46610934 evaluation of portfolio performance

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Evaluation of Portfolio Performance

What is Required of a Portfolio Manager (PM)?

We have two major requirements of a PM:

1. The ability to derive above average returns for a given risk class (large risk-adjusted returns);and

2. the ability to completely diversify the portfolio to eliminate all unsystematic risk.

May also desire large real (inflation-adjusted) returns, maximization of current income, highafter-tax rate of return, preservation of capital.

Requirement #1 can be achieved either through superior timing or superior security selection. APM can select high beta securities during a time when he thinks the market will perform well and

low (or negative) beta stocks at a time when he thinks the market will perform poorly.Conversely, a PM can try to select undervalued stocks or bonds for a given risk class.

Requirement #2 argues that one should be able to completely diversify away all unsystematicrisk (as you will not be compensated for it). You can measure the level of diversification bycomputing the correlation between the returns of the portfolio and the market portfolio. Acompletely diversified portfolio correlated perfectly with the completely diversified marketportfolio because both include only systematic risk.

Some portfolio evaluation techniques measure for one requirement (high risk-adjusted returns)

and not the other; some measure for complete diversification and not the other; some measure forboth, but don't distinguish between the two requirements.

Composite Equity Portfolio Performance Measures

As late as the mid 1960s investors evaluated PM performance based solely on the rate of return.They were aware of risk, but didn't know how to measure it or adjust for it. Some investigatorsdivided portfolios into similar risk classes (based upon a measure of risk such as the variance ofreturn) and then compared the returns for alternative portfolios within the same risk class.

We shall look at some measures of composite performance that combine risk and return levels

into a single value.Treynor Portfolio Performance Measure (aka: reward to volatility ratio)

This measure was developed by Jack Treynor in 1965. Treynor (helped developed CAPM)argues that, using the characteristic line, one can determine the relationship between a securityand the market. Deviations from the characteristic line (unique returns) should cancel out if youhave a fully diversified portfolio.


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Treynor's Composite Performance Measure: He was interested in a performance measure thatwould apply to ALL investors regardless of their risk preferences. He argued that investorswould prefer a CML with a higher slope (as it would place them on a higher utility curve). Theslope of this portfolio possibility line is:

A larger Ti value indicates a larger slope and a better portfolio for ALL INVESTORSREGARDLESS OF THEIR RISK PREFERENCES. The numerator represents the risk premiumand the denominator represents the risk of the portfolio; thus the value, T, represents theportfolio's return per unit of systematic risk. All risk averse investors would want to maximizethis value.

The Treynor measure only measures systematic risk--it automatically assumes an adequatelydiversified portfolio.

You can compare the T measures for different portfolios. The higher the T value, the better theportfolio performance. For instance, the T value for the market is:

In this expression, b m = 1.

Demonstration of Comparative Treynor Measures: Assume that you are an administrator of alarge pension fund (i.e. Terry Teague of Boeing) and you are trying to decide whether to renew

your contracts with your three money managers. You must measure how they have performed.Assume you have the following results for each individual's performance:

InvestmentManager

Average Annual Rateof Return

Beta

Z 0.12 0.90

B 0.16 1.05

Y 0.18 1.2

You can calculate the T values for each investment manager:

Tm (0.14-0.08)/1.00=0.06

TZ (0.12-0.08)/0.90=0.044


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TB (0.16-0.08)/1.05=0.076

TY (0.18-0.08)/1.20=0.083

These results show that Z did not even "beat-the-market." Y had the best performance, and both

B and Y beat the market. [To find required return, the line is: .08 + .06(Beta).

One can achieve a negative T value if you achieve very poor performance or very goodperformance with low risk. For instance, if you had a positive beta portfolio but your return wasless than that of the risk-free rate (which implies you weren't adequately diversified or that themarket performed poorly) then you would have a (-) T value. If you have a negative betaportfolio and you earn a return higher than the risk-free rate, then you would have a high T-value. Negative T values can be confusing, thus you may be better off plotting the values on theSML or using the CAPM (in this case, .08+.06(Beta)) to calculate the required return andcompare it with the actual return.

Sharpe Portfolio Performance Measure (aka: reward to variability ratio)

This measure was developed in 1966. It is as follows:

It is VERY similar to Treynor's measure, except it uses the total risk of the portfolio rather thanjust the systematic risk. The Sharpe measure calculates the risk premium earned per unit of totalrisk. In theory, the S measure compares portfolios on the CML, whereas the T measure comparesportfolios on the SML.

Demonstration of Comparative Sharpe Measures: Sample returns and SDs for four portfolios(and the calculated Sharpe Index) are given below:

Portfolio Avg. Annual RofR SD of return Sharpe measure

B 0.13 0.18 0.278

O 0.17 0.22 0.409

P 0.16 0.23 0.348

Market 0.14 0.20 0.30

Thus, portfolio O did the best, and B failed to beat the market. We could draw the CML giventhis information: CML=.08 + (0.30)SD


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Treynor Measure vs. Sharpe Measure. The Sharpe measure evaluates the portfolio manager onthe basis of both rate of return and diversification (as it considers total portfolio risk in thedenominator). If we had a fully diversified portfolio, then both the Sharpe and Treynor measuresshould given us the same ranking. A poorly diversified portfolio could have a higher rankingunder the Treynor measure than for the Sharpe measure.

Jenson Portfolio Performance Measure (aka differential return measure)

This measure (as are all the previous measures) is based on the CAPM:

We can express the expectations formula (the above formula) in terms of realized rates of returnby adding an error term to reflect the difference between E(Rj) vs actual Rj:

By subtracting the risk free rate from both sides, we get:

Using this format, one would not expect an intercept in the regression. However, if we hadsuperior portfolio managers who were actively seeking out undervalued securities, they couldearn a higher risk-adjusted return than those implied in the model. So, if we examined returns ofsuperior portfolios, they would have a significant positive intercept. An inferior manager wouldhave a significant negative intercept. A manager that was not clearly superior or inferior wouldhave a statistically insignificant intercept. We would test the constant, or intercept, in thefollowing regression:

This constant term would tell us how much of the return is attributable to the manager's ability toderive above-average returns adjusted for risk.

Applying the Jenson Measure. This requires that you use a different risk-free rate for each timeinterval during the sample period. You must subtract the risk-free rate from the returns duringeach observation period rather than calculating the average return and average risk-free rate as inthe Sharpe and Treynor measures. Also, the Jensen measure does not evaluate the ability of theportfolio manager to diversify, as it calculates risk premiums in terms of systematic risk (beta).For evaluating diversified portfolios (such a most mutual funds) this is probably adequate. Jensen

finds that mutual fund returns are typically correlated with the market at rates above .90.

Application of Portfolio Performance Measures

Calculated Sharpe, Treynor and Jenson measures for 20 mutual funds. Using the Jenson measure,only 3 managers had superior performance (Fidelity Magellan, Templeton Growth Funds, andValue Line Special Situations Fund) while 2 managers had inferior performance (OppenheimerFund and T. Rowe Price Growth Stock Fund).


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Relationship among Portfolio Performance Measures

For all three methods, if we are examining a well-diversified portfolio, the rankings should besimilar. A rank correlation measure finds that there is about a 90% correlation among all threemeasures. Reilly recommends that all three measures. [In my opinion the Jensen measure is the

most stringent. It is testing for statistical significance, whereas the other methods are not. Theother methods are also examining average returns, whereas the Jensen measure uses actualreturns during each observation period.]

Factors that Affect Use of Performance Measures

You need to judge a portfolio manager over a period of time, not just over one quarter or evenone year. You need to examine the manager's performance during both rising and fallingmarkets. There are also other problems associated with these measures:

w Measurement Problems: All of these measures are based on the CAPM. Thus, we need a real

world proxy for the theoretical market portfolio. Analysts typically use the S&P500 Index as theproxy; however, it does not constitute a true market portfolio. It only includes common stockstrading on the NYSE. Roll, in his 1980/1981 papers, calls this benchmark error.

We use the market portfolio to calculate the betas for the portfolios. Roll argues that if the proxyused for the market portfolio is inefficient, the betas calculated will be inappropriate. The trueSML may actually have a higher (or lower) slope. Thus, if we plot a security that lies above theSML it could actually plot below the "true" SML.

w Global Investing: Incorporating global investments (with their lower coefficients ofcorrelation) will surely move the efficient frontier to the left, thus providing diversification

benefits. It may also shift the efficient frontier upward (increasing returns). [However, we haveno proxy to measure global markets.]

Portfolio Performance Evaluation and Active

Portfolio Management

Chapter 17Outline

Conventional Measurement Techniques

2

Sharpe Index and M

Jensen Index

Treynor Index

Active Management


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Market Timing

Style Analysis Conventional Performance Measurement

One of the first direct applications of Markowitzs

portfolio theory was for risk-adjusted performance

measurement

Before the 1960s, risk adjustment took the form of

asset-type classifications, which were imprecise and

not very analytical

The Three main risk-adjusted measures:

(

2

Sharpe Index (or M

Treynor Index

Jensens AlphaSharpe Index

The Sharpe measure provides

an estimate of excess return per

unit of standard deviation (or

total risk). This can then be

compared to a benchmark

portfolio.

Which is better: Portfolio 1 or

2?

0

5

10


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15

20

25

5 10 15 20 25 30

Standard Deviation

Expected Return

p

fp

p

rR

S

=

roxy p M

1 Portfolio

2 PortfolioMeasure (Modigliani and Modigliani)

2

The M

Uses total volatility as risk measure (like Sharpe Index)

Calculate the portfolio variance 1.

Add T-Bills to the portfolio to make the risk the same as 2.

the Market:

2


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Mkt

= P, TBills

) + 2w(1-w)

2

TBills

(

2

) + (1-w)

2

p

(

2

Solve w

2

Mkt

) =

2

p

(

2

Or just w

This adjusted portfolio P* then has returns: 3.

) + (1-w)r P

= w(r P*

r


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f

M 4.

2

M -r P*

= rMeasure

2

The M

Measure gives

2

The M The

Sharpe the same results as the

measure, just in different form.

M - r P*

= r

2

M

Which is better: Portfolio 1 or

2?

0

5

10

15

20

25

5 10 15 20 25 30


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Standard Deviation

Expected Return

roxy p M

1 Portfolio

2 Portfolio

+M

2

-M

2Treynor Index

The Treynor measure provides

an estimate of excess return

per unit of beta (or market

risk). Again, this can then be

compared with a benchmark

portfolio.

Which is better 1 or 2?

Statistical problems?

p

fp

p

rR

T


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=

2 Portfolio

1 Portfolio

roxy p M

0

5

10

15

20

25

0.25 0.5 0.75 1 1.25 1.5

Beta

Expected ReturnJensen Index

The Jensen index provides an

estimate of excess return relative

to what is predicted by CAPM.

This is also the alpha of the

security characteristic line

is generated from regressions

We can also define other related

measures such as the appraisal

ratio: alpha relative to the

portfolios diversifiable risk

] [ fMpfpp

rRrR =


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0

5

10

15

20

25

-0.5 0 0.5 1 1.5 2 2.5

Beta

Expected Return

y rox p M

2 Portfolio

1 Portfolio Criticisms of Measures

All performance measures nest within the mean-

variance framework of CAPM. Thus, benchmark

error is always problem

An APT-based alternative developed by Gruber

accounts for other risk factors

Changing risk measures (betas and volatilities) plague

all testsWhats ahead?

New York City Trip Signup

Vicki Rollo 307 Purnell Hall

Cost is $25

2 options

1. Midtownvisit Nasdaq, Protiviti, ITG and

JPMorgan


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2. Wall Streetvisit the NYMEX, AMEX + ??

Homework #3 due on Thursday!!!

Test #2 next Wednesday, November 1 Grubers 4-Factor Model

captures managerial

i

Controlling for factor risk,

ability to select securities.

Actively managed mutual funds outperform by 65 basis

points (b.p.) or 0.65% per year

Expense ratios averaged 113 b.p. (or 1.13%)!

Overall, net result is that the average actively-managed

mutual fund underperforms by 48 b.p. or 0.48%

Since we can buy an S&P500 index fund for about 10-

12 b.p., we are better off, on average, by passive

indexingThe Lure of Active Management

Some portfolio managers have hot hands that appear

to be better than just lucky

Anomalies in past returns suggest that there may be

some value in finding predictable patterns in stock

returns

The potential benefits are large, if we exceed the market

averages

For 10% returns over 40 years (until retirement),

FV = 10,000*1.10

40


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= $452,593

For 10.5% returns over the same horizon,

FV = 10,000*1.105

40

= $542,614Market Timing

The act of moving in and out of the market, based

on future expectations

Get price appreciation while

Avoiding bad periods

Enticing since potential benefits are large here too!

Example in book (p. 591) Invest $1 in 1924

1. In T-bills, get $17.56 at end of 2003

2. In SP500, get $1,992.80

3. If perfect timing, get $148,472!Actual Market Timing Results

See Wall Street Journal article on actual mutual fund

investment returns

Average investor falls victim to psychological biases

Buys more after prices run up

Doesnt sell to minimize losses

Net result is that the average investor dramatically

underperforms even the average mutual fund return

fees! Even before

Bottom Line: Market timing can be hazardous to your

wealthStyle Analysis

s to the style of assets that Process of benchmarking fund return


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comprise the portfolio

Sharpe comes up with 12:

1. T-Bills

2. Intermediate bonds

3. Long-term bonds

4. Corporate bonds

5. Mortgages

6. Value stocks

7. Growth stocks

8. Mid-cap stocks

9. Smalll stocks

10. Foreign stocks

11. European stocks

12. Japanese StocksStyle becomes the benchmark

Compare fund returns to weighted average of the style

portfolio

Fidelity Magellan, for instance,

47% growth stocks

31% mid-cap stocks

18% small stocks

4% European stocks

Analogous to factors being other portfolio returns

Regress fund returns on these style portfolios

Residual returns signal under- or over-performance

Like the alpha in CAPM or APT models


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Average residual = -0.074% per month! (over 636

funds)International Investing

Chapter 18Summary

Global Markets offer unique risk/return tradeoffs

Should be included in true CAPM analyses

May be quantified as unique APT factors

Home country bias

Most investors notoriously overweight home country

stocks compared to international stocks

Many investors actually hold no foreign equities

Unique Risk Factors

Exchange rate risk

Country-specific (political) riskExchange Rate Risk

International investing gives returns denominated in

foreign currencies

Even if stock returns in the foreign currency are large,

dollar-denominated returns may not be

Exchange rate can make $-denominated returns higher or

lower

Can be hedged away using derivativesusually futures

See FINC416 Derivative Securities

See FINC415 International Finance

International mutual funds offer exchange rate hedged

returnsBenefits of International Diversification

Easy to over-estimate benefits


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Recent history of country-specific risk might suffer from

survivor bias

Unknown political risk makes recent actual

performance exceed the expected performance

Historic covariances underestimate future covariances

Past diversification benefits are over-estimated

Simple rule would be to invest in two other countries

Same benefits as 44 countries

andard deviation than the Benefits amount to 1% less st

simple U.S. index portfolioBehavioral Finance and Technical Analysis

Chapter 19Returns and Behavioral Explanations

Calendar effects

1. Seasonal flow of funds gets translated into stock

purchases (end of year bonuses, end of month

paychecks).

2. Window dressing by institutional traders each quarter

SEC requires quarterly reporting

Managers, wanting to be seen as smart, load up on

good stocks, dump bad stocks before reporting

3. Good and bad news released around calendar year turns.Technical Analysis--Overview

Using past stock prices and volume information to

predict future stock prices

The premise is that there would be predictable patterns in

returns

Charting Techniques


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Technical Indicators

Value Lines System Charting

The Dow Theory

1. Primary trend (long-term)

Last for several months, years

2. Secondary (intermediate) trend

when prices corrected Shorter term deviations get

revert back to trend values

3. Tertiary (minor) trends

Unimportant daily fluctuationsOther Charting Techniques

Point and Figure Charts

Traces up and down movements without regard to time

See Figure 19.4, Table 19.2 in book

Buy and sell signals when prices penetrate previous highs

and lows

Candlestick Charts

Used to identify support and resistance

Used to identify rallies, trendsTechnical Indicators

Sentiment Indicators give bullish/bearish signals

Trin statistics use advances, declines and volume

Odd-lot theory assumes that individual investors miss key

market turning points

Confidence index is the ratio of 10 top-rated bond yields

to 10 intermediate-grade yields

Put/Call ratios look at options market activity


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Mutual fund cash positions assumes that mutual fund

investors miss key market turning points Technical Indicators

Flow of Funds

Short Interest (reflects smart money)

Credit Balances in brokerage accounts (signals intent

for future purchases)

Market Structure

Moving averages

Breadth (advances minus declines cumulated over time)

Relative strength (momentum)

The Value Line system

1. Relative earnings momentum

2. Earnings surprises

3. Value index (a 3 factor model of value)


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i

Diplomarbeit

zur Erlangung des akademischen Grades

Magister rerum socialium oeconomicarumque

(Mag. rer. soc. oec.)

Portfolio Performance Evaluation

Institut fr Betriebswirtschaftslehre

Universitt Wien

Studienrichtung: Internationale Betriebswirtschaft

o. Univ.-Prof. Dr. Josef Zechner

eingereicht von

Johann Aldrian

(Matr.nr.: 9501942)

Wien, 8. September 2000ii

Eidesstattliche Erklrung

Ich erklre hiermit an Eides statt, da ich die vorliegende Arbeit selbstndig und

ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe. Die

aus fremden Quellen direkt oder indirekt bernommenen Gedanken sind als

solche kenntlich gemacht.

Die Arbeit wurde bisher in gleicher oder hnlicher Form keiner anderen

Prfungsbehrde vorgelegt und auch nicht verffentlicht.


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Wien, 8. September 2000 .iii

Portfolio

Performance

Evaluationiv

TABLE OF CONTENT

1. INTRODUCTION 1

1.1. THE RELEVANCE OF PORTFOLIO-MANAGEMENT-EVALUATION 1

1.2. STRUCTURE OF THIS MASTER'S THESIS 2

2. TRADITIONAL MEASURES OF PORTFOLIO PERFORMANCE

EVALUATION AND ITS IMPLICATIONS. 4

2.1. FUNDAMENTALS 4

2.1.1. THE CONCEPT OF EFFICIENT MARKETS 4

2.1.2. RETURN AND RISK AS DETERMINANTS OF THE MARKET 6

2.2. PORTFOLIO MANAGEMENT 8

2.2.1. ACTIVE PORTFOLIO MANAGEMENT 9

2.2.2. PASSIVE PORTFOLIO MANAGEMENT 12

2.2.3. WHAT INDEX TO USE 13

2.3. TRADITIONAL MEASURES OF PERFORMANCE 15

2.3.1. SECURITY-MARKET-LINE BASED PERFORMANCE MEASURES 15

2.3.2. CAPITAL-MARKET-LINE BASED PERFORMANCE MEASURES 18

2.4. WEAKNESSES OF TRADITIONAL MEASURES OF PERFORMANCE 21

3. ALTERNATIVE MEASURES OF PORTFOLIO PERFORMANCE 24

3.1. THE FAMA AND FRENCH THREE & FIVE FACTOR APT-MODEL 24

3.2. THE GRINBLATT & TITMAN NO BENCHMARK MODEL 27

3.3. THE SHARPE APPROACH: ASSET ALLOCATION AND STYLE ANALYSIS 31


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3.3.1. DETERMINANTS OF THE MODEL 32

3.3.2. THE PROCEDURE 35

3.3.3. CRITICISMS AND IMPROVEMENTS 37

4. APPLIED STYLE ANALYSIS 40

4.1. THE DATA 40

4.1.1. AUSTRIAN INVESTMENT FUNDS 40

4.1.2. ASSET CLASSES 45

4.1.2.1. Equity Asset Classes 45

4.1.2.2. Fixed Income Asset Classes 47

4.1.2.3. Statistical Properties of the Employed Asset Classes 48v

4.2. DETERMINING THE FUNDS STYLE AND SELECTION RETURN 50

4.2.1. THE FUNDS AVERAGE COMPOSITION 50

4.2.2. ROLLING A WINDOW 55

4.2.3. COMPARISON OF REAL AND ESTIMATED STYLE WEIGHTS 61

4.2.4. CONTRIBUTION THROUGH SELECTION 63

4.2.5. SUMMARY OF FINDINGS 70

4.3. SOME ADDITIONAL INSIGHT USING US MUTUAL FUNDS 71

5. CONCLUSION AND FINAL REMARKS 79

DATA APPENDIXvi

Abbreviations

Con: Constantia Privat Invest Fund

A 4: Appollo 4 Fund

Gen: Generali Mixfund

Rai: Raiffeisen Global Mix Fund

Ers: SparInvest Fund


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Spa: Global Securities Trust Fund

EVALUE: European Value Stock Index Net Dividends Reinvested

EGROWTH: European Growth Stock Index Net Dividends Reinvested

ESTAND: European Composite Stock Index Net Dividends Reinvested

NAVALUE: North American Value Stock Index Net Dividends Reinvested

NAGROWTH: North American Growth Stock Index Net Dividends Reinvested

NASTAND: North American Composite Stock Index Net Dividends Reinvested

JPSTAND: Japanese Composite Stock Index Net Dividends Reinvested

ATX: Austrian Trading Index (Composite Stock Index)

G7GOV: Government Bond Index of the 7 Largest European Countries

API: Austrian Performance Index (Government Bond Index Interest Reinvested)1

1. Introduction

1.1. The Relevance of Portfolio-Management-Evaluation

Whenever an investor employs resources, be it in the form of hiring employees

for his company, establishing a charitable fund or investing money in an

investment fund he will want to measure the performance of his investment. In

any of the above named cases the investor will establish an evaluation system

that provides him with the feedback needed to determine whether the investment

generates the predetermined utility. In the case of the employee the investor will

demand from him the accomplishment of the agreed on work objectives. From

the manager of the charity fund he will demand evidence that the money was not

spent lavishly. Both times he will bind the executing subjects to some kind of

charta which was defined in advance. In the very same manner he will consider

the evaluation of the investment manager. The investment manager will be

bound to the investment policy and subject to a constant evaluation of his


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achievements. His achievement will be the return on the capital the investor

provided.

At this point one will have to determine whether the achieved return was good or

poor and whether it was skill or luck?

This is the punchline investors are are always facing when entrusting their money

to an investment manager. The evaluation now boils down to two main

questions. The first question the investor will want to address is the question of

performance. What is good and what is poor performance and where is the line

in between - the benchmark - and what to take as the benchmark. Should we

employ the performance of a riskless asset e.g. a T-bond, a generic like the S&P2

500 or other portfolio manager's performance as the benchmark? Unfortunately,

these simplistic measures of performance generally do not produce the desired

degree of specification. The investor will also want to find out whether his

investment manager is skillful of fortunate through an evaluation process, which

can be applied to his manager and thereby finding what kind of constranints may

help to get the investment manager to achieve the goal set by the investor. In

answering how to destinct between a skilled and unskilled portfolio manager and

what is good and poor performance, I will address the question central to this

master's thesis. Can Sharpe's asset allocation model and resulting style analysis

be a useful tool in assessing an investment portfolio's performance and the level

of skill of its investment manager?

1.2. Structure of this master's thesis

The first chapter is devoted to the definition of the problem and its justification in

order to give the reader a general overview of this works content.

In chapter 2 CAPM implications on performance measurement are being


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elaborated and conventional measures of performance are being discussed in a

critical context. The last part of Chapter 2 will emphasize on weaknesses and

critiques of traditional measures of performance. In Chapter 3 I will introduce

alternative measures of portfolio performance. The Fama & French Model, the

Grinblatt & Titman Model and Sharpe's Asset Allocation and Style Analysis

Model will be described. The Sharpe Model will then be explained in further

detail, as it will be the core subject of this master's thesis.

Chapter 4 will comprehend a regression analysis according to Sharpe's Model. It

will be performed on 6 Austrian investment funds. The investment funds will be:

Raiffeisen Global Mix Fund

Appollo 4 Fund3

SparInvest Fund

Generali Mixfund

Global Securities Trust Fund

Constantia Privat Invest Fund

Through constrained quadratic programming the composition of the specific

funds will be determined and the performance of each of them evaluated. In the

end of this chapter the findings will be compared to traditional measures of

performance and its influence on rankings illustrated.

In Chapter 5 I will conclude the findings of this work and critically evaluate the

initially addressed question, whether Sharpe's portfolio evaluation model is a

good and useful model in assessing a portfolio's performance based on evidence

from Austrian and US investment funds.4

2. Traditional measures of portfolio performance

evaluation and its implications.


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2.1. Fundamentals

The traditional evaluation of investment management is based on a few key

concepts. In many cases the framework therefore is provided by the CAPM. In

some other cases it is the risk return relationship of an individual portfolio, its total

risk, that provides the environment for portfolio performance evaluation. On this

basis the essential concepts will be explained in this chapter, as they will be

indirectly relevant in applying and explaining some investment management

evaluation tools.

2.1.1. The Concept of Efficient Markets

The efficient market concept assumes that all investors have free access to

currently available information about the future. All investors are capable of

processing the information as well as adjusting their holdings according to the

information appropriately.

1

This concept guarantees that security prices fully

reflect the investment value of the security. This further implies that there exists

no possibility to generate abnormal return - in a systematic way - with generally

available information. Eugene Fama

2

classified the efficient market hypothesis

into 3 forms:

The weak form of market efficiency is defined by Fama as reflecting all

historical prices in the value of a security. According to this definition it should be

impossible for a technical analyst to systematically make profits by looking at

past prices.


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1

SHARPE, ALEXANDER, BAILEY (1998), p. 93

2

FAMA (1970), p. 383 - 4175

The semi-strong form of market efficiency is defined as incorporating all

publicly available information. This is the form currently assumed to hold,

although there is a discussion if maybe only the weak form of market efficiency

may hold.

The strong form of market efficiency is defined as including all publicly and

privately available information. If this form of market efficiency held true one

could in no circumstances make abnormal profits by using either of the three

above mentioned sources of information.

Market efficiency is of importance to CAPM, because one of its underlying

assumptions is the competitive investor. This means that prices of securities are

in equilibrium and the expected security return tomorrow based on the

information today will be zero. Security price changes are assumed to follow a

random walk, as positive "surprises" are assumed to be as likely as negative

"surprises". If a pattern can be found to detect mispriced securities on a

systematic basis, it would mean that returns are not random walk any more and

that CAPM would not hold and therefore evaluation measures based on CAPM

would be inaccurate.

The paradox that arises with the efficient markets hypothesis is that if there aren't

investors that do not believe in the efficient market hypothesis, efficient markets

can not exist. If information is free for all participants in the market than none of


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the participants has an incentive to gather information. But if no one gathers

information, the market price can not reflect the information. This problem can be

overcome if the cost of gathering information (supporting a squad of analysts) is

the same as the excess return generated through their analysis.

3

The short

discussion above indicated the importance of efficient markets on portfolio

management and in the same way on its evaluation.

3


2.1.2. Return and Risk as Determinants of the Market

Return can be defined as the rate of change in the value of an asset in a defined

time interval. The mean return, which is interesting if one looks at the prices of an

investment at the beginning and the end of the investment horizon, covers

several time periods and can be measured geometrically or arithmetically. Using

geometric mean calculation is preferable when the "calculation basis" is changing

and has the additional advantage of being additive in every case. Arithmetic

mean calculation is useful when the "calculation basis" remains constant during

the observation period. Arithmetic mean computation returns the average

increase in wealth of a constant investment and does not regard reinvestments of

its proceeds. When analyzing financial time series the basis often varies and

proceeds are reinvested and thus making geometrical mean calculation more

suitable.

Risk is the uncertainty in what a security price - and in consequence the return -


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will be at a certain point in the future. Another term would be volatility. Volatility is

equal to the statistical measure of standard deviation. Generally one uses

historical volatility when introducing risk into a financial model. There is also an

alternative way to determine volatility - calculating it implicitly by using the BlackScholesFormula.

4

The Chicago board of trade provides several implied volatility

indexes for different commodity futures and options. This should help market

participants formulating their trading strategies.

The entire CAPM universe is described by risk and return where risk ischaracterized through variance. Through different combinations of risk and

return, the combination of securities with different risk - return characteristics, an

investor can reach every point on the security market line.

5

These two

determinants are positively correlated in the CAPM-world. The more risk one

takes the more "reward" he should expect. The linear relationship between

systematic risk and return is at the core of the CAPM. The graph on the next

4

HULL (1997), p. 246

5

REILLY, BROWN (1997), p. 247

page shows the relationship between risk-return and the derivation of the security

market line. The formula for the CAPM is:


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j f

[ M

] f j

E(r ) = r + E(r ) r

E(rj

) = Average expected return of security (j)

r(f) = Average risk free rate (f)

E(rM) = Average return of the market (m)

(j ) = Sensitivity of the expected return of security (j) to changes in the expected

return of the market (m)

Figure 1: Capital Market Line, Security Market Line and the linear risk return relationship

8

The relationship between beta and the expected return is known as the SML.

The slope of the line is given by (Rm-Rf), in other words the units of return over

the risk-free rate per unit of systematic risk.

This linear relationship shows that an investor can increase his expected return

by increasing the risk as according to CAPM securities with higher risk must have

a higher return in order to compensate the investor for the risk. This goes along

with the risk aversion assumption put forth in the CAPM. The question of utility

functions of investors will not be treated here but it should be mentioned that

investors are assumed to have convex indifference curves. This means that for

the more risk they take they demand an even higher return.

6

(The marginal rate

of substitution, return for risk, increases as risk increases.)


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Another important outcome of CAPM for the risk return relationship is that the

risk for which the investor can demand to be rewarded is the systematic risk of a

security as the unsystematic risk can be diversified away. This systematic risk is

reflected in a securities beta i.e. a securities co-movements with the market. The

beta reflects the systematic risk for which the investor can expected to be

rewarded for through return. Questions concerning the validity and the testability

of CAPM shall not be addressed in this work as they are of minor importance to

the central object of this work - the evaluation of portfolio management through

Sharpes' asset allocation and style analysis framework.

2.2. Portfolio Management

Portfolio management or in other words investment management is the process

by which money is managed.

7

The way portfolios are managed has severely

changed over the last 100 years. Traditionally portfolio management was strongly

based on fundamental analysis of securities or assets which were to be included

6

FISCHER (1996), p. 40 - 43

7


in the portfolio.

8

Fundamental analysis researches the capabilities of a company

to generate future cash flows. This system was by far not as elaborate in terms of


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mathematical analysis as it is performed in modern portfolio management. Also

the belief in the possibility of "beating the market" had more acceptance than

today. With the tremendous rise in the US equity market in the nineties the issue

of beating the index (e.g. S&P 500) has become more and more difficult.

9

The

controversy over the possibility to outperform the market through active portfolio

management has been reinforced.

2.2.1. Active Portfolio Management

Active portfolio management aims to beat an index by detecting securities that

are under-priced. Securities are under-priced to a certain investor who takes an

active position because his view about the future, his forecast of the securities

price in the future, differs from that of the market. This in turn implies that an

investor or portfolio manager of this sort disregards the conclusion of CAPM that

securities are priced accurately. Active portfolio management is only worthwhile if

the additional return realized through active management is higher than the cost

of maintaining the necessary staff. Costs incurred through active management

are manager fees, analyst reimbursement and higher turnover of securities held

in the portfolio. Manager fees are typically in a range from 0.2 - 1.5 % of the

assets under management.

10

Another cost an active fund is more prone of is the

potentially higher turnover of investment managers who, if not reaching their

predetermined returns, are fired quickly. Different styles and beliefs of different

managers will cause (conditioned by high "manager turnover) additional turnover


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cost. The cost of turnover depends on the size of the trade and the liquidity of a

title.

8

comp. GRAHAM (1949)

9

SORENSON, MILLER, SAMAK (1998), p. 18

10

SORENSON, MILLER, SAMAK (1998), p 1810

Size of Trade

Number of $100 $300 $500

Portfolio Universe Stocks Million MillionMillion

Salornon Smith Barney large-cap /growth 50 36 bps 53 bps 64 bps

Salomon Smith Barney large-cap/value 50 26 37 44

Salomon Smith Barney small-cap /growth 50 131 196 246

Salomon Smith Barney small-cap /value 50 113 183 239

S&P large-cap /growth 162 27 38 45

S&P large-cap/value 338 27 34 44

S&P small-cap /growth 234 136 187 226

S&P small-cap /value 366 132 189 234

Note: Costs estimated at a point in time using Salomon Smith Barney's impact-cost model.

Figure 2: Typical turnover cost for different trade sizes and different asset classes

Active managers can be categorized in three groups: market timers, sector

selectors and security selectors.

Market timers change the beta of their portfolio according to their forecast on how


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the market will do.

11

Market timers will increase the beta on their portfolio above

the beta of the market portfolio if their forecast is bullish. Securities with a higher

beta than the market will result in the higher appreciation of the specific security

than the appreciation of the market. The reverse will be true if their forecast is

bearish. There were multiple tests on market timing ability. Treynor and Mazuy

conducted the first study on market timing.

12

They found that the management of

mutual funds did not exhibit any market timing ability.

11

ELTON, GRUBER (1992), p. 708

12

TREYNOR , MAZUY (1966), p. 131 - 13611

Figure 3: Characteristic line for a mutual fund that has outguessed the market.

Mutual fund managers with market timing ability show above than average

performance through detecting when the market will be bullish and when it will be

bearish. This is essentially what the graph above shows.

Further studies on market timing abilities of mutual fund managers were

conducted, showing little evidence of successful market timing.

13

Sector Selectors increase their exposure to a certain sector when they believe it

will perform above average in the future and decrease their exposure to a sector


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when their belief is that it will under-perform. Sectors can be classified by

industries, products, or particular perceived characteristics like size, cyclical,

growth etc. The sector selection idea is very prominent in the investment

industry. Investment managers often specialize in sectors. The investor in turn

can choose from different "specialists" and from a portfolio of managers that he

13

IPPOLITO, (1993), p. 4612

considers most appropriate for his investment strategy. Sector selection

additionally exerts influence on the later on of discussed style analysis.

The third type of active manager is the security selector. Security selection is the

most traditional form of active portfolio management. By security selection the

investment manager tries to identify securities with higher expected returns than

suggested by the market. By identifying and getting exposure to them the active

manager will realize a higher than market performance if his judgment was right.

Security selection, like all active strategies, neglects the concept of equilibrium

prices on CAPM. There are numerous tests on the ability of active managers to

detect mispriced securities and through that generating excess returns. Excess

return is the return realized above the one with the same risk predicted by

CAPM. An early and notable study on the performance of mutual funds was

conducted by William Sharpe.

14

He concluded that mutual funds did not show

better performance than the Dow Jones Industrial Index and that corollary mutual

fund managers did not have stock picking ability. Jensen


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15

also conducted a

study on mutual fund performance and confirmed the findings of Sharpe. There

was positive evidence found in favor of stock picking by Grinblatt & Titman.

16

After all it remains still an open issue if stock-picking ability exists.

2.2.2. Passive Portfolio Management

Index funds have seen a remarkable rise in the past five to seven years.

17

Elton

& Gruber also aknowledged: "One of the major companies evaluating manager

performance estimated in 1989 that during the past 20 years the S&P 500 has

outperformed more than 80 % of active managers."

18

Portfolio managers who try to replicate the return pattern of a predetermined

index are said to pursue passive portfolio management. The simplest way to

14

SHARPE, (1966), p. 119 - 138

15

JENSEN, (1968), p. 389 - 416

16

GRINBLATT, TITMAN (1989), p. 393 - 416

17

SORENSON, MILLER, SAMAK (1998), p. 18


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18

ELTON, GRUBER (1992), p. 70513

follow passive portfolio management is to exactly replicate the index or

benchmark. Replicating an index can be very tricky and expensive. Replicating

the S&P 500 may still be feasible without incurring excessive cost but replicating

a Russell 3000 may almost be unfeasible due to excessive turnover cost and

little liquidity in small stocks. This highlights the tradeoff between accuracy and

turnover cost in duplicating an index for a passively managed portfolio.

There are two alternative ways to reproduce an index. By finding a

predetermined number of stock which best tracked the index historically or by

finding a set of stocks that represents all the industry segments in the portfolio in

the same portion as present in the index. A mixture of the three approaches may

very well be found as well as the benefits of the different methods can be

realized. The main benefit of exactly replicating the index is that the tracking error

will be relatively low compared to the other measures. In that sense an index

fund may hold exactly the same weight of large stocks in its fund as represented

in the index. Applying one of the alternative measures presented above,

therefore realizing the benefit of lower transaction cost can solve the problem

with small and illiquid stocks. Cash holdings caused by dividend payments and

cash inflows from investors will also make it harder to track an index due to the

different risk-return characteristics of cash compared to the index.

2.2.3. What Index to use

Portfolio performance evaluation traditionally involves the application of a

benchmark or index to which the portfolios return is compared. If indices are

used as benchmarks the method used to measure the market return needs to be


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considered. Friend, Blume and Crockett found in their study that the average

performance of an equally weighted NYSE index differed from the one obtained

when applying a value weighted NYSE index by 2.5 %. The equal weighed

NYSE index yielded 12.4 % whereas the value weighed index yielded only 9.9 %

on average.

19

The difference may be attributed to the size effect. The size effect

19

FRIEND, BLUME, CROCKETT (1970) in IPPOLITO (1993), p. 4414

or small firm effect states that small firms stocks tend to have higher returns than

large firms.

There are three commonly used weighting methods in computing a market index

the price weighting method, the value weighting method and the equal weighting

method.

A price-weighted index is computed by summing up the prices of the securities

that are included in the index and dividing them by a constant. This returns the

average price of the securities at time t and when divided by the average price at

time 0 and added to the base of the index, it will return the value of the index at

time t. In the case of stock splits, the constant is adjusted in order to reflect the

price changes due to the stock split. The prestigious Dow Jones Industrial

Average is a price weighted index.

The value weighting method is the most common. Indices like the S&P 500,

Russell 1000, Russell 3000 and the ATX are value weighted. In calculating the

index one simply takes the market value of the securities included in the index at


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time t and divides it by the market value of the securities at time 0 and adds the

value to the index base at time 0.

An equal-weighted index is calculated by multiplying the level of the index at time

t-1 with the price relatives at time t. The price relatives are calculated by dividing

the price of every single security in the index at time t by its price at t-1 and then

dividing the sum these price relatives by the number of securities included

herein. An example for an equal weighted index would be the Value Line

Composite Index.

When evaluating the performance of a portfolio and applying an index as the

benchmark one has to make sure that the return measurement method for the

index is the same as for the portfolio under evaluation. Using general market

indices as benchmarks has been criticized as being to general and not

representative for a manager's "habitat" or his style. More elaborate and15

specialized measurements of portfolio performance have been developed. They

will be introduced in the following chapters.

2.3. Traditional Measures of Performance

The foundation of these performance measures is that the return of a portfolio is

adjusted for the risk it bore over the time period under consideration. Traditionally

the adjustment was either based on the security-market-line or on the capital

market line. The security market line based performance measures are Jensen's

Alpha and the Treynor Index. Traditional capital market line based measures of

portfolio performance are the Sharpe Ratio and the RAP (Risk-Adjusted

Performance) Ratio proposed by Modigliani. Morningstar's RAR (Risk-Adjusted

Rating) falls also into this category.

2.3.1. Security-Market-Line based performance measures


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In 1965 Jack L. Treynor

20

introduced a risk-adjusted measure to rank mutual fund

performance. As a measure of risk he used the beta. Beta reflects the nondiversifiable portion ofa securities total risk and can be calculated from CAPM.

The equation is the following:

( )

( ) ( )

( )

pR p R f

TR p

=

R(p) = Average return of portfolio (p)

R(f) = Average risk free rate (f)

(p) = Sensitivity of portfolio (p) to market return changes

20

TREYNOR (1965), p. 63 - 7516

The Treynor Ratio gives the slope of the security market line. The higher the TR

the better a portfolio will rank. That can be seen if one introduces indifference

curves of a risk-averse investor. Through a greater TR higher indifference curves

of a risk-averse investor can be reached and the greater will be his utility.


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Beta

Return

r2

r1

2 1

SML1

SML2

rf

Beta

Return

r2

r1

2 1

SML1

SML2

rf

Indifference Curves

Figure 4: Relationship between TR and an investors' utility.

The second measure that uses the CAPM as the underlying concept is Jensen's

Alpha.

21

Jensen's Alpha measures the positive or negative abnormal return

relatively to the return predicted by the CAPM. With the subsequent formula the

value for Alpha can be calculated.

( p) = R( p) R( f ) + R(m) [ ] ( ) R( f ) ( p)


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R(m) = Average return of the market (m)

(p) = Sensitivity of portfolio (p) to market return changes

21

JENSEN (1968), p. 389 - 41617

Alpha represents the return differential between the return of the portfolio and the

return predicted by the CAPM adjusted for the systematic risk of portfolio (p). The

following table shows the popularity of Jensen's Alpha.

1971-75 1976-80 1981-85 1986-90 Total

Sharpe 54 63 38 36 191

Jensen 51 81 36 52 220

Total 105 144 74 88 411

Treynor-Mazuy 6 10 8 10 34

Friend II 37 31 7 5 80

Contradictory Studies* 0 11 11 21 43

Grossman-Stiglitz 0 0 78 117 195

Source: Institute for Scientific Informaion, Social Science Citation Index , annual.

*Studies by McDonald (1974), Mains (1977), Kon and Jen (1979) and Shawky (1982)

Figure 5: Citations for the SR and the Jensen Alpha and some additional studies.

The Treynor Ratio and Jensen's Alpha are related to the systematic risk

component implied by the Sharpe-Lintner Model. There are 2 problems with the

application of these two performance measures:

1) Is the systematic risk the appropriate risk measure for an investor?


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2) Does the Sharpe-Lintner Model regard all relevant information in predicting a

securities or portfolios expected return?

The answer to question 1 will depend on whether the investor holds a single

security or a portfolio of securities. In the case that he holds a portfolio of

securities the systematic risk may well be the relevant measure of risk. In the

case of holding a single security the total risk of the specific security will be the

just measure of risk.

22

The second question will be addressed in point 2.4.

22

SARPE, ALEXANDER, BAILEY (1998), p. 83518

2.3.2. Capital-market-line based performance measures

When risk-adjusted portfolio performance measures are grounded on the capitalmarket-line, therisk adjustment is accomplished by using the total risk of a

portfolio or security. The main difference to security-market-line based

performance measures is, that a capital asset pricing model is not required and

thus alleviating the problem of making assumptions concerning a certain model.

The sole measure of risk is total risk which is equivalent to the statistical measure

of standard deviation or . The two traditional measures based thereon are the

Sharpe Ratio and the RAP (Risk-Adjusted Performance) measure.

Another popular measure to rank investment funds in the United States is

Morningstar's RAR (Risk-Adjusted Rating) and as it is also based on a portfolios

total risk adjustment although using a special procedure to adjust for it, it will be

briefly described too.


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The Sharpe Ratio

23

essentially measures a portfolios average performance over

the risk-free rate per unit of total risk of the portfolio.

( )

( ) ( )

( )

p

R p R f

SR p

=



(p) = Ex post standard deviation of portfolio (p)

The Sharpe Ratio's simplicity may be of major appeal to ranking agencies. Even

the Austrian periodical "trendINVEST"

24

reports the SR although the funds are

not ranked according to it. Modigliani & Modigliani mention it to be "probably the

23

SHARPE (1966), p. 119 - 138

24


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trendINVEST (2000), p. 56 - 9019

most popular measure of risk-risk adjusted return"

25

Following SR the portfolio .

with the highest SR can be considered to be performing best.

Franco Modigliani and Leah Modigliani

26

propose a modified version of Sharpe's

measurement approach. They call the ratio they calculate RAP but it is also

referred to as M. In opposite to Sharpe who ranks funds according to the slope

of the capital market line, they lever or un-lever, depending if the sigma of the

portfolio is higher or lower than that of the market, the portfolios risk to equal the

market risk and present the resulting risk-adjusted return as the ranking variable.

This procedure produces the exact same ranking as obtained by applying the

Sharpe Ratio. They justify their approach with the argument that the average

investor who is not familiar with advanced finance techniques can easier

understand RAP. Analytically their approach is the following:

( ) ( ) ( ) ( ) *

( )

( )

( ) R p R f R f

p

m

RAP p = +


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R(f) = Average return of the risk-free rate (f)

(m) = Ex post standard deviation of market (m)

(p) = Ex post standard deviation of portfolio (p)

The relationship between SR and RAP can be shown to be the following:

RAP( p) = SR( p) * (m) + R( f )

The benefit of RAP is that it can be readily compared to the market index yield.

The portfolio with the highest value of RAP is corollary the best performing one.

25

MODIGLIANI, MODIGLIANI (1997), p. 51

26

MODIGLIANI, MODIGLIANI (1997), p. 45 - 5420

Morningstar's risk-adjusted rating (RAR) is one of the most popular ratings in the

United States.

27

In 1995 90 % of new money invested in stock funds went into

four-star or five-star ratings awarded by Morningstar. I will not pursue the exact

procedure and its implications on traditional concepts in this project as it is very

complex and lengthy and therefore may be the subject of another work. Rather I

would like to mention the paper

28

in which Sharpe analyzed RAR and summarize

his findings.


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Sharpe compared the ranking of mutual funds calculated on the basis of RAR to

the ranking obtained through calculating the excess return sharpe ratio. The

excess return sharpe ratio takes the return of a portfolio over the risk free rate

and divides it by the standard deviation differential between the risk-free rate's

standard deviation and the portfolio's standard deviation. Sharpe finds that if

funds have good average historical returns the excess return sharpe ratio ERSR

and RAR are closely related with a correlation coefficient of 0.985.

Figure 6: Correlation between Morningstar's RAR and Excess Return Sharpe Ratio (ERSR).

27

SHARPE (1998), p. 21

28

SHARPE (1998), p. 21 - 3321

He further concludes that RAR should be view as an attempt to determine a best

single fund and assumes that the investor holds only one single fund. The

findings lay out that also in the case of poor overall market performance RAR is

appropriate in determining which fund is best performing assuming an investor

holds only one fund. The weakness Sharpe specifies is that RAR fails to capture

an important property of investors preferences - the desire for portfolios that are

neither the least nor most risky available. He finally concludes that if the only

choice for a measure by which to select funds is between RAR and ERSR, the

evidence favors selecting the ERSR but he acknowledges also that a more

appropriate choice would be to use either a different measure or none at all.

2.4. Weaknesses of Traditional Measures of Performance

The main problem with traditional performance measures is the usage of a


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benchmark, especially in estimating the security market line. Whenever the

security market line is incorrectly estimated that means the market index is

inefficient, it can have severe impacts on the outcomes of the Treynor Index and

Jensen's Alpha. The incorrect positioning of the security market line can have

two reasons, neither of which is related to statistical variation:

29

1) The true risk free return is different from the risk-free return used in the

model. This problem can be caused by the circumstance that the investor

under consideration can not borrow at the assumed risk-free rate used in the

model. This problem is not only limited to the Treynor Index and Jensen

Alpha as will be explained later on.

29

ROLL (1980), p. 5 - 1222

2) A non-optimized market index has been employed that means an index

whose expected return differs from the expected return of the optimized index

appropriate for the true risk-free return.

These factors cause the security market line to be positioned incorrectly as

shown below.

Figure 7: Possible performance measurement errors due to mis-specification of the benchmark.

On the basis of these evaluations it can be seen that the Teynor Ratio and

Jensen's Alpha rate funds take on more risk relatively better compared to the

market. Lehmann and Modest

30

concluded further that the application of a


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specific factor model has major implication on the performance measures yielded

by benchmarks thus fueling the discussion over what is a proper model to

describe return characteristics of securities. At this point it becomes clear that the

relevant problem in determining performance of mutual funds is finding and

providing the correct input measures for the model and assumptions in models

about risk reflection parameters may often not be as clear cut as seeming.

The problem of defining the appropriate risk-free rate has also implications on the

Sharpe Ratio and therefore on RAP. The Sharpe ratio assesses performance in

assuming a linear relationship between total risk and excess return over the risk-

30

LEHMANN, MODEST (1987), p. 233 - 26523

free rate. If an investor has to pay higher interest rates the higher the presumed

level of risk than that will also lead to a misclassification of funds as his

investment universe compared to the benchmark differs.24

3. Alternative Measures of Portfolio Performance

Traditional measures have shown several points of concern when applied in

performance evaluation. In this chapter I will introduce alternative approaches to

determine a portfolios required return.

3.1. The Fama and French three & five Factor APT-Model

The Fama and French

31

model is built on the Arbitrage Pricing Theory Model

developed by Ross in 1976.

32


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It states that in an equilibrium market the arbitrage

portfolio must be zero or in other words an arbitrage portfolio can not exist. If this

condition did not hold market participants would sell assets whose expected

return is lower than implied by the detected common risk factors of the market

and buy assets whose expected return is higher than implied by the risk factors.

This process of arbitrage ensures equilibrium market as market participants

engage in it until there is no further possibility in making a riskless profit through

trading one security for another.

On this basis Fama and French tried to define the factors which are relevant in

predicting a securities expected return. The equation to measure a security's

expected return is given below:

i ik k

R(i) = 0

+ 1

F1

+ ... + F

R(i) = Return on security (i)

(0) = The risk-free rate or zero beta portfolio

(ik ) = Factor sensitivity of security (i) to factor (k)

F(1-k) = Factors that explain a security's return

31

FAMA, FRENCH (1993), p. 3 - 56

32

ROSS (1976), p. 341 - 36025


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Through regression analysis the factors responsible for a security's variation can

be detected. One setback of APT-model is that the model does not specify the

specific risk factors. Fama and French detected three risk factors for stock

portfolios and two risk factors for bond portfolios. The factors for stock portfolios

are

The excess return of the market over the risk free rate

The size of the firm

The book-to-market equity ratio

and for bond portfolios they are

The time to maturity

The default risk premium

Fama and French propose their findings as being useful for portfolio performance

evaluation but did not pursue it per se.

Lehmann and Modest

33

conducted an extensive study on different benchmarks.

They use the CRSP

34

equally weighted and value weighted returns to construct

the different benchmarks. The number of securities they used in the construction

of their benchmarks was 750. The fund returns were taken from 130 mutual

funds over the period of 15 years that is from January 1968 to December 1982.

They compared the Sharpe-Lintner Model's excess return predictions with the

APT-Model's excess return predictions over the above mentioned time period.

They found that the Sharpe-Lintner model produces alphas that are less negative


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and less statistically significant than the APT-Models alpha predictions. See table

below.

33

LEHMANN MODEST (1987), p. 233 - 265

34

University of Chicago Center for Research in Security Prices (It's files contain complete data onNYSE

listed stocks since July 1962)26

Values in % except for t-value(absolute)

APT-M Alpha S-L-M

Alpha

Difference APT - SLM Alpha

VWER EWAR VWER

Jan. 1968 to Dec. 1972 -4,85 -1,41 -0,15 -3,44

(Standard deviation) 3,86 4,37 4,23

(t-value) 14,33 3,68 0,40

Jan. 1973 to Dec. 1977 -5,45 -0,79 -6,32 -4,66


(t-value) 17,26 1,98 14,68

Jan. 1978 to Dec. 1982 -3,85 1,4 -3,19 -5,25


(t-value) 13,30 4,01 11,12

Figure 8: S-L-M is the Sharpe-Lintner-Model. VWER denotes the excess return when using the


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value weighted CRSP and EWAR denotes the excess return when using the equally weighted

CRSP as the benchmark. I calculated the t-value the following: (i)/((i)/130). 130 is the

number of funds they used in their study.

They found that the Sharpe-Lintner model and APT benchmarks "differ more

than they agree on the Treynor-Black benchmarks over all three periods"

35

(they

split the 15 year period in three 5-year periods). On the application of Jensen's

Alpha on the Sharpe-Lintner model benchmark they conclude that this is more

similar to no risk-adjustment at all than it is to the application on the APT

benchmark. The typical rank difference between the APT based Jensen Alpha

and no risk-adjustment was twenty two, nineteen and forty seven positions for

the three 5-year periods. In contrast, the typical rank difference between the

Sharpe-Lintner model based Jensen Alpha and no risk-adjustment are seven,

seven and twelve positions for the three 5-year periods. They conclude that

inferences about mutual fund performance are dramatically affected by the

choice between an APT model benchmark and a Sharpe-Lintner model

benchmark.

Their tests do not say anything about the basic validity of the Sharpe-Lintner

model and the APT mode. The explanation they give for the significant negative

abnormal returns is that their benchmarks, the Sharpe-Lintner model benchmark

35

LEHMANN, MODEST (1987), p. 26027

and the APT model benchmark, are possibly not mean-variance efficient. They


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further acknowledge that the APT model could explain anomalies involving

dividend yield and own variance but could not account for size-effect.

Beyond that they tested different numbers of factors in the APT-Model and found,

that between five, ten and fifteen factors the result-changes were very small. This

can be considered as support for the Fama-French APT approach using five

factors to represent market risk.

Kothari and Warner

36

conducted another study that shows the difference in

Jensen Alphas when applying the Sharpe-Lintner model and APT-Model in

defining the benchmark. Kothari and Warner built a 50 stock portfolio through

randomly drawing from the population of the NYSE/AMEX securities. They

repeated this procedure at the beginning of every month over 336 month that is

from January 1964 to December 1991. The portfolio's returns were than tracked

for 36 months. This formed the basis for their benchmark. They found that when

they compared the performance of their randomly selected stock portfolios to a

Sharpe-Lintner model benchmark their random portfolios showed a Jensen Alpha

of over 3 %. The Fama-French APT model performed better as setting a

benchmark by which it only had a Jensen Alpha of -1.2 %. These empirical

results are very similar to the ones found in Lehmann and Modest as their

average performance difference was (3.44% + 4.66% + 5.25%)/3 that is -4.45 %

(APT-M minus SL-M). They conclude that standard mutual fund performance

measures are unreliable and mis-specified.

3.2. The Grinblatt & Titman no Benchmark Model

The encountered problems with benchmarks have led to alternative approaches


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to determine a portfolio's performance. Grinblatt and Titman

37

pursued one

36

KOTHARI, WARNER (1997), p. 1 - 44

37

GRINBLATT, TITMAN (1993), p. 47 - 6828

where no benchmark is needed and thus alleviating several problems associated

with the use of a benchmark. Their analysis in turn is only applicable if the

evaluator has knowledge about the exact composition of the portfolio under

evaluation. This is in strong contrast to the portfolio performance measures

introduced earlier since they allowed portfolio performance evaluation without

apprehending a portfolio's composition.

The underlying concept of their measure, they call it the "Portfolio Change

Measure"

38

, is that an informed investor will hold securities that will have a higher

return when they are included in the portfolio than when they are not included.

Further, an informed investor will tilt his portfolio weights towards assets with

expected returns higher than average and away from assets with expected

returns lower than average. This will cause a positive covariance between

portfolio weights and the return of a security for an informed investor whereas it

should not be any covariance between portfolio weights and the return of an

asset for the uninformed investor. The way Grinblatt and Titman propose to


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measure this covariance is the following:

PCM [R w( ) w ] T

N

j

T

t

jt jt j t k

/

1 1

,

= =

=

PCM = Portfolio Change Measure

R(jt) = Return of security (j) at time (t)

w(jt) = Weight of security (j) at time (t)

w(j,t-k) = Weight of security (j) at time (t - k)

T = Number of time periods under consideration

38

GRINBLATT, TITMAN (1993), p. 5129

Under the null hypothesis of no superior information, both current and past

weights are uncorrelated with current returns and thus the PCM measure should

be indistinguishable from zero.

Potential problems with this measure can arise from the violation of the key


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assumption to this concept namely that mean returns of assets are constant over

the sample period. Portfolios that specialize in takeover targets or bankrupt

stocks will realize positive performance with this measure because they include

assets whose expected returns are higher than usual. The same holds true for

managers who are exploiting serial correlation in stock returns. One must also

keep in mind that this measure can only be applied if the evaluator knows the

exact composition of the portfolio over time, which may be the cause for its

sparse use.

Despite that the PCM approach overcomes the problems of measuring the SML

as described in 2.4.

Grinblatt and Titman applied the PCM measure on 155 mutual funds over a 10-

year time period from December 31

st

1974 to December 31

st

1984 on quarterly

holdings. On this basis they formed two portfolios, the first lagged one quarter

and the second lagged 4 quarters. These differenced weights where then

multiplied by CRSP monthly stock returns where the weights were held constant

over 3 months and therefore a time series of monthly portfolio returns was

created for the one quarter and four quarter lagged PCM. For example with the

one quarter lag, the April, May and June returns were multiplied by the difference

between the portfolio weights held on March 31

st

1975 and the weights held on


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December 31

st

1974 and so forth.

They found that for the one quarter lagged PCM measure the value was

statistically indistinguishable from zero which indicates that informed investors

can not realize the benefits of their information in one quarter. The 4 quarters

lagged PCM showed statistically significant abnormal returns indicating that

investors do have superior information and that it is revealed with a one-year lag.30

The average abnormal returns of the entire sample are about 2% per year. The

table below shows the abnormal returns for different mutual fund categories and

its level of significance.

Performance Measure

Lagged 1 Quarter Lagged 4 Quarters

No. of Mean Wilcoxon Mean Wilcoxon

Funds Performance t-statistic

a

Probability

b

Performance t_statistic

a

Probability

b

Total sample 155.37 1.47 .233 2.04 3.16* .004

Aggressive growth funds 45 . 39 .98 .475 3.40 3.55* .004

Balanced funds 10 -.48 -1.87 .057 .01 .03 .902


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Growth funds 44 .66 2.01* .017 2.41 2.94* .009

Growth-income funds 37 .14 .61 .095 .83 1.75 .107

Income funds 13 .54 1.54 .475 1.33 2.64* .002

Special purpose funds 3 -.10 -.16 .233 .21 .19 .711

Venture capital/special

situation funds 3 1.26 1.07 .812 2.661.43 .035

Fl-statistic (Abnormal performance in every category = 0)

F = 3.1438*

Prob > F = .0028c

F2-statistic (Abnormal performance across categories is equal)

F ~ 3.6590*

Prob > F = .0014

c

a) The mean over all months divided by the standard error of mean.

b) The probability that the absolute value of the Wilcoxon-Mann-Whitney Rank z-statistic isgreater than the absolute value of the

observed z-statistic under the null.

c) The probability of the F-statistic being greater than the outcome shown, tinder the nullhypothesis (Type 1 error).

*) Type I error < .05.

Figure 9: Performance estimates for 155 surviving mutual funds grouped by investment objective

categories (Return in % per year).

Grinblatt and Titman report that the PCM measure results in smaller standard

errors than approaches that use the security market line. They attribute the


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increased estimation precision to the higher correlation between their

"benchmark" (the current returns of a funds historical portfolio) and the returns of

the current portfolio than any traditional benchmark portfolio.31

Their final conclusion was that mutual funds on average achieved positive

abnormal performance during the 10-year period under estimation but that after

considering transaction cost and fund expenses the net abnormal average

performance is close to zero. They further conclude that traditional measures of

performance add noise to true performance and thus bias the measure towards

finding no performance. This is because outside evaluators are not measuring

the true performance of a fund but only the performance of some hypothetical

portfolio that is correlated with the fund instead of evaluating holdings that

correspond to each transaction. Consequently they found that managers who

performed well in one period were likely to do so in a following period thus

inferring manager skill.

3.3. The Sharpe Approach: Asset Allocation and Style

Analysis

The portfolio evaluation models described in this master's thesis does not require

the knowledge of the exact composition of the portfolio except for the Grinblatt

and Titman model described in 3.2. For an outside evaluator this is of practical

importance as it is the condition for making portfolio evaluation feasible. The

inconvenience is that the resulting portfolio measures are of general nature. In

light of that Sharpe

39

developed an "evaluation system" that reflects a higher

degree of specification and regards an investment manager's universe also


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labeled his specific "investment style". He argued that it would be more adequate

to measure an investment manager by the asset class returns he invested in

instead of comparing his return to a universal benchmark. This idea of "grouping"

funds was put forth first time by LeClair

40

Brinson, Hood and Beebower .

41

found

in their study in 1986 that the staggering part of the portfolio performance of 91

pension plans came from asset allocation. In 1988 Sharpe introduced a method

39

SHARPE (1992), p. 7 - 19

40

LeCLAIR (1974), p. 220 - 224

41

BRINSON, HOOD, BEEBOWER (1986), p. 39 - 4432

to determine a funds "effective asset mix"

42

through constrained regression

analysis and thereon he grounded his renowned paper of 1992 titled "Asset

Allocation: Management Style and Performance Measurement".

3.3.1. Determinants of the Model

The main input in Sharpe's asset class factor model is the single asset classes.

Sharpe defined certain standards that an asset class should meet in order to


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assure the usefulness of the model. This is not found to be strictly necessary, but

it is desirable for the usefulness of the model. The qualitative exigencies on an

asset class are

1. Mutually exclusive

2. Exhaustive

3. Have returns that differ

The asset class should represent a capitalization-weighted portfolio of securities

in order to mimic return variation created by different weights of asset classes in

the returns of the portfolio under evaluation. Sharpe pointed out further that asset

class returns should either have low correlations with one another or, in cases

where correlations are high, different standard deviations.

43

If independent

variables are highly correlated, as two indexes representing different approaches

to investing with the same asset class, the reliability of the estimated coefficients

in meaningfully describing the underlying relationship is very much in doubt.

44

The problem of multicollinearity can reduce the explanatory power of a model

and therefore the asset classes should show low correlation, possibly none,

following Sharpe's qualification mentioned above.

The number of asset classes Sharpe uses in his proposed model is twelve. Each

of the twelve indexes is supposed to represent a strategy that could be followed

42

SHARPE (1988), p. 59 - 69


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43

SHARPE (1992), p. 8

43

LOBOSCO, DiBARTOLOMEO (1997), p. 8033

passively and at low cost using an index fund. The possibility of investing in the

index at low cost is of importance as this is the alternative the manager is

measured against. If the benchmark we apply is not a feasible investment

alternative it will be a biased measure. The twelve classes he uses are

1. T-Bills Cash equivalents with less than 3 months to maturity. Index: Salomon

Brothers' 90-day Treasury Bill Index.

2. Intermediate-Term Government Bonds Government bonds with less than

10 years to maturity. Index: Lehman Brothers' Intermediate-Term Government

Bond Index

3. Long-Term Government Bonds Government bonds with more than 10

years to maturity. Index: Lehman Brothers' Long-Term Government Bond

Index

4. Corporate Bonds Corporate bonds with ratings at least Baa by Moody's or

BBB by Standard & Poor's. Index: Lehman Brothers' Corporate Bond Index

5. Mortgage Related Securities Mortgage-backed and related securities.

Index: Lehman Brothers' Mortgage-Backed Securities Index

6. Large-Capitalization Value Stocks Stocks in S&P 500 stock index with high

book-to-price ratios (50% of the stocks in the S&P 500 index). Index:

Sharpe/BARRA Value Stock Index

7. Large-Capitalization Growth Stocks Stocks in the S&P 500 stock index with

low book-to-price ratios (remaining 50% of the stocks in the S&P 500 index).


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Index: Sharpe/BARRA Growth Stock Index

8. Medium-Capitalization Stocks Stocks in the top 80% of capitalization in the

US equity universe after the exclusion of stocks in the S&P 500 stock index.

Index: Sharpe/BARRA Medium Capitalization Stock Index

34

9. Small-Capitalization Stocks Stocks in the bottom 20% of capitalization in

the US equity universe after the exclusion of stocks in the S&P 500 stock

index. Index: Sharpe/BARRA Small Capitalization Stock Index

10. Non-US Bonds Bonds outside the US and Canada.

Index: Salomon Brothers' Non-US Government Bond Index

11. European Stocks European and non-Japanese Pacific Basin stocks.

Index: FTA Euro-Pacific Ex Japan Index

12. Japanese Stocks Index: FTA Japan Index

Every six months the equity categories are reclassified. The S&P 500 stocks are

reviewed and if the change in book-to-price ratios implies a change in the

classification, for example a stock that falls from the top 50% (relatively high

book-to-price ratio) into the bottom 50% (relatively low book-to-price ratio) than

the stock is regrouped. Non-S&P stocks, stocks in the medium-cap and smallcap class, areclassified in order that 80% of these stocks are in the medium-cap

class and 20% in the small-cap class. To avoid excessive turnover in the

composition of these indexes of relatively illiquid stocks and an associated high

cost for index tracking, any stock that has "recently crossed over the line"

45

a

relatively small distance is allowed to remain in its former index. A relatively small


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distance is defined with 20% within the boundary value. The remaining eight

asset classes are self-explanatory all together the twelve asset classes were

constructed to cover the investment universe from which portfolio managers

chose their assets.

The explained variables will be the individual fund returns, which can be

observed in newspapers or bought from specialized research companies.

45

SHARPE (1992), p. 935

3.3.2. The Procedure

After asset classes have been defined and the desir

46610934 evaluation of portfolio performance

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