Measuring Portfolio Manager Performance: Returns, Luck, and Ability, Study Guides, Projects, Research of Finance

Download Measuring Portfolio Manager Performance: Returns, Luck, and Ability and more Study Guides, Projects, Research Finance in PDF only on Docsity!

Department of Accounting and

Finance

M.Sc. FINANCE

PORTFOLIO

THEORY

UNIT

PORTFOLIO PERFORMANCE AND

EVALUATION

PREVIE

W Aim

The aim of this unit is to provide an introduction to the evaluation of the performance of portfolio managers, and consider how in an uncertain environment it is possible to differentiate between luck and ability in the explanation of investment performance.

Objecti ves

After completing this unit you should be able to

0 0 8 3 determine^ the^ most^ appropriate^ basis^ on^ which^ to^ assess^ investment performance over time;

0 0 8 3 differentiate between different ways of calculating a portfolio’s rate of return;

0 0 8 3 explain^ and^ assess^ the^ Sharpe,^ Modigliani/^ Modigliani,^ Treynor^ and Jensen measures of performance; and 0 0 8 3 decompose performance on the basis of Fama’s framework.

INTRODUCT

ION

If markets are completely efficient and all security prices are continuously in equilibrium there is will be no scope for any professional manager to produce superior returns. Not only will it be impossible to identify undervalued investments or bargains, but it will also be impossible to forecast market movements so as to move in and out of equities and bonds so as to enhance returns. Securities can be chosen to eliminate diversifiable risk and combined with a risk free asset so as to produce the risk‐return combination required by

an investor. This is often referred to as a passive investment policy in contrast to an active policy which relies on the skill and judgment of the investment manager. To consider the possibility that there is a role for active portfolio management requires the relaxation of the assumption that the capital market is completely efficient. Whilst it is generally recognised that it is very different to outperform the market it also tends to be accepted that markets in which information is costly cannot be fully efficient. We will proceed in this unit to develop the analysis on the basis that markets are highly but not fully efficient.

MEASURING PORTFOLIO

RETURNS

There are two ways in which returns over a number of time periods can be measured:

0 0 8 3 The^ dollar^ weighted^ rate^ of return; and

0 0 8 3 The time weighted rate of return.

The dollar weighted rate of return is simply the internal rate of return, calculated on the cash inflows and outflows. It is referred to as the dollar weighted return as the measure allows for different levels of investments in different time periods. If investment increases in a particular sub period the performance of the investment for that sub period will contribute more to the overall determination of the internal rate of return or the dollar weighted return. The time weighted

return factors less one. This gives the average compound

rate of return over the period.

Assuming that all cash flows are reinvested and there is no injection of funds following the initial investment, the geometric rate of return will be below the arithmetic rate. The periods of poor returns exert a greater influence in the geometric averaging process than they do in the arithmetic. The difference in the geometric and arithmetic average returns increases the greater the variability of returns over time. it can be demonstrated that

yG^ ≈^ y^ A

σ 2

2

Where σ 2 is the variance of average returns and returns are specified in decimal form.

The difference between the dollar and time weighted return is best examined through an illustrative example.

Table 4.1 Time Cash Outflow Cash Inflow

0 100 ‐

1 108 4 (dividend)

2 ‐ 220 (resale proceeds) + 8 (dividend)

At time zero one share is bought for 100p and this pays a dividends of 4p at the end of the initial period. By the end of the period the price of the share has increased to 108p, and the share could be sold at this price. However, the investor purchases a second share at this price. The two shares yield a dividend of 8p at the end of the second period, and are sold at a price of 110p to produce an overall cash flow of 228. The internal rate of return or yield is given by y in the following equation

(1 + y 1 )

The rate of return in the second period is given by y 2

(1 + y^2 )

(1 + y 2 )

y 2 = 0.0556 = 5.56 per cent

For the second period it is assumed that the investment constitutes two shares valued at 108p each of the start of the period. The average rate of return over the two periods is given by 0.12 plus 5.56 per cent divided by two, ie. 8.76 per cent.

The geometric average generally provides a better indication of the historical performance of investments, and their ability to contribute to the wealth creating process. On the other hand the arithmetic average will provide a better estimate of the expected rate of return for a future time period.

The dollar weighted return would appear to be the better measure of performance over the two year period. It is more closely tied to the monetary benefits generated by the investment policy. It takes into account both the productivity of investments and the level of commitment. However, it is possible that the investment or portfolio manager does not have any influence on the level of commitment. This will be the case for a pension fund manager who is expected to invest the difference between contributions received and benefits paid out. In these circumstances the time weighted return is the most appropriate basis for evaluating managers, and tends to be the most frequently employed in the appraisal of portfolio managers.

R p − RF

SD ( R p )

A superior performance is recorded when the managed portfolio outperforms the passive benchmark

R p^ −^ R^ F

SD ( R p )

Rm − RF

SD ( Rm )

This implies that any portfolio performance producing a return risk combination lying above the capital market line records a superior performance.

Figure 4.1: Sharpe’s Reward to Risk Measure

E(R)

st CML

SD(R p)

SD(R p)^ SD(R^ m)

C 2

The market portfolio offers a return of 0.67 per cent for each one per cent increase in the standard deviation of returns:

Rm − RF = .19 − 7 = 12 = 0. 7 SD ( R m ) 18 18 Now consider the three portfolios

RA −

RF

SD ( R A )

R B^ −

R F

SD ( RB )

RC^ −

RF

SD ( R C ) 25 35

Only portfolio B outperforms the benchmark provided by the capital market line

Figure 4.3: Using the Sharpe Model

R p

Ex Post CML

SD(R p)

σ B σ m σ A σ C

The Sharpe performance is most appropriate when the portfolio being evaluated constitutes the overall portfolio of the investor. However, if the portfolio is but one component of the investor’s overall portfolio the investment will not be so concerned with the portfolio’s total risk. Th e variability of this portfolio may be offset by the variability of the returns on other assets held by the investor. The relevant risk of such a portfolio is its covariance with the rest of the investor’s holdings.

The Sharpe measure ranks performance in the basis of abnormal return per unit of risk exposure rather than in terms of the absolute level of the abnormal return. This is illustrated in figure 4.

Although the absolute abnormal return on portfolio X is greater than that in portfolio Y the management of Y is deemed to outperform that of X. The slope of the portfolio line through Y is greater than that through X.

SHARPE’S ALTERNATIVE

MEASURE

Sharpe has also put forward another measure of portfolio performance. The measure first of all focuses on the difference between the average return on the portfolio under consideration and the average return on the benchmark portfolio. The average value of this differential is then divided by its standard deviation over the period being examined.

D

ie, Sharpe Alternative Measure =

σ D

D = R pt

− Rst = the differential return

in period t

R pt

= the return on the portfolio on period t

P st

= the return on the standard or benchmark portfolio in period t

D = the average value of D t

σ D = the standard deviation of D t

MODIGLIANI AND MODIGLIANI

MEASURE (M 2 )

Franco Modigliani and Leah Modigliani have proposed a modified form of the Sharpe ratio to measure portfolio performance in a way that they believe is intuitively appealing and easier to interpret than the Sharpe measure. They suggest that the risk of any portfolio can be adjusted so that it has the same risk exposure as the market portfolio. This involves the creation of a notional portfolio. The risk adjustment is achieved by

0 0 8 3 diluting the risk of a portfolio with a higher risk exposure than the market