© K. Cuthbertson and D. Nitzsche

Chapter 29

Performance of Mutual Funds

Investments

Learning Objectives

© K. Cuthbertson and D. Nitzsche

To explain how we assess risk-adjusted performance of mutual funds using funds alpha

To examine the historic performance of mutual funds

To examine whether it is possible to pick groups of funds that earn positive abnormal return in the future

To examine whether investors put money in into funds that do well and withdraw from funds that do perform badly

A Lesson from a Few Mutual Funds

3

The two key points with performance evaluation: The arithmetic mean is not a useful statistic in

evaluatingConsider the historical returns of two mutual

funds on the following slide

4

A Lesson from a Few Mutual Funds (cont’d)

23.5%

30.7

6.5

16.9

26.3

14.3

37.8

12.0

Mutual Shares

19.3%

19.3

–34.6

–16.3

–20.1

–58.7

9.2

6.9

44 Wall Street

Mean

1988

1987

1986

1985

1984

1983

1982

Year

8.7-23.61981

19.036.11980

39.371.41979

16.132.91978

13.216.51977

63.146.51976

24.6%184.1%1975

Mutual Shares

44 Wall StreetYea

r

Change in net asset value, January 1 through December 31.

5

A Lesson from a Few Mutual Funds (cont’d)

Mutual Fund Performance

$-$20,000.00$40,000.00$60,000.00$80,000.00

$100,000.00$120,000.00$140,000.00$160,000.00$180,000.00$200,000.00

Year

En

din

g V

alu

e (

$)

44 WallStreet

MutualShares

6

A Lesson from a Few Mutual Funds (cont’d)

44 Wall Street and Mutual Shares both had good returns over the 1975 to 1988 period

Mutual Shares clearly outperforms 44 Wall Street in terms of dollar returns at the end of 1988

7

Why the Arithmetic Mean Is Often Misleading: A Review

The arithmetic mean may give misleading information e.g., a 50 percent decline in one period followed by a

50 percent increase in the next period does not produce an average return of zero

8

Why the Arithmetic Mean Is Often Misleading: A Review (cont’d)

The proper measure of average investment return over time is the geometric mean:

1/

1

1

where the return relative in period

nn

ii

i

GM R

R i

9

Traditional Performance Measures

Sharpe MeasureTreynor MeasuresJensen MeasurePerformance Measurement in Practice

10

Sharpe and Treynor Measures

The Sharpe and Treynor measures:

Sharpe measure

Treynor measure

where average return

risk-free rate

standard deviation of returns

beta

f

f

f

R R

R R

R

R

11

Sharpe and Treynor Measures (cont’d)

Example

Over the last four months, XYZ Stock had excess returns of 1.86 percent, –5.09 percent, –1.99 percent, and 1.72 percent. The standard deviation of XYZ stock returns is 3.07 percent. XYZ Stock has a beta of 1.20.

What are the Sharpe and Treynor measures for XYZ Stock?

12

Sharpe and Treynor Measures (cont’d)

Example (cont’d)

Solution: First, compute the average excess return for Stock XYZ:

1.86% 5.09% 1.99% 1.72%

40.88%

R

13

Sharpe and Treynor Measures (cont’d)

Example (cont’d)

Solution (cont’d): Next, compute the Sharpe and Treynor measures:

0.88%Sharpe measure 0.29

3.07%

0.88%Treynor measure 0.73

1.20

f

f

R R

R R

Portfolio Performance Measures:Treynor’s versus Sharpe’s Measure

Treynor versus Sharpe Measure Sharpe uses standard deviation of returns as the

measure of risk Treynor measure uses beta (systematic risk) Sharpe evaluates the portfolio manager on basis of

both rate of return performance and diversification Methods agree on rankings of completely diversified

portfolios Produce relative not absolute rankings of performance

15

Jensen Measure

The Jensen measure stems directly from the CAPM:

it ft i mt ftR R R R

16

Jensen Measure (cont’d)

The constant term should be zero Securities with a beta of zero should have an excess

return of zero according to finance theory

According to the Jensen measure, if a portfolio manager is better-than-average, the alpha of the portfolio will be positive

17

Academic Issues Regarding Performance

Measures

The use of Treynor and Jensen performance measures relies on measuring the market return and CAPM Difficult to identify and measure the return of the

market portfolioEvidence continues to accumulate that may

ultimately displace the CAPM Arbitrage pricing model, multi-factor CAPMs,

inflation-adjusted CAPM

18

Industry Issues

“Portfolio managers are hired and fired largely on the basis of realized investment returns with little regard to risk taken in achieving the returns”

Practical performance measures typically involve a comparison of the fund’s performance with that of a benchmark

19

Industry Issues (cont’d)

“Fama’s return decomposition” can be used to assess why an investment performed better or worse than expected: The return the investor chose to take The added return the manager chose to seek The return from the manager’s good selection of

securities

20

21

Industry Issues (cont’d)

Diversification is the difference between the return corresponding to the beta implied by the total risk of the portfolio and the return corresponding to its actual beta Diversifiable risk decreases as portfolio size increases,

so if the portfolio is well diversified the “diversification return” should be near zero

22

Industry Issues (cont’d)

Net selectivity measures the portion of the return from selectivity in excess of that provided by the “diversification” component