Chapter Seventeen
Performance Evaluation
KEY POINTS
Performance evaluation is a critical part of the portfolio management process, but one
that is often casually done or overlooked altogether.
Any measurement of performance should somehow tie together the return of the
investment and the riskiness of that return. The popular press very often focuses only on
return, largely ignoring risk.
The Sharpe and Treynor performance measures are classic elements of performance
evaluation, and are useful (the M2 performance measure is also presented in a portfolio
memo). They become less useful when there are additions to or withdrawals from the
portfolio. In such a case, the Daily Valuation and Modified BAI methods are appropriate
in measuring the return (an approximate method proposed by the AAII is also presented
in the text).
The presence of options in a portfolio complicates the performance evaluation process.
Two methods for comparing an optioned portfolio with an unoptioned counterpart are the
Residual Option Spread and the Incremental Rate of Return from Options.
TEACHING CONSIDERATIONS
There are two key points that must be clear to students after this discussion. First, the
performance of a portfolio cannot be determined in the absence of information about the
riskiness of the portfolio. The popular financial press routinely reports which mutual
funds “did best” by ranking them by their realized returns from the previous year. Such a
procedure ignores very real differences in volatility (and consequently investor utility)
associated with them.
The other key point is the return that counts is that which is realized from an increase in
the market value of the portfolio and from income received. A portfolio that receives a
cash inflow will show an increase in value, but not one attributable to the fund
management (this was the problem with the misrepresented return claimed by the
Beardstown ladies). Similarly, if funds are withdrawn from the portfolio, this should not
count against the manager's performance evaluation.
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Chapter Seventeen
Performance Evaluation
I recommend the 44 Wall Street & Mutual Shares comparison discussed in the chapter.
This is an effective case study showing the additional information provided by volatility
information.
ANSWERS TO QUESTIONS
1. Risk, by definition, is the chance of loss. A risky situation involves an uncertain
outcome, and some possible outcomes are adverse. Repeated draws from the
probability distribution will periodically result in the selection of an adverse outcome.
It is important to know something about the distribution before choosing to draw one.
Because you were lucky once does not mean you will be again.
2. Investors like return and dislike risk. Utility comes from getting more return and
reducing risk. Securities are priced to provide a level of return consistent with their
perceived level of risk. Over the long term, a portfolio of risky securities should earn
a higher return than a safer portfolio. Some portfolio components, however, probably
will be losers. Risk-adjusted performance measurement seeks to associate a measure
of the likelihood of loss with the return statistic.
3. Investors do not like risk. Everything else being equal, they prefer the least risky
alternative.
4. You would want to know how long it took to double, and what its interim price
behavior looked like. It also would be useful to compare the security to the return
and risk of a market index over the same period.
5. Examples include legal lists of eligible investments, regulatory constraints, special
tax incentives/disincentives, and statutory restrictions (the state of Indiana, for
instance, once disallowed any common stock investments in its retirement fund).
6. It makes no difference. The geometric mean return is invariant to the order of the
returns.
7. a. arithmetic
b. geometric
c. geometric or arithmetic, depending on what you were going to do with the
information
8. Returns can be negative. You cannot take an even root of a negative number, and if
you have an odd number of negative returns the geometric mean will be an imaginary
number. Return relatives are only positive.
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Chapter Seventeen
Performance Evaluation
9. When looking at a single security, it is best to use the Treynor measure, as the market
only rewards you for bearing systematic risk. The Treynor measure is based on beta,
which measures systematic risk.
10. Writing covered calls partially offsets changes in the value of the portfolio either up
or down. This attenuates the volatility of the portfolio.
ANSWERS TO PROBLEMS
1. x a  .026
 a  .0459
SH a 
.026  .03
 -.087
.0459
x b  .032
 b  .0462
SH b 
.032  .03
 .0433
.0462
x c  .040
 c  .0927
SH c 
.040  .03
 .1079
.0927
2. The annual returns of the equally weighted portfolio are 5%, 0%, -6.33%, 12%, and
5.67%. Their mean is 3.27% with a standard deviation of .0613. The Sharpe measure
is then
SH p 
.0327  .03
 .0440
.0613
Return
C
Portfolio
B
A
Risk
3. A: [(1.05)(1.0)(.95)(1.08)(1.05)].2 - 1 = .0250
B: [(1.04)(1.01)(.96)(1.10)(1.05)].2 - 1 = .0310
C: [(1.06)(.99)(.90)(1.18)(1.07)].2 - 1 = .0358
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Chapter Seventeen
Performance Evaluation
Portfolio: [(1.05)(1.0)(.9367)(1.12)(1.0567)].2 - 1 = .0308
Ranking by geometric mean:
C (best)
B
Portfolio
A (worst)
4. Using Excel, the monthly IRR is 0.0026, for an annual rate of 3.12%.
5. IRAR = (SH0 – SHu)o = (.0433 - (-.087))(.0462) = 0.0060
Return
optioned
unoptioned
benchmark
RF
Standard deviation
Sigma
(optioned)
6. IRAR = (SHo - SHu)o
= (.0433 – (-.087)).0462 = .0060
12
7.  783000  
t 1
4550
773000

0
t
(1  R)
(1  R)12
R = 0.004776 per month, or 5.73% per year.
8. Student response.
114
Sigma
(unoptioned)
Chapter Seventeen
Performance Evaluation
9. a.
Date
Description $ Amount
January 1 Balance fwd
January 3
purchase
February 1
purchase
March 1
purchase
March23
liquidation
April 3
purchase
May 1
purchase
June 1
purchase
July 3
purchase
August 1
purchase
$300
$300
$300
$5000
$300
$300
$300
$300
$300
Price
Shares
$7.00
$7.00
$7.91
$7.84
$8.13
$8.34
$9.00
$9.74
$9.24
$9.84
42.857
37.927
38.265
615.00635.971
33.333
30.801
32.468
30.488
Date
Sub Period
MVB
Cash
Flow
January 1
January 3
February 1
March 1
March23
April 3
May 1
June 1
July 3
August 1
1
2
3
4
5
6
7
8
9
$7,560.08
$7,860.08
$9,181.89
$9,400.63
$4,748.63
$5,171.01
$5,880.22
$6,663.71
$6,621.63
$300
$300
$300
-$5,000
$300
$300
$300
$300
$300
Ending
Value
$7,560.08
$7,860.08
$9,181.89
$9,400.63
$4,748.36
$5,171.01
$5,880.22
$6,663.71
$6,621.63
$7,351.61
Total
Shares
1,080.011
1,122.868
1,160.795
1,199.060
584.054
620.025
653.358
684.159
716.627
747.115
Value
$7,560.08
$7,860.08
$9,181.89
$9,400.63
$4,748.36
$5,171.01
$5,880.22
$6,663.71
$6,621.63
$7,351.61
MVE
MVE/MV
B
$7,560.08
$8,881.89
$9,100.63
$9,748.36
$4,871.01
$5,580.22
$6,363.71
$6,321.63
$7,051.61
1.0
1.130
0.991
1.037
1.026
1.079
1.082
0.949
1.065
Product of MVE/MVB values = 1.406  40.6%
b. Approximate R 
$7,351.61 - .5(-$2,600)
$8,651.61

 1.382  38.2%
$7,560.08  .5(-$2,600) $6,260.08
The daily valuation worksheet with $300/month gives precisely the same answer
as with the $100/month investment, while the approximate method produces an
answer considerably different. This illustrates that while the time-weighted rate of
return is invariant to the size of the periodic investments (and is therefore more
accurate), the approximate method is sensitive to them.
10. Student response.
115