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Mutual Fund Policy statement By G.M.ARIF Submitted in fulfillment of the requirements for the degree of MSc Risk Management and Financial Engineering In the Subject of Modern Portfolio Management At the 15 th of April 2010

MUTUAL Fund Policy Statement Final Report

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Page 1: MUTUAL Fund Policy Statement Final Report

Mutual Fund Policy statement

By

G.M.ARIF

Submitted in fulfillment of the requirements for the degree of

MSc Risk Management and Financial Engineering

In the Subject of

Modern Portfolio Management

At the

15th of April 2010

Page 2: MUTUAL Fund Policy Statement Final Report

Contents

1. Statement of Investment objectives and policies…………………………….1

1.1 Investment objective statement………………………………………………...2

1.2 Investment strategy…………………………………………………………….3

1.3 Investor’s profile……………………………………………………………….4

1.4 Risk and return profile………………………………………………………….5

1.5 Investment constraints………………………………………………………….6

2. Asset allocation………………………………………………………………..7

2.1 Asset class ……………………………………………………………………..8

2.2 Economic and global view……………………………………………………10

2.3 Why investing in MSCI Index………………………………………………….9

2.4 Equity selection……………………………………………………………….11

2.5 Bond Selection………………………………………………………………..14

1. Why EFFAS diversified bond index………………………………………18

2. Some economic aspects of investment in bonds…………………………..17

2. Canadian Government bond…………….………………….………………15

3. Newzeland government bond…….………………………………………...16

4. Euro zone bond…………….…..……………….………………………….17

3. Data Analysis

4. Portfolio construction…………………………………………………………19

5. The efficient frontier…………………………………………………………..20

6. Computing return……………………………………………………………..22

7. Benchmarking…………………………………………………………………23

8. Decision on Investment……………………………………………………….25

9. Reference…………………………………………………………….………..26

10. Bibliography………………………………………………………….……….27

Appendix 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

Page 3: MUTUAL Fund Policy Statement Final Report

List of Charts 1. MSCI Bara Equity index.

2. Material sector market price performance.

3. Metal and Mining market price

4. Textile sectors market price

5. Utilities Market price performance

6. Pharmaceuticals sectors price performance

7. Portfolio equity sectors performance

8. Portfolio Bond sectors performance

9. Percentage of total return of the Portfolio

10. Individual asset risk of the portfolio

11. Sector’s performance of the portfolio

12. Efficient Frontier of the portfolio

13. Equity Performance on Portfolio

14. Debts ( Fixed income security) instruments performance on portfolio

15. Equally weighted portfolio

16. Initial sectors performance movement

17. MSCI global index’s equity sectors performance

18. EFFAS Bond index

19. Graph price of Australian bond of EFFAS

20. Australian bond composite quote

21. Australian economy

22. NZ economy forecast

23. NZ graph price of EFFAS

24. Euro zone Bond graph price

Page 4: MUTUAL Fund Policy Statement Final Report

List of models:

1. The mean of a portfolio along with the Optimal CAL.

2. The Portfolio Performance measurement as follows.

3. Treynor Portfolio performance measure.

4. Jensen portfolio Measure

5. Information ratio calculation.

6. Sharp ratio measurement.

7. Rate of Inflation

8. Calculation of Expected return on Portfolio

9. Formula for standard deviation of “n” Number of securities

10. Formula for minimum variance of a portfolio

11. The Standard deviation of each stock.

12. The correlation coefficient between securities

13. The Optimal risky portfolio

14. The adjustment for the Beta.

15. The Index’s tracking error.

16. Actual tracking error.

17. Sharp ratio for the combined portfolio

18. A mutual fund SML model.

19. The model of Historical risk of an asset.

20. Standard deviation

21. Covariance calculation formula

22. Correlation calculation formula

23. Portfolio standard deviation formula

24. The Model for the Future Bond price calculation

25. Percentage of the Change in Bond price calculation

26. The Model for the Bond Price volatility

27. Variance

28. Determinants of Convexity

29. The model for the variance of returns for a risky asset

30. The Bond holding period model.

31. The formula for the risk measure for the CML

32. Tracking error.

Page 5: MUTUAL Fund Policy Statement Final Report

1. STATEMENT OF INVESTMENT OBJECTIVES AND POLICIES

Shavron portfolio fund investment is a professional structured mutual fund which

involves diversified securities and fixed income investments. Strategically spread

among two assets classes, namely equities and bond particularly government bond

which also known as fixed income debt instruments. It is a mutual fund based in New

York, US and the portfolio is denominated in US Dollar ($). It is a passively managed

portfolio with a short term horizon. A top-down approach is used for the portfolio

construction.

1.1 Investment objective statement

Shavron Mutual fund is designed to achieve a balance between capital growth and

income over a short duration framework. It also designed to concentrate on the

medium risk tolerated investors.

1.2 Investment strategy

In this Mutual fund we aim to create a balance between capital income and growth by

diversified investments into most popular MSCI index for equity and the EFFAS

bond index for the fixed income debt securities that measures the performance of the

world’s most prominent companies including, different investment banks and fund

management companies United States. Furthermore, in this mutual fund we diversify

investments by exploring the different best performed sectors in the MSCI index and

higher returned and low duration bonds. Then we allocate the assets into different

weights which are equally weighted. Afterwards, we benchmark the portfolio

performance to measure the best performance out of this portfolio.

1.3 Investor’s profile

The investor’s class we are catering to, belongs to the above 45 years age group. The

investors are nearing the retirement and the spending phase of their life-cycle. (Figure

given below)

Investor characteristics: Moderately aggressive

Investor goals: Growth, income and capital gains thereby seeking balance between

current income and total returns.

Page 6: MUTUAL Fund Policy Statement Final Report

Figure: 1 rise and fall of personal net worth over a lifetime

Source: Reilly&Brown, Chapter 2.

Investor’s needs: Since the investors are in the spending phase of their life, he/she is nearing

retirement. They need a cushion against their accumulated capital at the same time they need

liquidity to fulfill their desires of a decently high standard of living.

Investor risk tolerance: Moderate risk

1.4 Risk and return profile

Considering the investor profile and their needs and preferences, we intend to make a

risk-medium return portfolio. We can modestly call ourselves a moderately aggressive

portfolio. Our risk-return profile can be described in figure 2:

Figure 2: Portfolio risk and return diagram.

Target risk-

return

Page 7: MUTUAL Fund Policy Statement Final Report

1.5 Investment constraints

1. Liquidity:

The portfolio must be liquid at any point of time since the investor may have cash

requirements from time to time to meet unexpected expenses. At any point the portfolio

manager must be able to liquidate positions and provide cash to the investors.

2. Time horizon:

The portfolio is constructed for a 5 months’ time horizon with the moderate risk profile and

short term return objective.

3. Other constraints:

The funds goal is not to exceed a 8% risk for a potential 9%-10% profit on the portfolio

returns.

4. Restriction on short-selling:

Sort selling is not permitted, however re-allocation of one asset class after at least 3 months

of tracking is permitted under certain condition.

5. Restriction on usage of derivative products:

No derivatives products are to be used in this portfolio

6. The portfolio is restricted to three securities:

The tax factor is not considering into the Shavron portfolio management.

7. Important dates

January1st 2010 – beginning of the fund

March 1st 2010 – evaluation rebalancing of the fund

April 2nd

2010 – closing of the fund

April 13th

2010 – Final payout to investors.

Page 8: MUTUAL Fund Policy Statement Final Report

2. Asset allocation

One must have often noticed that street vendors often sell apparently unrelated products -

such as umbrellas and sunglasses. After all, when would a person buy both items at the same

time. Probably never - and that's the point. Street vendors know that when it's raining, it's

easier to sell umbrellas but harder to sell sunglasses (Anthony Hatherley, 2009). And when

it's sunny, the reverse is true. By selling both items- in other words, by diversifying the

product line - the vendor can reduce the risk of losing money on any given day. We follow

the ‘Portfolio diversification’ policy for our portfolio, thus ensuring that we meet our investor

goals.

Our asset allocation decision aims to balance the overall portfolio risk and create

diversification by dividing assets into equities and bonds.

Asset class

Stocks – time and again stocks have proven to have the higher risk and higher returns among

the asset categories. As an asset category, stocks are ideal to be a portfolio's "heavy hitter,"

offering the greatest potential for growth thus meeting our objectives. Stocks, not only hit

home runs, but also strike out. The volatility of stocks makes them a very risky investment in

the short term. Yet most of the investor class have been willing to ride out the volatile returns

of stocks over long periods of time generally with a view of being rewarded with positive

returns.

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Page 9: MUTUAL Fund Policy Statement Final Report

Figure 1: Performance of the initially selected sectors of MSCI Index.

Figure 2: Sectors position in the performance chart based on the recent market price.

Bonds - Bonds are generally less risky and less volatile than stocks (Natarajan, 2008).

However, bonds have less return as well. As this has risk free interest rate and relatively

stable investment instruments. That is why bonds are ideal assets to support the stability of

the portfolio. Thus bond helps to reduce the risk of holding more bonds would be an

attractive strategy for our investors despite their lower potential for growth. Indeed, equities

are more lucrative in the long run, bonds are more dependable for capital preservation.

Economic and global view

The financial crisis is currently the main issue in the global economy. Almost every major

economy in the world has been affected by the crisis. The crisis starts from the collapse of the

US sub-prime mortgage market and the reversal of the housing boom in other industrialized

economies have had a ripple effect around the world.

Furthermore, other weaknesses in the global financial system have surfaced. Some financial

products and instruments have become so complex and twisted, that as things start to unravel,

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Energy

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utilities

Page 10: MUTUAL Fund Policy Statement Final Report

trust in the whole system started failing. The extent of this problem has been so severe that

some of the world’s largest financial institutions have collapsed. The crisis became so severe

that after the failure and buyouts of major institutions, the Obama Administration offered a

$700 billion bailout plan for the US financial system. (Akkas, February 28, 2009).

In Europe, the Bank of England pledged US$ 87 billion in direct support to the country’s

major financial institutions. British Prime Minister Gordon Brown’s rescue package which

involves direct capitalization and guarantee of inter-bank lending has been adopted by other

major European countries and the U.S. government. Furthermore, central banks around the

world (Fed, ECB, Canada, Sweden, Switzerland, and China) introduced co-ordinate interest

rate cuts to lower the cost of borrowing, with the aim of restoring confidence in the global

economy.

However, the flipside of the financial turmoil was that the downfall provided extremely low

valuations of many asset categories to levels that had not been seen in years or even decades.

This provided attractive asset prices for 2009 and bargain-hunting became silver lining with

plenty of assets available at sales prices not witnessed in years.

2.2 Why investing in MSCI Index

MSCI index is the diversified and most reliable global equity index maintained by Morgan

Stanley, the one of the most prominent global investment bank. This index is widely use by

the funds and asset managers worldwide. Besides, different investment banks used this index

for the benchmarking purpose of their portfolio

Page 11: MUTUAL Fund Policy Statement Final Report

Chart 1: MSCI index Source: Bloomberg

2.4 Equity selection

Metal and Mining:

Metal and Mining is one the mostly common sectors. The reason behind choosing this sectors

is the current metal and mining industry performance in the global economy. As this metal is

essential to support the growth and mining industry is doing well in the recent years,

particularly for the oil, coal, aluminum and steel etc.

Chart 2: Current market price of Metal and mining sector. Source: Bloomberg.

Materials:

Materials sector is another well performing sector in the MSCI diversified index.

The reason for choosing this sector is, it is performing well in the recent market

and the materials is necessary for the post crisis construction industry around

the world. The following chart illustrates the overall picture.

Chart 3: Graph price of Materials industrial sectors of MSCI Index

Page 12: MUTUAL Fund Policy Statement Final Report

Source: Bloomberg.

Textile:

Textile has always been a good sector to invest in. With the growing developing

countries economy, most of the countries concentrate on this sector to develop

which makes this sector well performed. The following charts illustrate the

industry situation.

Chart 4: Textile sectors current market price. Source: Bloomberg.

Utilities:

Utilities are recently doing well in the market as the construction is rapidly

going on in some countries like china, Dubai and India. So, the sectors generally

will do well in the recent future which would be attractive investment sector.

Chart 5: Recent market price performance of Utilities sectors of MSCI index.

Source: Bloomberg.

Page 13: MUTUAL Fund Policy Statement Final Report

Pharmaceuticals:

Pharmaceuticals are always been a well performed investing sectors. As the

newly development continuously going on. So, it a better choice of stock in the

MSCI Index.

Chart 6: Market price of Pharmaceuticals sectors of MSCI Index.

Source: Bloomberg.

3. Bond Selection

Bonds are the most reliable source of Investment vehicle among other assets. In this Shavron

portfolio we are considering 3 types of bonds as debts securities (Park, 2008). This debts

instruments are powerful assets in a sense that it has risk free interest rate and it is low risky

investment vehicle. Although many investors doesn’t like to invest in the bonds, however, we

are considering Bonds as an investment instruments to support our portfolio (Qu, 2008) to

reduce the overall risk and diversify the asset classes. We aim to invest in 3 types of bond of

EFFAS index. EFFAS index is the diversified bond index where it is lower risky than the

individual country’s sovereign bonds. As it is diversified. The following chart shows the

EFFAS index bond’s performance.

Page 14: MUTUAL Fund Policy Statement Final Report

Chart 7: EFFAS index diversified bond performance. Source: Bloomberg

3.1 Canadian Sovereign bond (EFFAS Index)

Canada is one of the developed countries. In the recent financial crisis it was hardly affected

by the crisis on its economy. Because of its rich mining industry and its stable economy helps

to overcome the crisis relative earlier. The government and political situation is well

established and its bond price is comparably high in the recent market price. According to the

theoretical concept there is an inverse relationship between the country ‘s interest rate and the

bond price. Canada’s interest rate is relative lower to support its economy which cause the

bond price increase since mid of 2009 to 2010. The following chart illustrate the functions of

the bond price.

Chart 8: Canadian bond’s market price of EFFAS Index. Source: Bloomberg.

Page 15: MUTUAL Fund Policy Statement Final Report

3.2 Newzeland Sovereign bond

Newzeland is one of the developed and stable economies in the Asia-Pacific region. We

choose the EFFAS NZ Bond index as the price of the NZ bond price is well performed in the

market. Besides, for the short run investment we consider that it would be one of the ideal

bond instruments for the moderate investors. In chart 9, illustrates the current market price of

the NZ bond of EFFAS Index. And Chart 10 shows the overall recent and past economic

condition of the Newzeland.

Chart 9: EFFAS Index NZ bond market price Source: Bloomberg.

Chart 10: Newzeland economy forecast. Source: Bloomberg.

Page 16: MUTUAL Fund Policy Statement Final Report

3.3 Euro zone bond

Euro zone is one of the well established economic area in the financial world. Although the

recent financial crisis (2007-2009) badly effect the financial market of the Euro zone.

However, some countries like Germany and France and other Scandinavian countries were

not as badly as US or UK affected. However, the lower interest rate and continuous bonds

issue in this area attract the liberal investors to invest in the bond market. In our portfolio we

choose these EFFAS euro zone as this is risk diversified and its high market price which

would helps us to liquid our assets at any point of time.

Chart 11: current market price graph of Euro Zone bond. Source: Bloomberg.

2.5 Data analysis

Here we will discuss how we calculate our individual assets on our portfolio. Once we

collected our data from Bloomberg we calculate the risk and return on each assets weekly

basis, then we turn them on annually. The risk can be calculated as:

Standard deviation:

Portfolio risk measure:

However, the overall portfolio standard deviation is measure as in this portfolio is:

Page 17: MUTUAL Fund Policy Statement Final Report

√∑

World Eq. Bench. Returns

S.D.

Country

Canadian bond 0.7 3.0

Canada( EFFAS)

Euro Zone bond 6.2 0.2

Euro Zone ( EFFAS)

NZ bond 3.0 0.5

Newzeland (EFFAS)

Metals and mining 40.5 35.5

MSCI INDEX

Materials 48.6 29.3

MSCI INDEX

Textiles 47.8 22.2

MSCI INDEX

Utilities 15.0 12.6

MSCI INDEX

Pharmaceuticals 31.5 12.0

MSCI INDEX

Indeed, when we calculate more than 2 asset’s standard deviation in our portfolio we use the

following model as:

Portfolio Returns %

Canadian bond

Euro Zone bond

NZ bond

Metals and mining

Metarials

Textiles

Utilities

Pharmaceuticles

Risk distribution on Portfolio%

Canadian bond

Euro Zone bond

NZ bond

Metals and mining

Metarials

Textiles

Utilities

Pharmaceuticles

Page 18: MUTUAL Fund Policy Statement Final Report

σρ = [ ∑ i = 1 to n ∑j = 1 to n Xi. Xj. Σ ij] ½

Then to find out the expected return on our portfolio we calculate the return as:

After finding the assets return and the risk we deciding upon the asset classes that this fund is

going to invest in, it is essential to specify the exact securities from each asset class that will

be used. According to the Markowitz optimal portfolio (Anthony, 2008) construction

theory, the element that diversifies risk is the covariance between the risky assets. The

covariance, as described in the following formula is directly linked with the correlation

between the assets multiplied with their standard deviation.

Covariance:

(Please see Appendix 1 for covariance Matrix table)

Correlation comes to mind when we think about the benefits of diversification (Zhang,

2008) of different assets class because increasing the correlation diminish the benefits of

diversification. The smaller the correlation between the securities, the lower covariance we

will receive .So our first step is to gather securities from the asset classes we have picked and

calculate a correlation matrix .The qualities that the securities had in order to be part of this

matrix were high performance, median or low volatility and liquidity .The final correlation

matrix chosen by the fund is:

Correlation:

=

(Please see Appendix 2 for Correlation Matrix table)

But the statistical data by themselves cannot back up the funds decision to proceed in

constructing a portfolio based only on this information (Gintschel, 2008). Economic data

provides evidence of the goodness-of-pick from this correlation matrix.

Page 19: MUTUAL Fund Policy Statement Final Report

We also use the following model to sort out the minimum variance of our portfolio. This is as

follows:

+ (i.e. 2

securities)

Based on the calculation our portfolio assets performed as follows:

Bonds performance:

Mean Variance STD.

Canadian Bond 0.01 0.00086 0.03

Eurozone Bond 0.06 0.00 0.00

NZ Bond 0.03 0.00 0.01

Equity Performance:

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Mean Variance STD.

Canadian Bond

Eurozone Bond

NZ Bond

0.67, 2.97

6.16, 0.20 2.96, 0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.00 2.00 4.00 6.00 8.00

Bo

nd

re

turn

%

Bond risk%

Debts instruments performance on

Portfolio

Debts instruments

performance on

Portfolio

Page 20: MUTUAL Fund Policy Statement Final Report

Mean Variance STD.

Metal and Mining

0.40 0.12 0.36

Materials

0.49 0.08 0.29

Textile

0.48 0.05 0.22

Utilities

0.15 0.02 0.13

Pharmaceutics

0.31 0.01 0.12

Overall Portfolio’s individual asset’s return is:

0.00

0.50

Metal

and

Mining

Metaria

ls

Textile Utilities Pharma

ceutices

Mean 0.40 0.49 0.48 0.15 0.31

Variance 0.12 0.08 0.05 0.02 0.01

STD. 0.36 0.29 0.22 0.13 0.12

Equity sector performance

0.01, 0.03

0.06, 0.00 0.03, 0.01

0.40, 0.36

0.49, 0.29

0.48, 0.22

0.15, 0.13 0.31, 0.12

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Po

rtfo

lio

Retu

rn %

Portfolio Risk %

Sector's performance of the Portfolio

EFFAS Canadian Bond

EFFA Euro zone Bond

EFFAS NZ Bond

Metal and Mining

Metarials

Textile

Utilities

Pharmaceuticals

Page 21: MUTUAL Fund Policy Statement Final Report

4. Portfolio construction

After analyzing the reasons, both statistically and economically, of choosing the specific

securities and assets it essential for the fund manager to find a way to forecast expected

returns and expected risk (KUMAR, 2008) .A common way used to forecast such data is by

using historic data from the securities in the portfolio.

The following model can be used to forecast the expected return on equities.

Expected return =∑

Beside, the variance of returns for risky assets such as equities could be described

as:

)

Indeed, Bonds are fixed income securities. So, bonds price are less volatile then the equity. It

also less risky with less return. However, the calculation for the fixed income is a bit different

from the equities. Here, in our portfolio we follow the following models to calculate the

price volatility and convexity of our bonds (Fask, 2008). Particularly a bond

which varies inversely with its coupon and directly with its term to maturity, it

is may necessary to determine the best combination of these two variables to

achieve the objective. The model is as follows:

= ∑

Determinants of Convexity:

Convexity is a measure of the curvature of the price-yield relationship (C.Brown,

2003). Mathematically, Convexity is the second derivative of price with respect

to yield divided by price. Specifically, convexity is the percentage change in

⁄ for a given change in yield.

Page 22: MUTUAL Fund Policy Statement Final Report

Convexity =

The Bond holding period yield (HPY) is:

In this scenario we calculate the future bond price by applying the following

model in our portfolio.

(

)

(

)

However, in the future bond price calculation inflation rate of a country is very important.

Although in our portfolio we did not consider the inflation and interest rate as because it was

not instructed. But we are considering to tell the investors about the inflation rate calculation

model which helps them to analyze the future price with inflation of the currency.

1. Rate of Inflation:

2. Throughout this market, A bond price change is measured as the

percentage change in the price of the bond, computed as follows:

Percentage change is Bond price =

Here,

EPB = The ending price of the Bond

BPB = The beginning price of the Bond

Indeed, the larger the variance for an expected rates of return on portfolio, the

greater the dispersion of expected returns and the greater the uncertainty on

risk of the investment (Chow, 2008), the variance or risk of the investment. The

variance of the perfect certainty would be:

Page 23: MUTUAL Fund Policy Statement Final Report

3. Expected return of a portfolio:

Obviously, such an estimate contains a great deal of uncertainty. In order to use this way of

forecasting one must assume that the returns are normally distributed (Sharpe, 1995).

In this situation This time horizon was selected in order to include at least one whole

economic cycle and provide as much feedback on the reaction of the securities during all

holding periods. The data are weekly and denominated in the currency of the funds

country of origin (USD$).

Firstly we must calculate the weekly returns and the standard deviation:

Returns=ln (

σ=√∑ ̅̅ ̅

After calculating the monthly returns for the past 1 year we must annualize them as well as

the standard deviation:

Annual Returns = √ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ -1

Annual standard dev. = σ

The goal of the manager is to minimize his expected risk and maximize his expected returns.

The standard dev. of the three securities of our portfolio is equal to:

= ∑ ∑

(A)

Page 24: MUTUAL Fund Policy Statement Final Report

The expected return of the portfolio is equal to the sum of each security times the weight

they have in it.

∑ (B)

So are next step is to Minimize equation (A) and Maximize equation(B) at the same time .As

the expected returns have already been calculated the only thing left to alter in order to reach

an efficient portfolio is the weights of the securities. In order to select our optimum portfolio

we insert into the equations different expected returns so we can find the weights that

minimize the risk we must endeavor.

The efficient frontier

S ER SHARP RATIO

3.0 0.7 0.224398649

0.2 6.2 30.7711

0.5 3.0 5.90844

35.5 40.5 1.138913851

29.3 48.6 1.656799317

22.2 47.8 2.149087719

12.6 15.0 1.186049206

12.0 31.5 2.632459866

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10

Sharp ration of Portfolio

securities

SHARP RATIO

Page 25: MUTUAL Fund Policy Statement Final Report

A portfolio is considered efficient if it is not possible to obtain a higher return without

increasing standard deviation.

This is the efficient frontier line as described in the Markowitz portfolio theory .Every

point on this line is efficient for the investor (Özekici, 2008). To compute points along the

efficient frontier we use the Excel Solver which helps us to find the objective of portfolio.

Once bring up Solver, you are asked to enter the cell of the target (objective) function. In our

application, the target is the variance of the portfolio, given in cell C56. Solver will minimize

this target.

Perfect positive correlation is the only case in which there is no benefit from

diversification. With any correlation coefficient less than 1.0( 1 ), there will be a

diversification effect, the portfolio standard deviation is less than the weighted average of the

standard deviations of the component securities. Therefore, there are benefits to

diversification whenever asset returns are less than perfectly correlated. Negative correlation

between a pair of assets is also possible. Where negative correlation is present, there will be

even greater diversification benefits.

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35

Po

rtf

oli

o R

etu

rn

(%

)

Portfolio Risk (%)

Portfolio Efficient Frontier

Page 26: MUTUAL Fund Policy Statement Final Report

Figure 5: Investment opportunity sets for our portfolio with various correlation

coefficients between different securities.

Figure 6: Indifference Curves and Efficient frontier

In order to simplify the determination of optimal risky portfolio, we use the capital allocation

line (CAL), which depicts all feasible risk-return combinations available from different asset

allocation choices, to determine the optimal risky portfolio. To start, however, we will

0

B

A

Standard Deviation

Ex

pe

cte

d R

etu

rn

Minimum

variance

portfolio Efficient

frontier of

risky assets

1U

2U

0 Standard Deviation

Ex

pecte

d R

etu

rn

0 1

Page 27: MUTUAL Fund Policy Statement Final Report

demonstrate the solution of the portfolio construction problem with only two risky assets (in

our example, asset A and asset B) and a risk-free asset. In this case, we can derive an explicit

formula for the weights of each asset in the optimal portfolio. This will make it easy to

illustrate some of the general issues pertaining to portfolio optimization.

The solution shows that the optimal position in the risky asset is, as one would expect,

inversely proportional to the level of risk aversion and the level of risk (measured by the

variance) and directly proportional to the risk premium offered by the risky asset. Once we

have reached this point, generalizing to the case of many risky assets is straightforward.

Before we move on, let us briefly summarize the steps we followed to arrive at the complete

portfolio.

1. Specify the return characteristics of all securities (expected returns, variances,

covariance).

2. Establish the risky portfolio:

a. Calculate the optimal risky portfolio S.

b. Calculate the properties of portfolio S using the weights determined in step

and equations X.5 and X.13.

3. Allocation funds between the risky portfolio and the risk-free asset:

a. Calculate the fraction of the complete portfolio allocated to Portfolio S (the

risky portfolio) and to risk-free asset (equation X.14).

b. Calculate the share of the complete portfolio invested in each asset and in

risk-free asset.

Figure7: Determination of the optimal portfolio

Indifference Curve

Opportunity Set of Risky

Assets

Optimal

Complete

Portfolio

CAL

0

Optimal Risky Portfolio

Standard Deviation

Ex

pecte

d R

etu

rn

fr

Page 28: MUTUAL Fund Policy Statement Final Report

6. Computing return

In this stage, we now compute the portfolio returns over the last three months by following a

step by step procedure:

Step1: Compute each securities return using the following formula

Returns =

(9)

Step2: Compute the portfolio’s return with the use of formula (8) (shown previously)

After completing the above calculation we will derive the following table

Portfolio securities Weights Return

Canadian bond 3.19 0.7

Euro Zone bond 0.19 6.2

NZ bond 0.58 3.0

Metals and mining 43.29 40.5

Materials 37 48.6

Textiles 28.9 47.8

Utilities 15.47 15.0

Pharmaceuticles 14.92 31.5

7. Benchmarking

From the above different models and calculation, we observe that our performance is

relatively better than the earlier portfolio performed .Although there is still opportunity to

observe the data from the market as the industry sectors continuously fluctuate but positive

sign for the portfolio is the constant growing of the value, we compare the performance to the

benchmark, in order to see the true value of it, by determining if its returns are better than that

of the benchmark.

Page 29: MUTUAL Fund Policy Statement Final Report

It must be noted that the benchmark is a synthetic boundary that is constructed from the equal

weights of the securities in the portfolio.

By the end of March the fund manager’s view has changed considering the bond market and

he decides to proceed in a re-allocation from Brazilian individual sovereign bond to EFFAS

indexed Canadian and Euro zone bond which are more diversified and comparably higher

returned. This has as a consequence to repeat the construction of the portfolio from the

beginning . .Because in our original correlation matrix we had used data from more than just

different countries individual bond. We will now pick the immediate best correlated after the

polish government bond that we substituted. In the following graph illustrate the portfolio

securities weights compare with the targeted bench mark.

Figure: Benchmarking with our portfolio securities’ weights. We found that our portfolio weights

relative constant and better. Performed.

0

5

10

15

20

25

30

35

40

45

50

Portfolio

Benchmark

Page 30: MUTUAL Fund Policy Statement Final Report

9. Decision on Investment

The rationale behind the picking of the securities included in this mutual fund portfolio was

presented in the earlier of this report. Although the decisions were well based on the

interpretations of economic and statistical data a deviation was observed after calculating the

market’s performance.

At the beginning we selected the well performed equities from the MSCI index about 18 of

the equities has been selected. The we tried to identify the problem we can refer to the poor

data selection, although the prices were as updated but their market performance based on our

calculation doesn’t satisfy us. On the other hand, the bright side of our selection was the good

weighting of our securities which entitled us to beat the artificial benchmark created to

compare our performance. For the second period of our project we re-allocated one of our

securities for two reasons. The first is that the returns in contrast with the risk do not satisfy

our policy making the bond not desirable for our portfolio after the first three months. On top

of that our view of the market had changed and that has led us to believe that the three bonds

mentioned in chapter 4.2 if allocated in our portfolio will give higher returns than the

previous one. To strengthen this opinion, we would suggest the investors that the last 3 month

trend in the correlation between our Euro zone bond and the Newzeland bond of EFFAS

Index is comradely better. From the optimal portfolio construction theory it is known that low

correlations are a way to diversify the risk between our assets. For all the above reasons our

fund went on with substitution of the Bond Index. Although this was a breakthrough

comparing to the first period the total gains did not manage to coop with the funds policy .To

make matters worse the benchmark that measures the performance was not beaten showing

weak weighting in our portfolio securities. The argument to this is that the weighting of the

portfolio was based on minimizing expected risk and maximizing expected return. The

problem is seen in the poorness of the model or use of historical economic data.

In future projects it is strongly advised that the use of more than one measures of expected

return and risk is used and a larger scale of economic data from the securities selected in

order for a more accurate forecast of future movements. This model over estimated risk and

under estimated returns leading to these weightings in the last 3 months.

Page 31: MUTUAL Fund Policy Statement Final Report

10. Reference

1. kkas, D. S. (February 28, 2009). Review of Global Financial Crisis 2008: Issues,

Analytical Approaches and Interventions.

2. Anthony Hatherley, J. A. (2009). Portfolio construction incorporating asymmetric

dependence structures: a user’s guide. Journal of Accounting and Finance .

3. Anthony, L. (2008). Why Risk Is Not Variance: An Expository Note. Journal of risk

analysis.

4. C.Brown, F. K. (2003). Investment analysis and portfolio management. Thomson.

5. Chow, K. V. (2008). Style Fund Investment: Performance and Efficiency.

6. Fask, A. (2008). OPTIMIZING THE RETURN ON INVESTMENTS FOR

PHARMACEUTICAL PROMOTIONAL EXPENDITURES.

7. Gintschel, A. (2008). Optimal asset allocation for sovereign wealth funds.

KUMAR, W. N. (2008). Equity Portfolio Diversification.

8. Natarajan, K. (2008). Incorporating Asymmetric Distributional Information in Robust

Value-at-Risk Optimization. Journal of management science .

9. Özekici, E. Ç. (2008). Portfolio selection in stochastic markets with exponential utility

functions.

10. Park, A. K. (2008). OPTIMAL PORTFOLIO DIVERSIFICATION USING THE

MAXIMUM ENTROPY PRINCIPLE.

11. Qu, X. M. (2008). Robust portfolio optimization with a generalized expected utility model

under ambiguity.

12. Sharpe, W. F. (1995). Investment. Prentice Hall.

13. Zhang, L. B. (2008). Dynamic mean-variance problem with constrained risk.

Page 32: MUTUAL Fund Policy Statement Final Report

Appendix 1: Covariance Matrix

Co

vari

an

ce M

atr

ix

Cana

dia

n

bond

Euro

Zone

bond

NZ

bon

d

Meta

ls

and

min

ing

Mate

rials

Textile

s

Utilit

ies

Pharm

ac

eutica

ls

Cana

dia

n

bond

8.7

6

0.2

5

0.7

6

53.4

8

58.3

4

38.6

3

24.0

5

19.7

9

Euro

Zone

bond

0.2

5

0.0

4

0.0

7

5.1

1

2.2

3

1.7

0

1.3

4

1.1

4

NZ

bon

d

0.7

6

0.0

7

0.2

5

15.2

8

7.3

8

6.0

4

4.0

0

3.6

0

Meta

ls

and

min

ing

53.4

8

5.1

1

15.2

8

1261

.67

477.1

2

435.0

0

280.4

6

242.3

6

Mate

rials

58.3

4

2.2

3

7.3

8

477.1

2

858.4

9

504.9

0

225.9

1

233.8

0

Textile

s

38.6

3

1.7

0

6.0

4

435.0

0

504.9

0

494.1

7

176.5

8

192.5

7

Utilit

ies

24.0

5

1.3

4

4.0

0

280.4

6

225.9

1

176.5

8

158.7

6

118.7

3

Pharm

ac

eutica

ls

19.7

9

1.1

4

3.6

0

242.3

6

233.8

0

192.5

7

118.7

3

143.0

4

Page 33: MUTUAL Fund Policy Statement Final Report

Appendix 2: Shavron Portfolio individual assets Weights:

Sh

av

ron

Co

vari

a

nce

Matr

ix:

Eq

ually

Weig

hte

d

Po

rtfo

lio

Cana

dia

n b

ond

Euro

Zone

bond

NZ

bon

d

Meta

ls

and

min

ing

Mate

rials

Textile

s

Utilit

ies

Pharm

ac

eutica

ls

We

ights

0.1

25

0.1

25

0.1

25

0.1

25

0.1

25

0.1

25

0.1

25

0.1

25

0.1

25

0.1

4

0.0

0

0.0

1

0.8

4

0.9

1

0.6

0

0.3

8

0.3

1

0.1

25

0.0

0

0.0

0

0.0

0

0.0

8

0.0

3

0.0

3

0.0

2

0.0

2

0.1

25

0.0

1

0.0

0

0.0

0

0.2

4

0.1

2

0.0

9

0.0

6

0.0

6

0.1

25

0.8

4

0.0

8

0.2

4

19.7

1

7.4

6

6.8

0

4.3

8

3.7

9

0.1

25

0.9

1

0.0

3

0.1

2

7.4

6

13.4

1

7.8

9

3.5

3

3.6

5

0.1

25

0.6

0

0.0

3

0.0

9

6.8

0

7.8

9

7.7

2

2.7

6

3.0

1

0.1

25

0.3

8

0.0

2

0.0

6

4.3

8

3.5

3

2.7

6

2.4

8

1.8

6

0.1

25

0.3

1

0.0

2

0.0

6

3.7

9

3.6

5

3.0

1

1.8

6

2.2

4

1.0

00

3.1

9

0.1

9

0.5

8

43.2

9

37.0

0

28.9

0

15.4

7

14.9

2

Page 34: MUTUAL Fund Policy Statement Final Report

Appendix 3: Targeted weighted portfolio at 25% minimum

return.

Bo

rdere

d

Co

vari

a

nce

Matr

ix:

Targ

et

Retu

rn

Po

rtfo

li

o

Cana

dia

n b

ond

Euro

Zone

bond

NZ

bon

d

Meta

ls

and

min

ing

Mate

rial

s

Textile

s

Utilit

ies

Pharm

a

ceutica

ls

We

ights

0.1

6

0.1

3

0.1

4

0.0

0

0.0

0

0.0

0

0.0

8

0.4

9

0.1

552

0.2

1

0.0

0

0.0

2

0.0

0

0.0

0

0.0

0

0.3

1

1.5

1

0.1

275

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

1

0.0

7

0.1

437

0.0

2

0.0

0

0.0

1

0.0

0

0.0

0

0.0

0

0.0

5

0.2

5

0.0

000

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

000

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

000

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

833

0.3

1

0.0

1

0.0

5

0.0

0

0.0

0

0.0

0

1.1

0

4.8

5

0.4

903

1.5

1

0.0

7

0.2

5

0.0

0

0.0

0

0.0

0

4.8

5

34.3

9

1.0

000

2.0

5

0.0

9

0.3

2

0.0

0

0.0

0

0.0

0

6.3

2

41.0

7

Page 35: MUTUAL Fund Policy Statement Final Report

Appendix: 4

1. Metal and Mining

Chat 1: Beta regression analysis of MSCI Index Source: Bloomberg

Chart 2: Correlation of MSCI Materials sector . Source: Bloomberg

Page 36: MUTUAL Fund Policy Statement Final Report

Chart : MSCI Metal and Mining sector ratio analysis Source: Bloomberg

Chart : MSCI metal and mining index Spread analysis. Source: Bloomberg.

Page 37: MUTUAL Fund Policy Statement Final Report

Appendix 5

2. Materials ( MSCI index)

Chart: Beta regression analysis of Material sector . Source: Bloomberg.

Chart: Correlation of Material sector. Source: Bloomberg.

Page 38: MUTUAL Fund Policy Statement Final Report

Chart: Material sector spread analysis. Source: Bloomberg.

Chart: Ratio analysis of material sector. Source: Bloomberg

Page 39: MUTUAL Fund Policy Statement Final Report

Appendix 6

3. Textile Sector of MSCI index

Chart: Beta analysis of MSCI textile sector. Source: Bloomberg.

Chart: Correlation of the MSCI textile sector. Source: Bloomberg.

Page 40: MUTUAL Fund Policy Statement Final Report

Chart: MSCI Textile spread analysis. Source: Bloomberg.

Chart : MSCI Ratio analysis of Textile sector. Source: Bloomberg

Page 41: MUTUAL Fund Policy Statement Final Report

Appendix 7

4. Utilities

Chart: MSCI Utilities sector Beta analysis. Source: Bloomberg

Chart: MSCI Utilities correlation. Source: Bloomberg.

Page 42: MUTUAL Fund Policy Statement Final Report

Chart: Utilities Spread analysis. Source: Bloomberg.

Chart: Ratio analysis. Source: Bloomberg.

Page 43: MUTUAL Fund Policy Statement Final Report

Appendix 8

MSCI Pharmaceuticals Sector

Chart: Beta analysis of MSCI Pharmaceutical sector. Source: Bloomberg

Chart: Correlation of Pharmaceutical sector

Page 44: MUTUAL Fund Policy Statement Final Report

Chart: MSCI Pharmaceutical sector spread analysis. Source: Bloomberg.

Appendix 9

EFFAS (Australian government bond)

Chart: EFFAS Australian bond yield analysis

Page 45: MUTUAL Fund Policy Statement Final Report

Chart : Correlation of EFFAS AUS Bond Index.

Chart : Aus Bond Beta analysis. Source: Bloomberg.

Page 46: MUTUAL Fund Policy Statement Final Report

Appendix 10

EFFAS (Newzeland government bond)

Chart : EFFAS NZ Bond index’s Beta analysis. Source:

Bloomberg

Chart : EFFAS NZ Bond correlation. Source: Bloomberg

Page 47: MUTUAL Fund Policy Statement Final Report

Chart : EFFAS NZ Bond Ratio analysis. Source: Bloomberg.

Appendix 11

Euro zone bond (EFFAS index)

Chart: Euro Zone bond Scenario of EFFAS index.