CHAPTER 12
SOME LESSONS FROM CAPITAL MARKET HISTORY
Answers to Concepts Review and Critical Thinking Questions
1.
They all wish they had! Since they didn’t, it must have been the case that the stellar
performance was not foreseeable, at least not by most.
2.
As in the previous question, it’s easy to see after the fact that the investment was terrible, but
it probably wasn’t so easy ahead of time.
3.
No, stocks are riskier. Some investors are highly risk averse, and the extra possible return
doesn’t attract them relative to the extra risk.
4.
On average, the only return that is earned is the required return—investors buy assets with returns in
excess of the required return (positive NPV), bidding up the price and thus causing the return to fall to
the required return (zero NPV); investors sell assets with returns less than the required return
(negative NPV), driving the price lower and thus the causing the return to rise to the required return
(zero NPV).
5.
The market is not weak form efficient.
6.
Yes, historical information is also public information; weak form efficiency is a subset of semi-strong
form efficiency.
7.
Ignoring trading costs, on average, such investors merely earn what the market offers; the trades all
have zero NPV. If trading costs exist, then these investors lose by the amount of the costs.
8.
Unlike gambling, the stock market is a positive sum game; everybody can win. Also, speculators
provide liquidity to markets and thus help to promote efficiency.
9.
The EMH only says, within the bounds of increasingly strong assumptions about the information
processing of investors, that assets are fairly priced. An implication of this is that, on average, the
typical market participant cannot earn excessive profits from a particular trading strategy. However,
that does not mean that a few particular investors cannot outperform the market over a particular
investment horizon. Certain investors who do well for a period of time get a lot of attention from the
financial press, but the scores of investors who do not do well over the same period of time generally
get considerably less attention from the financial press.
10. a.
b.
c.
If the market is not weak form efficient, then this information could be acted on and a profit
earned from following the price trend. Under ii, iii, and iv, this information is fully impounded
in the current price and no abnormal profit opportunity exists.
Under ii, if the market is not semi-strong form efficient, then this information could be used to
buy the stock “cheap” before the rest of the market discovers the financial statement anomaly.
Since ii is stronger than i, both imply that a profit opportunity exists; under iii and iv, this
information is fully impounded in the current price and no profit opportunity exists.
Under iii, if the market is not strong form efficient, then this information could be used as a
profitable trading strategy, by noting the buying activity of the insiders as a signal that the stock
is underpriced or that good news is imminent. Since i and ii are weaker than iii, all three imply
that a profit opportunity exists. Under iv, this information does not signal any profit opportunity
for traders; any pertinent information the manager-insiders may have is fully reflected in the
current share price.
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Solutions to Questions and Problems
Basic
1.
R = [($51 – 62) + 1.50] / $62 = –15.32%
2.
Dividend yield = $1.50 / $62 = 2.42%; Capital gains yield = ($51 – 62) / $62 = –17.74%
3.
R = [($81 – 62) + 1.50] / $62 = 33.06%
Dividend yield = $1.50 / $62 = 2.42%; Capital gains yield = ($81 – 62) / $62 = 30.65%
4.
a. $1,100 – 1,080 + 100 = $120;
c. r = (1.1111 / 1.04) – 1 = 6.84%
5.
a. Average nominal return (Table 12.2) = 10.29%
b. Average real return = 1.1029/1.0435 – 1 = 5.69%
6.
RG = 1.0901/1.0435 – 1 = 4.47%;
7.
b. R = [($1,100 – 1,080) + 100] / $1,080 = 11.11%
N 
.16  .18  .09  .21  .02  9.60%
X   xi  N 
;
5
 i 1 
N 
.34  .07  .12  .41  .10  13.20% ;
Y   yi  N 
5
 i 1 
N
2
2
s X   xi  x   N  1
 i 1

1
.16  .096 2  .18  .096 2   .09  .096 2  .21  .096 2  .02  .096 2  .01613

5 1
1
2
.34  .132 2   .07  .132 2   .12  .132 2  .41  .132 2  .10  .132 2  .05647
sY 
5 1
s X  .01613  0.1270  12.70%; sY  .05647  0.2376  23.76%





8.
Year
1970
1971
1972
1973
1974
1975
a.
b.


Large co. stock return
– 3.57%
8.01
27.37
0.27
–25.93
18.48
24.63
T-bill return
6.89%
3.86
3.43
4.78
7.68
7.05
33.69
Risk premium
10.46%
4.15
23.94
–4.51
–33.61
11.43
–9.06
Large company stocks: average return = 24.63 / 6 = 4.105%
T-bills: average return = 33.69 / 6 = 5.615%
Large company stocks:
variance = 1/5[(–.0357 – .04105)2 + (.0801 – .04105)2 + (.2737 – .04105)2 + (.0027 – .04105)2 +
(–.2593 – .04105)2 + (.1848 – .04105)2] = 0.034777
standard deviation = (0.034777)1/2 = 0.186486 = 18.65%
T-bills:
variance = 1/5[(.0689 – .05615)2 + (.0386–.05615)2 + (.0343–.05615)2 + (.0478–.05615)2
+ (.0768 – . 05615)2 + (.0705 – . 05615)2] = 0.00033001
standard deviation = (0.00033001)1/2 = 0.018165 = 1.82%
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c.
d.
9.
a.
b.
10. a.
b.
11.
Average observed risk premium = –9.06 / 6 = –1.51%
variance = 1/5[(–.1046 + .0151)2 + (.0415 + .0151)2 + (.2394 + .0151)2 +
(–.0451 + .0151)2 + (–.3361 + .0151)2 + (.1143 + .0151)2] = 0.03933388
standard deviation = (0.03933388)1/2 = 0.1983277 = 19.83%
Before the fact, for most assets the risk premium will be positive; investors demand compensation over and above the risk-free return to invest their money in the risky asset. After the fact,
the observed risk premium can be negative if the asset’s nominal return is unexpectedly low, the
risk-free return is unexpectedly high, or if some combination of these two events occurs.
Average return =(-.08 – .13 +.05 +.16 +.32 }/5 = .064 = 6.4%
Variance = 1/4[(-.08 – .064)2 + (-.13 – .064)2 + (.05 – .064)2 + (.16 – .064)2 +
(.32 – .064)2] = 0.03333
Standard deviation = (0.03333)1/2 = 0.1825651 = 18.26%
r = (1.064/1.035) – 1 = 2.8%
RP  R – R f = .064 – .042 = 2.2%
r f = (1.042/1.035) – 1 = 0.68%; rp  r – r f = 2.8% – 0.68% = 2.12%
12. T-bill rates were highest in the early eighties. This was during a period of high inflation and is
consistent with the Fisher effect.
Intermediate
13. P1 = $90(PVIFA10%,6) + $1,000(PVIF10%,6) = $956.45
R = [($956.45 – 1,020) + 90]/$1,020 = .0259
r = (1.0259/1.042) – 1 = – 1.55%
14. Pr(R< –3.7) = Pr [Z < (-3.7 – 9.01)/10.47] = Pr [Z < -1.2139] = 0.112 approximately (from tables)
95% level: R 
 = 9.01 ± 2(10.47) = –11.93% to 29.95%
99% level: R 
 = 9.01 ± 3(10.47) = –22.40% to 40.42%
15.  = 13.31%;  = 23.05%. Doubling your money is a 100% return, so if the return distribution is
normal, z = (100 – 13.31)/23.05 = 3.76 standard deviations above the mean; this corresponds to a
probability of  0.008%, or about one year in every 1,250 years. Tripling your money would be z =
(200 – 13.31)/23.05 = 8.099 standard deviations above the mean; this corresponds to a probability that
is very close to zero. In this case, you should never expect your money to triple.
16. It is impossible to lose more than 100 percent of your investment. Therefore, return distributions are
truncated on the lower tail at –100 percent.
Challenge
17. For problems 17 and 18, Z values should be rounded to the nearest value appearing in the cumulative
normal probability table. As an alternative the Excel function =NORMSDIST can be used to provide
greater accuracy.
z = (0 – 10.29)/16.41 = –0.6271; Pr ( R ≤ 0) = 26.53%
18. a.
z1 = (10 – 9.01)/10.47 = 0.0946; Pr (R ≥ 10%) = 1 – Pr (R≤10%) = 1 – .5377 = 46.23%
z2 = (0 – 9.01)/10.47 = –0.8606; Pr (R ≤ 0) = 19.47%
b.
z3 = (10 – 6.89)/3.63 = 0.8567; Pr (R ≥ 10%) = 1 – Pr (R ≤ 10%) = 1 – .8042 = 19.58%
z4 = (0 – 6.89)/3.63 = –1.8981; Pr (R ≤ 0) = 2.88%
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c.
z5 = (–2.09 – 9.01)/10.47 = –1.0602; Pr (R ≤ –2.09%) = 14.45%
z6 = (19.11 – 6.89)/3.63 = 3.3664; Pr (R ≥ 19.11%) = 1 – Pr (R≤19.11%) = 1 – .9996 = 0.04%
380