Chapter 29
Performance of Mutual Funds
Investments
© K. Cuthbertson and D. Nitzsche
Learning Objectives
 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
© K. Cuthbertson and D. Nitzsche
A Lesson from
a Few Mutual Funds
3
 The two key points with performance evaluation:
 The arithmetic mean is not a useful statistic in evaluating
 Consider the historical returns of two mutual funds
on the following slide
A Lesson from
a Few Mutual Funds (cont’d)
4
Year
44 Wall
Street
Mutual
Shares
Year
44 Wall
Street
Mutual
Shares
1975
184.1%
24.6%
1982
6.9
12.0
1976
46.5
63.1
1983
9.2
37.8
1977
16.5
13.2
1984
–58.7
14.3
1978
32.9
16.1
1985
–20.1
26.3
1979
71.4
39.3
1986
–16.3
16.9
1980
36.1
19.0
1987
–34.6
6.5
1981
-23.6
8.7
1988
19.3
30.7
Mean
19.3%
23.5%
Change in net asset value, January 1 through December 31.
A Lesson from
a Few Mutual Funds (cont’d)
5
Ending Value ($)
Mutual Fund Performance
$200,000.00
$180,000.00
$160,000.00
$140,000.00
$120,000.00
$100,000.00
$80,000.00
$60,000.00
$40,000.00
$20,000.00
$-
44 Wall
Street
Mutual
Shares
7
19
7
8
19
0
8
19
Year
3
8
19
6
A Lesson from
a Few Mutual Funds (cont’d)
6
 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
Why the Arithmetic Mean
Is Often Misleading: A Review
7
 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
Why the Arithmetic Mean
Is Often Misleading: A Review (cont’d)
8
 The proper measure of average investment return
over time is the geometric mean:
1/ n


GM   Ri   1
 i 1 
where Ri  the return relative in period i
n
Traditional
Performance Measures
9
 Sharpe Measure
 Treynor Measures
 Jensen Measure
 Performance Measurement in Practice
Sharpe and Treynor Measures
10
 The Sharpe and Treynor measures:
Sharpe measure 
Treynor measure 
R  Rf

R  Rf

where R  average return
R f  risk-free rate
  standard deviation of returns
  beta
Sharpe and
Treynor Measures (cont’d)
11
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?
Sharpe and
Treynor Measures (cont’d)
12
Example (cont’d)
Solution: First, compute the average excess return
for Stock XYZ:
1.86%  5.09%  1.99%  1.72%
R
4
 0.88%
Sharpe and
Treynor Measures (cont’d)
13
Example (cont’d)
Solution (cont’d): Next, compute the Sharpe and
Treynor measures:
Sharpe measure 
Treynor measure 
R  Rf

R  Rf

0.88%

 0.29
3.07%
0.88%

 0.73
1.20
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
Jensen Measure
15
 The Jensen measure stems directly from the CAPM:
Rit  R ft     i  Rmt  R ft 
Jensen Measure (cont’d)
16
 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
Academic Issues
Regarding Performance
Measures
17
 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
portfolio
 Evidence continues to accumulate that may
ultimately displace the CAPM

Arbitrage pricing model, multi-factor CAPMs, inflationadjusted CAPM
Industry Issues
18
 “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
Industry Issues (cont’d)
19
 “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
Industry Issues (cont’d)
21
 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
Industry Issues (cont’d)
22
 Net selectivity measures the portion of the return
from selectivity in excess of that provided by the
“diversification” component