Performance and Attribution Analysis

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PORTFOLIO

PERFORMANCE

EVALUATION AND

ATTRIBUTIONANALYSIS

Date of Submission

22nd

June, 2011


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PORTFOLIO

PERFORMANCE

EVALUATION AND

ATTRIBUTIONANALYSIS

Submitted by:

Sakib Ahmed Chowdhury

B.B.A. 13th

Batch

Section: A, ID: 13-161

Group # 9

Department of Finance

University of Dhaka

Submitted to:

Mahmood Osman Imam, Ph.D.

Professor


University of Dhaka


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22nd June, 2011

Dr. Mahmood Osman Imam

Professor


Faculty of Business Studies

University of Dhaka

Sir,

With due respect, I, a student of B.B.A. Program (13th Batch) under Department of

Finance, University of Dhaka, submit the report entitled Portfolio Performance

Evaluation and Attribution Analysisthat you have assigned us as the project work for

the course Security Pricing and Portfolio Theoryin the running semester.

I thank you, sir, for this assignment which has enriched my knowledge of this topic.

Sincerely,

_________________

Sakib Ahmed Chowdhury

Section: A, ID: 13-161

B.B.A. 13

th

BatchDepartment of FinanceFaculty of Business StudiesUniversity of Dhaka


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TABLE OF CONTENTS

Table of Contents .............................................................................................. iv

Abstract ............................................................................................................. 1

Methodology ...................................................................................................... 1

Limitation .......................................................................................................... 1

Portfolio Construction ........................................................................................ 2

Selection of Stocks ............................................................................................. 2

Return Series..................................................................................................... 2

Individual Stock Returns .................................................................................. 2

Market Return ................................................................................................ 2

Benchmark Returns for Individual Sectors .......................................................... 3

Optimization of Weights ...................................................................................... 3

Portfolio Performance Measurement .................................................................. 4

Sharpe Portfolio Performance Measure .................................................................. 4

Treynor Portfolio Performance Measure ................................................................. 4

Jensen Portfolio Performance Measure .................................................................. 4

Fama Decomposition .......................................................................................... 5

Components of Overall Performance ..................................................................... 5

Investors Risk................................................................................................ 5

Managers Risk ............................................................................................... 6

Selectivity ...................................................................................................... 6

Diversification ................................................................................................. 6

Net Selectivity ................................................................................................ 6

Decomposition ................................................................................................... 6

Performance Attribution Analysis ....................................................................... 8

Benchmark Portfolio ........................................................................................... 8

Allocation Effect ................................................................................................. 8Selection Effect .................................................................................................. 9

Attribution ......................................................................................................... 9

Findings ........................................................................................................... 10


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INTRODUCTION

Portfolio performance evaluation and attribution analysis help the analysts to identify

their point of efficiency and improve. The focus of this project is to continue on the last

projects work and of portfolio performance evaluation and attribution analysis.

Methodology

The project involves analysis based on some listed companies from different industries.

The data range was 2005 to 2009 and is collected from Dhaka Stock Exchange Data

Library. Microsoft Excel software has been used to conduct some critical programming

work. Interpretation and justification are included as well.

Limitation

The numbers of stocks have been limited to ten. Therefore, this model needs to beexpanded if it to be applied in real world. Another drawback is that there were no

separate calculated indexes for stocks of different industries.


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PORTFOLIO CONSTRUCTION

Stock Selection

The stock selection criteria have been previously presented in the prequel project titled Portfolio Construction and Optimization. Focusing on the purpose of the current

project, the detailed description is irrelevant to include here. Therefore, from this point

forward, the method of measuring performance of previously constructed portfolio (or

any other portfolio) is illustrated.

The selected stocks are as followings:

Industry Company

Bank AB Bank Limited

Islami Bank Limited

Pubali Bank Limited

NBFI IDLC Finance Limited

Fuel & Power Padma Oil

Summit Power

Service & Real Estate Samorita Hospital

Eastern Housing

Pharmaceuticals Renata Limited

Cement Heidelberg Cement

Return Series

Individual Stock Returns

The average returns on stock have been calculated on the basis of capital gain yield and

dividend yield. It is worth mentioning that the capital gain yield was calculated based on

the adjusted stock prices where these adjustments were made to normalize the effect

stock dividend as bonus share. Stock price adjustments were also made when there

were any stock splits (or reverse splits).

Market Return

DSE General Index has been considered as the proxy variable. The rationales are,

It reflects all the price and volume of all the securities listed in Dhaka StockExchange Limited.

It reflects all the price sensitive information available in the stock market.The final market return is the simple average of monthly returns calculated on index.

The month returns on index is calculated with the following formula:


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Benchmark Returns for Individual Sectors

The DSE general index will not serve the purpose to identify the benchmark returns for

individual sectors. Therefore, separate indices for every sector are required to be

calculated the benchmark returns for them. First thing to consider is that DSE general

index is calculated by the contribution of the sectors based on their market

capitalization. If the market capitalization of a particular sector is multiplied to the index

value, the approximate index for that month and for that sector can be identified. For

example:

By repeating this process, the separate index for each of the sectors can be obtained by

applying their contribution in terms of market capitalization. From the separate indices

separate benchmark returns of different sectors can be calculated by applying the same

formula used to find the market return.

Weights and OptimizationThe objective for the optimization of the weights is to maximize the portfolio excess

return per unit of risk taken under the situation where no short selling is allowed. The

portfolio excess return is the weighted average excess returns of the individual

securities. The individual excess returns are the individual average returns in excess of

the monthly risk free rate of return. With the help of Microsoft Excel program it is very

easier to calculate the optimum percentage of weight to be put on individual securities in

order to reach the predefined objective. It is beyond the scope of the current project

because optimization process has been described in details in the previous project.

The optimum percentages of weights to that have to be put on are as followings.

Company Weights %

AB Bank Limited 0.00%

Islami Bank Limited 0.00%

Pubali Bank Limited 0.00%

IDLC Finance Limited 13.62%

Padma Oil 9.68%

Summit Power 4.67%

Samorita Hospital 11.33%

Eastern Housing 23.31%

Renata Limited 37.39%

Heidelberg Cement 0.00%


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PORTFOLIO PERFORMANCE MEASUREMENT

Sharpe Portfolio Performance Measure

The Sharpe ratio uses the total risk of the portfolio, not its systematic risk. The use oftotal risk is appropriate if the portfolio is an investors total portfolio that is, the

investor does not own any other assets. The portfolio with highest Sharpe ratio has the

best performance.

Treynor Portfolio Performance Measure

The Treynor ratio uses the systematic risk of the portfolio. Like, Sharpe ratio, the

portfolio with highest Treynor ratio has the best performance.

Both of the above performance measures suffer from a common limitation they can be

interpreted from a single number. Rather, they need to be compared with values

measuring other portfolios.

Following table summarizes the values of these two measures.

Portfolio Manager Investor X Investor Y Investor Z

Portfolio Excess Return 1.98% 1.95% 1.30%

Portfolio Standard Deviation 5.93% 6.90% 11.10%

Portfolio Beta 0.77 0.89 1.13

Sharpe Ratio 0.2864 0.2826 0.1171

Treynor Ratio 0.0261 0.0219 0.0115

Jensen Portfolio Performance Measure

Like the Treynor ratio, Jensens alpha is based on systematic risk. It is the vertical

distance from the SML measuring the excess return for the same risk as that of the

market and is given by

The following table shows the calculation of Jensens alpha for the optimized portfolio.

Portfolio Manager Investor X Investor Y Investor Z

Portfolio Annualized Return 30.02% 28.94% 26.38%

Market Return 22.08% 22.08% 22.08%

Risk-free Return 5.82% 5.82% 5.82%

Jensen's 0.1747 0.1447 0.0801


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FAMA DECOMPOSITION

Eugene F. Fama has suggested a somewhat finer breakdown of performance. 1 The basic

idea of his breakdown was that the overall performance, in other words, the excess

return of a portfolio can be decomposed into measures of risk-taking and securityselection skill. Decomposition process is described below.

The following graph can clarify the concept of the decomposition.

Where,

Components of Overall Performance

Investors Risk

Investors risk is referred to as the highest systematic risk the investor wants to assume

for his/her investment. For taking this risk s/he would require additional return as

1Eugene F. Fama Components, Components of Investment Performance,Journal of Finance 27, no. 3 (June1972): 551-567


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compensation to invest some portion of his wealth in risky assets. This is the return

against investors assumed risk.

Managers Risk

Managers risk is referred to as the highest systematic risk assumed by the portfolio

manager in a fully diversified portfolio. The return is the compensation for assuming thatrisk which is ultimately the referred to the security market line. This is the required rate

of return a portfolio manager has to earn with his portfolio for the investor to

compensate for taking additional risk than the target risk of the investor himself/herself.

Investors risk and managers risk together forms the portfolio risk.

Selectivity

Selectivity component represents the portion of the portfolios actual return beyond that

available to an unmanaged portfolio with identical systematic risk. This return represents

the superior skill of the portfolio manager in selecting the appropriate asset class (sector

in case of this project) to arrive at above average rates of return for the portfolio.Selectivity is the vertical difference between the return for assuming the market

systematic risk and the actual return of the portfolio.

Diversification

If a portfolio manager attempts to select undervalued stocks and in the process gives up

some diversification, it is possible to measure the added return necessary to justify this

diversification decision. This term emphasizes that diversification is the elimination of all

unsystematic variability.

Net Selectivity

Net selectivity is the vertical distance between the actual return on the portfolio and the

return on the combination of the riskless asset and the market portfolio that has return

dispersion equivalent to that of the portfolio being evaluated. The values of net

selectivity and diversification will be equal when the portfolio is completely diversified.

Decomposition

For decomposing, first the individual stock returns on securities have been annualized.

Then the individual beta of the stocks has been calculated. The beta of a security is the

covariance of the returns of the security itself with the market, divided by the variance

of the return of the market. In order to make the results more meaningful, the adjusted

beta has been used. The adjusted beta can be calculated to reflect the mean reversion

theory. Here, 2/3 weight is put on the market beta (1.00) and 1/3 weight is put on the

assets individual beta to find the result more correlated with the market beta.


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Company AnnualizedMean Return

Beta AdjustedBeta

Weights

AB Bank Limited 0.257916 1.39 1.13 0.00%

Islami Bank Limited 0.047319 0.37 0.79 0.00%

Pubali Bank Limited -0.147307 1.31 1.10 0.00%

IDLC Finance Limited 0.269079 0.82 0.94 13.62%

Padma Oil 0.266969 0.27 0.76 9.68%

Summit Power 0.229869 0.73 0.91 4.67%

Samorita Hospital 0.269169 -0.08 0.64 11.33%

Eastern Housing 0.382292 0.21 0.74 23.31%

Renata Limited 0.275669 0.36 0.79 37.39%

Heidelberg Cement 0.152585 0.94 0.98 0.00%

The following table lists the outcomes of the decomposition where the return for everycomponent except the breakdown of portfolio risk.

Portfolio Return 29.59%Portfolio Total Risk 0.06Portfolio Systematic Risk 0.78Market Return 22.08%Market Total Risk 0.08Risk Free Return 5.82%Ratio of Total Risk 0.74

Return for Systematic Risk SML 18.55%Return for Total Risk CML 17.88%

Return for Selectivity 11.04%Return for Diversification -0.67%Return for Net Selectivity 11.71%

As the return for diversification and return for net selectivity is not equal, it indicates

that the portfolio is not completely diversified. -0.67% additional return is there for

diversification in the portfolio.


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PERFORMANCEATTRIBUTIONANALYSIS

The purpose attribution analysis is to isolate the reason for any positive or negative

value-added performance. These factors are the two ways by which a portfolio manager

can earn above average return for the investors portfolios. The two ways are (1)selecting superior securities and (2) demonstrating superior market timing skills by

allocating funds to different assets classes or market segments. Specifically, this method

compares the total return to the managers actual investment holdings to the return for

a predetermined benchmark portfolio and decomposes the difference into an allocation

effect and a selection effect.

Benchmark Portfolio

For constructing the benchmark portfolio, first the market capitalization is used for

individual companies to find out the individual security weights against the market. Then

the weights have been rescaled in the scale of 100%. Followed by the annualizing ofsector returns for each of the sector, the process continues with calculation of

benchmark portfolio return from the sum of the products of rescaled weights for

securities and their benchmark returns of their respective industries.

Company Industry MarketCapitalization

(in Millions)

MarketWeight

(Individual)

RescaledWeight

MarketSegment

Return

AB Bank Limited Bank 29607.637 1.11% 14.02% 22.08%

Islami Bank Limited Bank 47986.979 1.79% 22.72% 22.08%

Pubali Bank Limited Bank 34678.344 1.30% 16.42% 22.08%

IDLC Finance Limited NBFI 20262.825 0.76% 9.59% 26.91%

Padma Oil Fuel & Power 21556.080 0.81% 10.20% 26.70%

Summit Power Fuel & Power 9773.179 0.37% 4.63% 22.99%

Samorita Hospital Service & Real Estate 855.393 0.03% 0.40% 26.92%

Eastern Housing Service & Real Estate 5848.853 0.22% 2.77% 38.23%

Renata Limited Pharmaceuticals 17199.690 0.64% 8.14% 27.57%

Heidelberg Cement Cement 23474.262 0.88% 11.11% 15.26%

Total Market 2676118.807

Benchmark PortfolioReturn

23.21%

Allocation Effect

The allocation effect measures the portfolio managers decision to over- or under-weight

a particular market segment or sector, i.e. (wai wpi) in terms of that segments return

performance relative to the overall return to the benchmark, i.e. (Rai Rp). Good timing

skill is therefore a matter of investing more money in those market segments that end

up producing greater than average returns. The allocation effect is measured by the

following formula.


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Selection Effect

The selection effect measures the managers ability to form specific market segment

portfolios that generate superior returns relative to the way in which the comparable

market segment is defined in the benchmark portfolio (i.e., (Rai Rpi), weighted by the

managers actual market segment investment proportion.

Attribution

Company Actual

Weight

Benchmark

Weight

Weight

Difference

Actual

Return

Benchmark

Return

Return

Difference

AB Bank Limited 0.00% 14.02% 25.79% 22.08% -14.02% 3.71%

Islami Bank Limited 0.00% 22.72% 4.73% 22.08% -22.72% -17.35%

Pubali Bank Limited 0.00% 16.42% -14.73% 22.08% -16.42% -36.81%

IDLC Finance Limited 13.62% 9.59% 26.91% 26.91% 4.03% 0.00%

Padma Oil 9.68% 10.20% 26.70% 26.70% -0.53% 0.00%

Summit Power 4.67% 4.63% 22.99% 22.99% 0.05% 0.00%

Samorita Hospital 11.33% 0.40% 26.92% 26.92% 10.93% 0.00%

Eastern Housing 23.31% 2.77% 38.23% 38.23% 20.54% 0.00%

Renata Limited 37.39% 8.14% 27.57% 27.57% 29.24% 0.00%

Heidelberg Cement 0.00% 11.11% 15.26% 15.26% -11.11% 0.00%

Actual Portfolio Return 29.59%

Benchmark Return 23.21%

Allocation Effect *(Wai - Wpi) (Rpi - Rp)]0.06

Selection Effect *(Wai) (Rai - Rpi)]0.00

Net Effect [Allocation + Selection]0.06

The difference in the benchmark portfolio return and actual portfolio return indicates that

the portfolio manager has succeeded to add value to his investors portfolio. In other

words, the portfolio manager, with his current constructed portfolio, has outperformed

the market on 1-point basis. This outperformance is attributable to the efficient

allocation to sectors.

Performance and Attribution Analysis

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