Chapter Nineteen
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.
1
Chapter Nineteen
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
Portfolio: [(1.05)(1.0)(.9367)(1.12)(1.0567)].2 - 1 = .0308
2
Chapter Nineteen
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)
Sigma
(unoptioned)
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.
3
Chapter Nineteen
9. a.
Date
Description
$ Amount
Price
January 1
January 3
February 1
March 1
March23
April 3
May 1
June 1
July 3
August 1
Balance fwd
purchase
purchase
purchase
liquidation
purchase
purchase
purchase
purchase
purchase
$300
$300
$300
$5000
$300
$300
$300
$300
$300
$7.00
$7.00
$7.91
$7.84
$8.13
$8.34
$9.00
$9.74
$9.24
$9.84
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
Shares
42.857
37.927
38.265
615.00635.971
33.333
30.801
32.468
30.488
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.
4