5.
Probability distribution of price and one-year holding period return for a 30-year
U.S. Treasury bond (which will have 29 years to maturity at year’s end):
Economy
Probability
YTM
Price
Capital
Gain
Coupon
Interest
HPR
Boom
0.20
11.0%
$
74.05
−
$25.95
$8.00
−
17.95%
Normal Growth
0.50
8.0%
$100.00
$
0.00
$8.00
8.00%
Recession
0.30
7.0%
$112.28
$12.28
$8.00
20.28%
6.
From Table 5.3, the average risk premium for large-capitalization U.S. stocks for
the period 1926-2005 was: (12.15%
−
3.75%) = 8.40% per year
Adding 8.40% to the 6% risk-free interest rate, the expected annual HPR for the
S&P 500 stock portfolio is: 6.00% + 8.40% = 14.40%

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7.
The average rates of return and standard deviations are quite different in the sub
periods:
STOCKS
Mean
Standard
Deviation
Skewness
Kurtosis
1926 – 2005
12.15%
20.26%
-0.3605
-0.0673
1976 – 2005
13.85%
15.68%
-0.4575
-0.6489
1926 – 1941
6.39%
30.33%
-0.0022
-1.0716
BONDS
Mean
Standard
Deviation
Skewness
Kurtosis
1926 – 2005
5.68%
8.09%
0.9903
1.6314
1976 – 2005
9.57%
10.32%
0.3772
-0.0329
1926 – 1941
4.42%
4.32%
-0.5036
0.5034
The most relevant statistics to use for projecting into the future would seem to be
the statistics estimated over the period 1976-2005, because this later period seems
to have been a different economic regime.
After 1955, the U.S. economy entered
the Keynesian era, when the Federal government actively attempted to stabilize the
economy and to prevent extremes in boom and bust cycles.
Note that the standard
deviation of stock returns has decreased substantially in the later period while the
standard deviation of bond returns has increased.
8.
a
%
88
.
5
0588
.
0
70
.
1
70
.
0
80
.
0
i
1
i
R
1
i
1
R
1
r
=
=
−
=
+
−
=
−
+
+
=
b.
r
≈
R
−
i = 80%
−
70% = 10%
Clearly, the approximation gives a real HPR that is too high.
9.
From Table 5.2, the average real rate on T-bills has been: 0.72%
a.
T-bills: 0.72% real rate + 3% inflation = 3.72%
b.
Expected return on large stocks:
3.72% T-bill rate + 8.40% historical risk premium = 12.12%
c.
The risk premium on stocks remains unchanged.
A premium, the difference
between two rates, is a real value, unaffected by inflation.

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