last k observations, namely

t

t=

k k 1i =0 (r m,t i r f,t i )k 1i =0 (r m,t i r f,t i )

k 1i =0 (r m,t i r f,t i )

2

1

(9)

k 1i =0 (r m,t i r f,t i )

k 1i =0 (r m,t i r f,t i ) ( r t i r f,t i )

.

These estimates describe the short-term choices of managers in term of port-

folio exposure to risk factors (or benchmark) and security selection. As a result,

these quantities replace the covariates of standard Conditional CAPM models or,

in other words, summarize the informative content of the covariates analyzed by a

single portfolio manager in implementing allocation strategies and choices. Their

changing behavior is inherently associated with the changing composition of the

underlying portfolio, which, in turn, is a consequence of investment and allocation

choices made by the portfolio manager tracking specic covariates. Therefore local

11


12/39

estimates track the following elements: the changing behavior of portfolio managers

with respect to the real set of covariates the managers consider, the portfolio man-

agers expectations about the future movements of the market, and the strategies

implemented by portfolio managers.Since estimates t and t are specic for each series, the model also accounts for

heterogeneity across portfolios and portfolio managers without the need to specify

different sets of covariates for each return series.

A distinguishing feature of model (6)-(8) is the interpretability of the components

of the parameters within an active management perspective. This aspect will be

extensively discussed in the next section. Of course, specication (6)-(8) cannot be

interpreted as equilibrium model any more, but simply as a peculiar factor model.

When 1 = 1 = 0, we have t = 0 and t = 0 , and models (2) and (6)-(8)

coincide. In addition, if the local estimates are constant and equal to t and t , then

t = 0 and t = 0 , showing that the coefficients 1 and 0 can be considered as

the long-run alpha and beta of the analyzed portfolio. As a result, the time-varying

coefficients t and t have two components: a constant element ( 0 or 0 ), which is

time-invariant and describes the long-term behavior of t or t , and a time-varying

term, 1 ( t 1 0 ) or 1 ( t 1 0 ), associated with the short-term performance

of the fund. The second term depends on 1 or 1 and on deviations of the local

estimates t 1 and t 1 from the long-term behavior.

The dynamics of t and t in model (6)-(8) can also be recast in the companion

form

t = 0 + 1 t 1 (10)

t = 0 + 1 t 1 , (11)

with 0 = 0 1 0 , 0 = 0 1 0 , 1 = 1 and 1 = 1 . This alternative

representation highlights that the model we proposed can be seen as a Conditional

CAPM where the conditioning variables are local estimates of the standard CAPM

parameters. Again, the model nests the traditional CAPM under the restrictions

1 = 1 = 0.

12


13/39

As mentioned in Section 2, we suggest estimating the Conditional CAPM in

(7)-(11) using daily data. In fact, we believe that the combination of daily data

and local estimates allows for the identication of portfolio manager strategies with

greater details with respect to models tted on monthly data. In fact, low frequencyanalysis could not properly identify the real operativity of fund managers.

Often, t is assumed to be a Gaussian iid process. However, when daily data

are involved, this assumption is questionable due to the presence of heteroscedas-

ticity. Both models (2) and (7)-(11) can be generalized, introducing conditionally

heteroscedastic errors. If we assume they follow a GARCH(1,1) process (Engle,

1982; Bollerslev, 1986), the dynamics of the errors t becomes

t |I t 1 N (0, 2t ) (12)

2t = 0 + 1 2t 1 + 2

2t 1 , (13)

with 0 > 0 and 1 , 2 0 being sufficient to ensure the positivity of the conditional

variances.

The Conditional CAPM model with local covariates is estimated by a two-step

procedure: i) rst, compute the local estimates t and t ; ii) then t the model (6)-

(8) using the local estimates of step i) as they were exogenous variables. The second

step requires a conditional maximum likelihood approach (due to the presence of

the non-linear relation between coefficients and/or to the innovation term including

a GARCH component, standard OLS approaches cannot be applied).

Finally, in our Conditional CAPM model, the local estimates have a relevant

role, but they depend on the window length used for their evaluation. In this case,

the choice of the parameter k , which denes the locality of t and t , should be

made carefully. An excessively small value may produce distortions due to excessive

variability whereas an excessively large value may create identication problems due

to the difficulty of distinguishing short-term from long-term components. Following

a statistical approach, the parameter k can be estimated by a maximum likelihood

procedure. Alternatively, it could be set to the average frequency used by managers

to rotate, modify, or update the portfolio. In this context, relevant values of k are

13


14/39

20/21 for monthly updates, 41/42 for bi-monthly, and 62/63 for quarterly.

The approach we introduced can be generalized in several directions. For exam-

ple, the evolution of parameters might follow a more detailed dynamics, including

several lags or autoregressive components. Additional risk factors could be includedallowing to the analysis of the short- and long-run exposure to these specic factors.

Timing could also be introduced following Treynor and Mazuy (1966) or Merton

and Henriksson (1981). Finally, we could also generalize in a similar way a mul-

tifactor model, introducing, for instance, local estimates in the style analysis of

Sharpe (Sharpe, 1992). In this paper, however, we will focus on the interpretation

and estimation of the baseline specication (6)-(8), leaving the extensions to future

research.

4 Model parameters and portfolio management styles

The main purpose of this paper is to introduce a model that is useful in performance

analysis and in the comparison of managed portfolios. With respect to this objective,

specication (6)-(8) is interesting because it allows associating the signicance of

estimated parameters, the sign of the components, and the signicance of specic

parameters with the strategies and abilities of portfolio managers. The introductionof local covariates permits the identication of the presence of dynamics in alpha and

beta, the association of these elements to the presence of TAA, timing, and security

selection strategies. In our specication, the t parameters 0 and 1 disentangle

the long-run exposure to the benchmark from the short-run deviations associated

with the active strategies. In the absence of both TAA strategies, timing, and

security selection, and with a passive investment policy, the long-run beta should

be 1. The long-run coefficient 0

is a measure of the overall aggressiveness if larger than 1 or defensiveness if lower than 1 of the analyzed portfolio with

respect to the benchmark. Assuming the benchmark is correctly identied, the

long-run coefficient 0 should be always positive, statistically signicant, but could

be different from 1. Mutual funds with 0 statistically equivalent to 1 could be

14


15/39

considered market (or benchmark) neutral, as in the standard CAPM case. As we

previously noted, deviations from 1 depend on the strategic (long-run) choices made

by portfolio managers. Negative values are not expected.

Our modeling approach introduces short-term dynamics into the evolution of thebeta. As a result, we are able to show the impact of short-term deviations from the

long-run exposure to the benchmark. We associate the relevance of the 1 coefficient

with i) the existence of TAA and timing strategies and ii) the relevance of a security

selection process. The distinction between the two effects is not possible without

complete knowledge of the portfolio holdings over time. However, some intuition

is still achievable. Firstly, a nonsignicant 1 can be associated with the absence

of TAA and timing strategies, while this coefficient cannot be read as the absence

of a security selection process. In fact, the portfolio manager may implement a

stock picking program while maintaining a stable exposure to the benchmark, for

instance, with appropriate derivative contracts. Secondly, assuming 1 is signicant

and positive, it identies a standard impact of TAA, timing, and selectivity on the

overall fund benchmark exposure, allowing the distinction between long-term and

short-term components of the beta. Negative values are possible and identify man-

agers with a mean-reverting (to the long-run beta) benchmark exposure. Positive

values of 1 characterize managers with a persistent deviation from the long-run 0

coefficient.

Moving to the interpretation of t , the coefficient 0 can be considered, similarly

to the t case, as the traditional out- or under-performance of the fund with respect

to the benchmark. The parameter 1 represents the signicance of short-term de-

viations from the unconditional extra-performance levels. The interpretation of t

depends on the signicance of the estimates 0 and 1 . If they are jointly not sig-

nicant, then the analyzed portfolio is not able to create under- or out-performancewith respect to a benchmark, either by a security selection ability or from the in-

vestment strategies adopted by the management. When only 0 is signicant and

positive, it expresses the ability of the managers in outperforming the target port-

folio. Differently, when 0 is statistically lower than zero, it signals the inability of

15


16/39

the manager in beating the benchmark. The 0 coefficient could be interpreted as

a long-run extra-performance measure or as a persistence measure. In fact, positive

signicant deviations of 0 from 0 are associated with portfolios that are persistently

beating the benchmark (negative values would identify mutual fund with long-runreturns lower than the benchmark).

Assume now that 1 is signicant, while 0 is not: in this case, although the

portfolio manager is not able to create a persistent and long-run over-(under-) per-

formance with respect to the benchmark, the local alphas have a signicant impact.

This may be read as the attempt of the portfolio manager to seek protable oppor-

tunities in the short-run, but without being able to persistently beat the benchmark.

Finally, if both 0 and 1 are signicant, we have a long-run extra-performance and

a short-term impact. This result can be read as the ability of a manager to reach

a long-run target extra-performance (if 0 is positive) by operating in the short-run

with selection ability or timing.

Thus, the analysis of the two components and of their signs provides information

on the strategy adopted by the managers and on how active the management is.

Again, when both 0 and 1 are signicant, a clear distinction between the effects of

the timing ability of the manager and the results coming from a selectivity ability

is not possible (see Avramov and Wermers, 2006).

In addition to the insights derived by separately looking at t and t coefficients,

some relevant cases may be identied jointly by analyzing all model parameters. In

this case, model (6)-(8) is used with the purpose of classifying the activeness of

portfolio management using empirical data. We consider two main classes: static

management and dynamic management. The second class is further detailed into

effective and ineffective dynamic management. All three cases include additional

sub-cases that are described in the following list:

A. Static management: when the managers choices are basically static, and 1

and 1 are both nonsignicant. Within this class, two situations can be iden-

tied:

16


17/39

A1. Long-run management skill: when both 0 and 0 are signicant. The

manager generates out-/under-performances without TAA, timing, and

security selection skills but beneting only from the assets included in

the portfolio (the strategic allocation). This situation may suggest thatthe portfolio holdings are quite stable over time, without any clear signal

of changes in the overall exposure to the benchmark or in the impact of

short-run selection skills;

A2. Passive management: when only 0 is signicant. The manager does not

create extra-performances. Given the absence of signals of TAA, timing,

and security selection abilities, it appears that a passive strategy has

been implemented. Note that this result may also be associated withmanagers implementing ineffective long-run active strategies, or short-

run active strategies that did not produce neither a changing behavior in

the local estimates or a signicant extra-performance. These managers

are thus equivalent to non-active managers. Fully passive management

is identied by portfolios with 0 statistically equal to 1.

Dynamic management: when short-term dynamics is present, that is, 1

and/or 1 are signicant. Active management itself does not guarantee any

effectiveness. Thus, it can be further divided in:

B. Persistent dynamic management: when it provides signicant long-run

extra-performances, either positive or negative. This can be due to:

B1. Effective beta dynamic: when 0 , 0 , and 1 are signicant. In this

case the manager implements active strategies resulting in under-

(negative 0 ) or out- (positive 0 ) performances with respect to the

benchmark;

B2. Effective alpha dynamic: when 0 , 1 , and 0 are signicant. Similar

to the previous case, but with a signicant impact of selection skills,

positive or negative, depending on the sign of 0 ;

17


18/39

B3. Effective alpha and beta dynamic: when all coefficients are signif-

icant. Active strategies are in place. The sign of the long-run de-

viations from the benchmark returns, and depends on the sign of

0 .

C. Nonpersistent dynamic management: when management produces only

transitory deviations from the benchmark, without signicant deviations

in the long run. This can be due to:

C1. Ineffective beta dynamic: when 0 and 1 are signicant. The man-

ager implements active strategies, but they do not provide extra-

performances, given that both 0 and 1 are not signicant;

C2. Ineffective alpha dynamic: when 1 and 0 are signicant. The man-

ager implements security selection strategies without being able to

generate long-run extra-performances with respect to the benchmark;

C3. Ineffective alpha and beta dynamic: when 1 , 0 , and 1 are signif-

icant. Both TAA, timing, and security selection are used, but they

do not produce any extra-performance.

Note that effective cases include both positive and negative results; the use of

the term effective should be interpreted as the ex-post evidence of the impact of

active management strategies on long-run alpha coefficients.

The combinations excluded from the previous list are associated with models

where the long-term exposure to the benchmark is not signicant. These combina-

tions could be read as an improper identication of the benchmark (the portfolio

managers are tracking a different benchmark) or to mutual funds with a zero expo-

sure to the benchmark.

In addition, we stress that the cases within groups B and C could not be further

detailed for distinguishing among TAA, timing, and security selection programs as

the two cannot be disentangled without complete knowledge of the true portfolio

compositions.

The analysis of the time-varying patterns of t and t themselves could also be

18


19/39

of interest because it may highlight periods where the funds are producing extra-

performances and/or deviating signicantly from the benchmark. Moreover, the

length of these periods provides information about the persistence of good and

bad performances and about investment strategies. Finally, the joint analysis of these patterns may help in the investment choices and in the actual state of funds

strategies. We may be interested in comparing the actual exposure of a mutual

fund to benchmark risk, as well as in realizing if in recent periods a fund has been

generating positive/negative extra-performances.

5 An analysis of U.S. mutual funds

To verify the abilities of the model previously introduced, we study the effective-

ness of active management, and the impact of the recent nancial crisis on active

management, using a large set of U.S. mutual funds. Thus we t our Conditional

CAPM model with local covariates and a CAPM model.

Our database contains 1823 U.S. mutual funds for the period January 1, 2003

through May 31, 2009. Daily return data were downloaded from Yahoo!Finance and

are organized with respect to two classications based on investment styles: Large

(1018 funds), Medium (389 funds), and Small (412 funds); Growth (730 funds),Blend (690 funds), and Value (403 funds). The database includes funds available

over the entire sample at Yahoo!Finance by mid-June 2009. As a result, funds

created after January 2003, or dead, are not included. Consequently, our results

may suffer from survivorship bias.

To identify the benchmarks, we used the nine groups obtained by crossing the two

classications previously dened. The indices Russell Top200, Russell MidCap, and

Russell 2000 are the benchmarks for funds belonging to the Large Blend, MediumBlend, and Small Blend categories, respectively. For the six Value and Growth

categories, we used the previous Russell indices in the corresponding Value and

Growth styles. The risk-free return is a daily return of a 13-week T-bill index.

We used maximum likelihood with Gaussian GARCH errors to estimate the

19


20/39

Conditional CAPM with local covariates and the CAPM models. In the follow-

ing, we label the models LC-HCAPM and HCAPM, respectively. We computed

robust standard errors of parameters following Bollerslev and Wooldridge (1992).

In addition, for the LC-HCAPM model, we based local estimates of and on awindow of 21 days (k = 21), which corresponds to a business month. Estimates

based on quarterly local estimates ( k = 62) provided similar nal results and are

not reported. In the following subsection, we show some examples of the possible

outcomes obtained with our model on single funds. This will highlight the pos-

sible uses of our approach in detecting the persistence of active management and

the managers impact on portfolio alphas and betas, which may deviate from their

long-run values. To evaluate the diffusion of active management across the mutual

funds in our database, and to determine the impact of the recent nancial crisis, we

run two separate analyses. At rst, we focus on data up to December 2007 to study

the diffusion and effectiveness of active management. In the second step, we also

include the more recent data, up to May 2009, to shed some light on the impact of

the nancial crisis on the investment management industry.

5.1 Some specic examples

To have an idea of the different behavior of funds with respect to the components

of the dynamics of t and t , and to show the informative content provided by the

estimation of model (6)-(8), we now analyze three particular funds. They are called

L2, L23, and L163, and they belong to the Large Blend category. A summary of

the signicance of the parameter for these three funds is given in Table 6. For the

fund labeled L2, the estimation of the HCAPM model leads to L = 0 .0070 (s.e.

0.00547) which is not signicant, and L = 0 .783 (s.e. 0.0140) which is signicantly

different from 1. The estimated parameters for LC-HCAPM model are 0 = 0 .0127

(s.e 0.0045), 1 = 0.118 (s.e. 0.155), 0 = 0 .764 (s.e. 0.0296), and 0 = 0 .690

(s.e. 0.0808). Thus, in the LC-HCAPM, 0 is signicant and almost twice the

L , while 1 is not signicant. Figure 1 (left) shows how t , 1 ( t 0 ), t and

1 ( t 0 ) (the short-run components t and t ) vary over time. Note that the

20


21/39

variability of t around 0 is quite small, and this highlights that the contribution

to t of the dynamic component is quite modest. With respect to the dynamics of

t , both 0 and 1 are signicant. In particular, Figure 1 (right) shows that 0 is not

very different from L and that the contribution to t of the dynamic component1 ( t 0 ) is clearly important. In fact, t ranges from about 0 .53 to about 0 .94,

pointing out that the exposure to the index is not constant over time. In the rst

part of the graph, t is almost always smaller than 0 , while in the second part it is

almost bigger, suggesting a frequent variation in the exposure to the market.

The second example is the case of fund labeled L163. For this managed product,

L = 0 .0029 is not signicant, and L = 0 .996 does not differ signicantly from 1.

In this case 0 = 0 .0033 is also not signicant. However, 1 = 0 .258 is signicantly

different from zero, showing that the variations of t around 0 are quite pronounced

(see Figure 2). In turn, this may indicate that the fund manager is actively searching

for protable opportunities in the short-run, but these do not translate in a successful

strategy in the long-run. Since 0 is not signicant, t 1 t . As regards t , both

0 = 0 .996 and 1 = 0 .538 are signicant. Again, CAPM = 0 .997 and 0 are almost

identical, but the dynamic component 1 ( t 0 ) makes t range from 0 .83 to 1.15,

showing once again that managers change the exposure of their portfolios over time.

The parameter estimation for the fund labeled L23 leads to L = 0.0049,

largely signicant, L = 1 .003, 0 = 0.0047 and 1 = 0.659 both signicant,

0 = 1 .003, and 1 = 0 .159. The last is not signicant. The patterns of t and t

are shown in Figure 3. The left panel of the gure clearly shows that the dynamic

component of t is almost constant (it ranges from 0.98 to 1.02) and underlines that

the fund manager probably is not implementing any TAA or timing strategies, but

generates extra-performances by a selection skill.

5.2 Active management and performance persistence

To study the diffusion and effectiveness of active management strategies, we now

estimate the LC-HCAPM and HCAPM models on all the funds included in our

database, and use data up to December 2007. Table 2 lists the number of signicant

21


22/39

parameters at the 1% level for the two tted models. As expected, parameters 0

are almost always signicant. The few cases with nonsignicant 0 coefficients refer

to funds possibly characterized by category or style misplacement, or by a very

large impact of short-run movements in the beta. Across the funds with signicant0 values, the largest part, 87% of the funds, is classied as defensive ( 0 < 1) or

benchmark neutral ( 0 = 1). Notably, the Small and Value categories contain the

largest fraction of defensive managers. Comparing the HCAPM and LC-HCAPM

results, we note that the fraction of funds with benchmark neutral exposure are

sensibly different, from 19 .5% for HCAPM to 37% in the LC-HCAPM case. We

interpret this result as a relevant outcome of our model. In fact, by allowing time

variation in the betas with local covariates, we are able to better estimate the long-

run beta of mutual funds, compared to standard CAPM models. As a result, we

found that the number of funds that track the benchmark in the long-run is larger

over all categories (generally, it doubles). The coefficient 1 is signicant in 84% of

the cases, and this points out that the dynamics of beta is widespread for all funds

of all three categories. A larger occurrence of signicant 1 values is observed for

the Medium and Growth classes.

The long-run performance of the funds, tracked by parameter 0 , is statisti-

cally signicant on 14% of the funds. Notably, the overall number of funds with a

persistent deviation from the benchmark does not change across the tted models.

Our estimates, however, provide evidence of a specic behavior with respect to the

long-run performance sign. In fact, most of the funds with signicant long-run per-

formance over-perform the benchmarks: 10% of the funds are over-performing the

benchmarks while only 4% are under-performing. This result is, however, not par-

ticularly surprising given the period we consider (2003 to 2007) and the database,

which suffers from survivorship bias. In more complete analysis including deadfunds and funds with a shorter history, we expect a larger fraction of negative 0 .

Across categories, we note some relevant differences: the Small group has the largest

fraction of funds with positive long-run performance, 15%, while the Medium group

has the largest fraction of negative long-run performance, 11%. These ndings are

22


23/39

not affected by the model and are almost equal for both CAPM and LC-HCAPM.

The dynamics of is less pervasive compared to that of , and the parameter

1 is signicant only for about 4% of the funds. Strong differences appear across

categories: funds investing in Small companies have the largest occurrence of sig-nicant 1 , more than 9%; the Large and Growth classes have the smallest values,

2.2% and 2.7%, respectively. More interestingly, the percentage of cases where both

0 and 1 are jointly statistically signicant is small, around 1%, while 18% of the

funds have at least one of the two parameters statistically signicant. With respect

to active management strategies, we infer that, overall, few managers are able to

persistently beat the benchmark.

Comparing the HCAPM and LC-HCAPM estimates of the extra-performances,

against 0 and 1 , we note that on 213 funds there is agreement ( and at least one

of 0 and 1 are statistically signicant), while there exist 107 mutual funds where

is not signicant while at least one of 0 and 1 is statistically signicant. This

is additional evidence of the difference between the HCAPM and our LC-HCAPM

model: the two are not equivalent, and the LC-HCAPM is more informative about

the real performance of the funds.

Summarizing our ndings, the introduction of local covariates adds some inter-

esting features to the traditional CAPM model, by allowing better identication of

the long- and short-run components of both the exposure to the benchmark ( t )

and the extra-performance ( t ).

Table 3 reports a possible classication of funds according to the results of model

(6)-(8) following cases A, B, and C described in the previous section. On the whole,

only 15% of the funds show evidence of a static strategy (case A), whereas about 85%

implement a dynamic strategy (cases B and C). Within case A, the vast majority of

funds (90%) refer to category A2 (fully passive management). Large and Value fundsare those with a large fraction of fully passive management cases, 17% and 19%,

respectively, while Medium and Growth have a smaller 6% and 8%, respectively.

Active management is dynamic and persistent only in 12% of the cases, with the

highest percentage on Small, 16%, and the smallest on Value funds, about 8%.

23


24/39

Within class B, persistent dynamic active management, the majority of funds is

within the subclass B1, Effective Beta Dynamic. This outcome could be interpreted

as evidence of a much more relevant impact of tactical strategies with respect to

security selection approaches. This result is conrmed by the ratio of cases withpositive long-run performance 0 , which is equal to 70% of the funds within class

B. Notably, even in this case, there are signicant differences across funds styles,

with better performances of Large and Growth classes, while the worst are observed

for the Medium. Finally, the largest part of funds are classied into group C,

Nonpersistent Dynamic Asset Management. More than 70% of the funds belong to

this group, the majority associated with class C1, Ineffective Beta Dynamic.

To explore the stability of results over time, we separately estimate the model for

the rst three and the last two years of the sample 2003 2007, when an increasing

trend characterized the stock market. Although numerically different, the results

were not qualitatively different, supporting our analysis. Focusing on the statistical

performances of the models, the heteroscedastic component is signicant in more

than 93% of the funds for LC-HCAPM while the component is close to 100% for

HCAPM. When we take into account the time-varying nature of the model param-

eters, some funds are no longer characterized by GARCH innovations.

5.3 Active management through the nancial crisis

To determine the impact of the recent nancial crisis on active management strate-

gies, we re-estimated both the HCAPM and LC-HCAPM specications using data

up to May 2009, and compare them with the results of the previous section. Results

are summarized in Tables 4 and 5. First, we note that the presence of heteroscedastic

components is not much different, close to 100% for HCAPM and a bit lower, 97%,

for LC-HCAPM. The increase observed for HCAPM is associated with the sudden

change in the volatility during the nancial crisis, which could be better captured

by GARCH innovations. Thus, the result is not surprising. Moving now to the

analysis of signicant parameters and of their values, we rst note that the percent-

age of funds with signicant or 0 decreased from 14% to 11 .3% for HCAPM and

24


25/39

10.3% for LC-HCAPM. There is now a 1% difference across the models, which we

associate with the better performances of the LC-HCAPM in capturing the long-run

persistence of mutual funds. Differences across funds by style are not affected by

the sample period.Consider now the exposure of the funds to the corresponding benchmarks. Com-

paring the results up to May 2009 with those up to December 2007, we note limited

changes in the percentages of funds with defensive ( 0 < 1), neutral ( 0 = 1) or

aggressive ( 0 > 1) strategies with respect to the benchmark exposure. These vari-

ations are marginally larger for the HCAPM, in particular for benchmark neutral

funds, which decrease by 4%. Focusing on data including the nancial crisis, the dif-

ferences between HCAPM and LC-HCAPM outcomes are still present, with relevant

differences in the number of funds characterized by benchmark neutral expositions

(15% for HCAPM and 35% for LC-HCAPM) and defensive strategies (63% and

51% for HCAPM and LC-HCAPM, respectively). More interestingly, the coefficient

1 is now signicant in more than 92% of the funds, with an increase of 8%. The

dynamics of the beta is thus much more present, and could be read as the effort

of fund managers to decrease and dynamically adjust the benchmark exposure to

reduce and manage the impact of the nancial crisis on their portfolios (both for

reducing market exposure and to modify the portfolio composition to control and

monitor company and sector specic risks). This result is also conrmed by the

increase in funds with both 0 and 1 statistically signicant, now 92% compared to

83% obtained with data up to December 2007.

A further conrmation of this outcome is given by the classication of funds

with respect to the active management categories dened in the previous Section. In

fact, the number of funds classied as Static (class A) decreased to 6 .4% compared

to the 14 .7% observed before the crisis (as for data up to December 2007, thelargest fraction of funds in class A is classied as Fully Passive). Clearly, many fund

managers previously classied as Static have used dynamic strategies to manage

the nancial crisis period. The decrease in the fraction of funds classied in group

A is common across all styles. Similarly, the fraction of funds classied in group

25


26/39

B, persistent dynamic management, is smaller after the nancial crisis, now 9%

compared to the 12% observed with data up to December 2007. Again, this result

is common across all management styles. The majority of funds is still classied

in group B1, Effective Beta Dynamic. In addition, we observe that, within classB, the fraction of funds with positive long-run performance is now 62%, with an

8% decrease, which is observed over all style with the exception of the Value one.

Given the previous observations, we have that the fraction of funds within class C

has increased from 73% (December 2007) to 84% (May 2009), and most of them is

in group C1, Ineffective Beta Dynamic. Similarly to the previous cases, this increase

is common across all styles.

To determine the impact of the nancial crisis on active management strategies,

we deeply analyze the signicance of the time-varying t and t parameters. In

fact, conditionally to the local estimates t and t , and assuming that the Quasi

Maximum Likelihood estimator of the coefficients = {0 , 1 , 0 , 1 } follow an

asymptotically normal density, N (, ), we have the following

t = 0 + 1 t 1 t N wt 1 ,1 , w t 1 ,1 wt 1 ,1 (14)

t = 0 + 1 t 1 t N wt 1 ,2 , w t 1 ,2 wt 1 ,2 , (15)

where wt 1 ,1 = {1, t 1 , 0, 0}, wt 1 ,2 = 0, 0, 1, t 1 , and the covariance is

estimated by the QML parameter covariance. As a result, we could test, for each

time index t , the signicance of the time-varying benchmark extra-performance or

check if it is positive or negative. In addition, we could test for each point in time if

the mutual fund benchmark exposure is equal to 1, or if it is deviating from 1, either

above or below. We ran this test across all funds and all days over our sample and

collected the number of funds with signicant extra-performances and signicant

deviations from a benchmark neutral exposure. Figure 4 reports the number of

funds with signicant values of t and t 1. As we observe, the fraction of funds

with benchmark neutral exposure is close to 200 for the entire sample. This result

is very different from the one reported in Tables 2 and 4, which were reporting more

than 600 funds with long-run beta equal to. This should not be surprising since

26


27/39

we are now analyzing the time-varying exposure to the benchmark, the long-run

exposure is just one of its two components. In fact, it could be possible that the

long-run exposure is 1 but that the short-run changes are shifting the local fund

exposure.More interestingly, the fraction of funds with statistically signicant t oscillates

between 250 and 600 until October 2008, when it peaks at 900 (24th to 29th October

2008). This jump is associated with signicant negative values of t , as shown in

Figure 5, where we observe that more than 600 funds had a negative t the same

days of October 2008. Notably, if we determine the rolling cumulated returns of the

last 21 days of the Russell 3000 index, we note this quantity peaks at more that

30% the 27th of October 2008. As a result, the model is correctly associating

negative time-varying alphas with negative market phases.

6 Conclusions

In this paper, we propose a Conditional CAPM model where covariates are com-

puted on an asset-specic case using short-run estimates. This approach avoids

problems associated with the appropriate identication of the optimal covariates

set and the possible breaks induced by changes in the management strategies of mutual funds. In addition, the model we propose allows interpreting the associated

coefficients with the purpose of detecting ex-post the presence and effectiveness of

some active management strategies. Our approach can be considered as a tool for

comparing alternative managed portfolios and could provide useful information for

fund managers as well as for private investors. In the empirical application, we show

how the model may be used over a large set of U.S. mutual funds (1823 managed

products) classied by the market dimension of the underlying assets or by the in-vestment style. Our empirical study highlights that during the period 2003 2007

many mutual fund managers, 14%, implemented in an effective way active manage-

ment strategies. In addition, 15% of the funds are detected as empirically passive.

By comparing the previous results to those obtained extending the sample up to

27


28/39

May 2009, we identied the effects of the nancial crisis that decrease the fraction

of managers with positive long-run performances and increase the fraction of funds

with dynamic active management. With a graphical analysis, we highlight that

the dynamic extra-performance (the time-varying alpha) peaks during the month of October 2008 and correctly identify the most relevant period of the nancial crisis.

References

Ang, A. and Chen, J. (2007), CAPM over the long run. 1926-2001, Journal of Em-

pirical Finance , 14, 1-40.

Avramov, D., and Chordia, T. (2006), Asset pricing models and nancial market

anomalies, The Review of Financial Studies , 19-3, 1001-1040.

Avramov, D. and Wermers, R. (2006), Investing in mutual funds when returns are

predictable, Journal of Financial Economics , 81, 339-377.

Barras L., Scaillet O., Wermers R., (2008). False discoveries in mutual fund per-

formance: measuring luck in the estimated alphas. Working Paper n. RHS-06-043,Robert H. Smith School of Business, University of Maryland.

Bollerslev T., Wooldridge J. M. (1992), Quasi-maximum Likelihood Estimation In-

ference in Dynamic Models with Time-varying Covariances. Econometric Theory ,

11, pp.143-172

Brown, S.J., Goetzmann, W., Ibbotson, R.G., Ross S.A. (1992), Survivorship biasin performance studied, Review of nancial studies 5, 553-580.

Chen, Z. and Knez, P.J. (1996), Portfolio performance measurement: theory and

applications, Review of Financial Studies , 11, 111-142.

28


29/39

Christopherson J.A., Ferson W.E., Turner A.L. (1998), Conditioning manager al-

phas on economic information: another look at persistence of performance, Review

of nancial studies , 11, 511-556.

Christopherson J.A., Ferson W.E., Turner A.L. (1999), Performance evaluation us-

ing conditional alphas and betas, Journal of portfolio management , 26, 59-72.

Cochrane, J. (1996), A cross-sectional test of a production-based asset pricing model,

Journal of Political Economy , 104, 572-621.

Fama E., French K.R. (1993), Common risk factors in the returns of stocks and

bonds, Journal of Financial Economics , 33, 3-53.

Fama, E., French, K.R. (1995), Size and book-to-market factors in earnings and

returns, Journal of Finance , 50-1, 131-155.

Fama, E., French, K.R. (1996), Multifactor explanations of asset pricing anomalies,

Journal of Finance , 51-1, 55-84.

Ferson, W.E., and Schadt, R. (1996), Measuring fund strategy and performance in

changing economic conditions, Journal of Finance , 51, 425-461.

Ferson W.E., Sarkissian S., Simin T. (2008), Asset Pricing models with conditional

betas and alphas: the effect of data snooping and spurious regression, Journal of

Financial and Quantitative Analysis , 4, 331-354.

Jagannathan, R. and Wang, Z. (1996), The conditional CAPM and the cross-section

of expected returns, Journal of Finance , 51, 3-54.

29


30/39


31/39

ment skill in the mutual fund industry. Working paper, Universidad Pompeu Fabra,

Barcelona.

Treynor, J. and Mazuy K. (1986), Can mutual funds outguess the market?, Harvard Business Review , 44, 131-136.

Zivot, E., Wang, J. and Koopman, S.J., (2004), State space modeling in macroeco-

nomics and nance using SsfPack in S+Finance, in A. Harvey, S.J. Koopman and

N. Shephard, eds., State Space and Unobserved Component Models - Theory and

Applications, Cambridge (UK), Cambridge University Press, 284-335.

31


32/39

0 200 600 1000

0

. 0 1

0 . 0

0

0 . 0

1

0 . 0

2

0 . 0

3

Index

0 200 600 1000

0

. 2

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

Index

Figure 1: Fund L2. Left: t (full line), 1 ( t 0 ) (dotted line), L (horizontalbroken line), 0 (horizontal full line). Right: t (full line), 1 ( t 0 ) (dotted line), L (horizontal broken line), 0 (horizontal full line).

0 1 0 1 1 2L2 NS S NS S S S S

L23 S S S S NS NS NSL163 NS NS S S S NS NS

Table 1: Some examples: S=signicant, NS=not signicant.

32


33/39

0 200 600 1000

0

. 0 4

0

. 0 2

0 . 0

0

0 . 0

2

0 . 0

4

Index

0 200 600 1000

0

. 2

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

Index


33


34/39

0 200 600 1000

0

. 0 4

0

. 0 2

0 . 0

0

0 . 0

2

0 . 0 4

Index

0 200 600 1000

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

Index


0 500 1000 1500

5 0 0

1 0 0 0

1 5 0 0

Time

a_

t s

i g ,

b_

t s

i g

Figure 4: Number of funds with signicant t (lower line) and number of funds withsignicant t 1 (upper line)

34


35/39

0 500 1000 1500

1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

Time

a_

t n e g

Figure 5: Number of funds with signicant negative t

35


36/39

Large Medium Small ALL Blend Growth ValueNumber of funds 1018 389 416 1823 690 730 403HCAPMn. GARCH 1016 387 410 1813 603 715 378n. sig. 140 45 81 266 124 99 43n. sig. and > 0 137 10 71 218 97 85 36n. sig. 1016 389 416 1821 689 730 402n. sig. and > 1 247 123 7 377 151 210 16n. sig. and < 1 523 187 382 1092 396 359 337n. sig. and = 1 248 79 27 354 143 161 50LC-HCAPMn. GARCH 941 372 383 1696 603 715 378n. 0 sig. 119 54 83 256 123 97 36n. 0 sig. and > 0 114 11 61 186 77 83 26n. 1 sig. 23 19 38 80 39 20 21n. 0 or 1 sig. 138 71 111 320 149 116 55n. 0 and 1 sig. 4 2 10 16 13 1 2n. 0 sig. 1009 387 415 1811 685 725 401n. 0 sig. and > 1 159 78 3 240 103 129 8n. 0 sig. and < 1 406 139 360 905 332 281 292n. 0 sig. and = 1 448 171 52 671 253 316 102n. 1 sig. 823 359 349 1531 553 659 319Comparison across models sig. and 0 sig. 102 38 62 202 95 79 28 sig. and 0 not sig. 38 7 19 64 29 20 15 not sig. and 0 sig. 17 16 21 54 28 18 8 sig. and 1 sig. 9 1 13 23 15 3 5 not sig. and 1 sig. 14 18 25 57 24 17 16 sig. and ( 0 and 1 not sig.) 33 7 13 53 24 18 11 not sig. and ( 0 and 1 sig.) 0 1 3 4 3 0 1 sig. and ( 0 or 1 sig.) 107 38 68 213 100 81 32 not sig. and ( 0 or 1 sig.) 31 33 43 107 49 35 23

Table 2: Number of signicant (sig.) parameters for k = 21 and data up to December2007. Expression n. GARCH means the number of funds for which there is asignicant GARCH component.

36


37/39

Large Medium Small ALL Blend Growth ValueA 188 25 55 268 121 65 82

(18.5) (6.4) (13.2) (14.7) (17.5) (8.9) (20.3)B 100 51 68 219 99 89 31

(9.8) (13.1) (16.3) (12.0) (14.3) (12.2) (7.7)with ( 0 > 0) 94 9 51 154 58 74 22

(94.0) (17.6) (75.0) (70.3) (58.6) (83.1) (70.9)C 721 311 292 1324 465 571 288

(70.8) (79.9) (70.2) (72.6) (67.4) (78.2) (71.5)OTHER 9 2 1 12 5 5 2

(0.8) (0.5) (0.2) (0.7) (0.7) (0.7) (0.5)

Table 3: Observed frequencies for classes A, B and C. Data up to December 2007.In brackets the relative frequencies.

37


38/39

Large Medium Small ALL Blend Growth ValueNumber of funds 1018 389 416 1823 690 730 403HCAPMn. GARCH 1015 387 410 1812 653 722 393n. sig. 117 26 64 207 112 56 39n. sig. and > 0 113 6 52 171 93 42 36n. sig. 1017 389 416 1822 690 730 402n. sig. and > 1 314 76 5 395 172 203 20n. sig. and < 1 510 249 395 1154 404 388 362n. sig. and = 1 194 64 16 274 114 139 21LC-HCAPMn. GARCH 986 382 400 1768 653 722 393n. 0 sig. 82 43 63 188 99 61 28n. 0 sig. and > 0 75 8 41 124 65 38 21n. 1 sig. 45 17 63 125 51 32 42n. 0 or 1 sig. 121 58 116 295 135 92 68n. 0 and 1 sig. 6 2 10 18 15 1 2n. 0 sig. 1009 385 415 1809 686 724 399n. 0 sig. and > 1 202 32 3 237 122 105 10n. 0 sig. and < 1 383 178 369 930 326 293 311n. 0 sig. and = 1 427 176 44 647 238 329 80n. 1 sig. 943 375 372 1690 610 701 379Comparison across models sig. and 0 sig. 68 21 48 137 74 41 22 sig. and 0 not sig. 49 5 16 70 38 15 17 not sig. and 0 sig. 14 22 15 51 25 20 6 sig. and 1 sig. 19 2 13 34 20 3 11 not sig. and 1 sig. 26 15 50 91 31 29 31 sig. and ( 0 and 1 not sig.) 36 4 10 50 30 13 7 not sig. and ( 0 and 1 sig.) 0 1 3 4 3 0 1 sig. and ( 0 or 1 sig.) 81 22 54 157 82 43 32 not sig. and ( 0 or 1 sig.) 40 36 62 138 53 49 36

Table 4: Number of signicant (sig.) parameters for k = 21 and data up to May2009. Expression n. GARCH means the number of funds for which there is asignicant GARCH component.

38


39/39

Large Medium Small ALL Blend Growth ValueA 69 12 35 116 66 28 22

(6.8) (3.1) (8.4) (6.4) (9.6) (3.8) (5.5)B 71 40 55 166 82 57 27

(6.9) (10.3) (13.2) (9.1) (11.9) (7.8) (6.7)with ( 0 > 0) 61 7 35 103 46 37 20

(86.0) (17.5) (63.6) (62.1) (56.1) (64.9) (74.1)C 869 333 325 1527 538 639 350

(85.3) (85.6) (78.1) (83.8) (77.9) (87.5) (86.8)OTHER 9 4 1 14 4 6 4

(0.9) (1.0) (0.2) (0.8) (0.6) (0.8) (1.0)

Table 5: Observed frequencies for classes A, B and C. Data up to May 2009. Inbrackets the relative frequencies.

39

Documents

Capm Condiz October09 MS