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Capital Market Theory
Return & Risk Calculations, Risk
Premiums, and Historical Averages
Returns
Dollar Returns have 2 components:
Income Component: Direct cash payments (e.g.,
dividends or interest)
Price Change: Capital gain or loss
• Whether realized or unrealized, capital gain/loss is
always part of the total return
Percentage Return:
Dividend yield % + Capital gains yield %
Rt = Dt+1/Pt
+
(Pt+1 - Pt)/Pt
Chhachhi/519/Ch. 9
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Average and Holding Period
Returns
Average or Mean returns: Rt /T
Arithmetic mean; Intuitive
Average annual return for 1991 - 2003:13.53%
Holding period returns:
[(1+R1) * (1+R2) * (1+R3) *…. * (1+RT)] - 1
HPR1991 - 2003 = 4.32175 -1 = 332.175%
$100,000 invested on 1/1/91 would have
grown to $432,175 on 12/31/03
Chhachhi/519/Ch. 9
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Geometric Mean Returns
Geometric Mean returns (superior):
[(1+R1) *(1+R2) *(1+R3) *…. * (1+RT)](1/T) - 1
G.M.1991 - 2003 = (4.32175)1/13 -1=11.92%
HPR1991 - 1999 = 5.48006 -1 = 448.01%
$100,000 invested on 1/1/91 would have
grown to $548,006 on 12/31/99
G.M.1991 - 1999 = (5.48006)1/9 -1=20.81%
Chhachhi/519/Ch. 9
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Risk
Variance = s2 = (Rt - R)2/(T-1)
Variance1991-2003 = 0.0475
S.D.1991-2003 = 0.2179
Normal distribution
Chhachhi/519/Ch. 9
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Average Returns and Risk
Premiums (Historical)
Risk Premium = excess return =
return on an asset - risk-free return
Real Return = Nominal Return (GM) Inflation
99 years of investing in T-Bills (@0.7%) to
double one’s REAL wealth
Only 9.6 years (@7.5%)of stock investment
Chhachhi/519/Ch. 9
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The Future Value of an Investment
of $1 in 1925
$1,775.34
1000
$59.70
$17.48
10
Common Stocks
Long T-Bonds
T-Bills
0.1
1930
1940
1950
1960
1970
1980
1990
2000
Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
Chhachhi/519/Ch. 9
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The Future Value of an Investment
of $1 in 1926
$1 (1  r1926 )  (1  r1927 )  (1  r1999 )  $2,845.63
1000
$40.22
$15.64
10
Common Stocks
Long T-Bonds
T-Bills
0.1
1930
1940
1950
1960
1970
1980
1990
2000
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
Chhachhi/519/Ch. 9
8
Historical Returns, 1926-2002
Series
Average
Annual Return
Standard
Deviation
Large Company Stocks
12.2%
20.5%
Small Company Stocks
16.9
33.2
Long-Term Corporate Bonds
6.2
8.7
Long-Term Government Bonds
5.8
9.4
U.S. Treasury Bills
3.8
3.2
Inflation
3.1
4.4
– 90%
Distribution
0%
+ 90%
Source: © Stocks, Bonds, Bills, and Inflation 2003 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
Chhachhi/519/Ch. 9
9
Historical Returns, 1926-1999
Series
Average
Annual Return
Standard
Deviation
Large Company Stocks
13.0%
20.3%
Small Company Stocks
17.7
33.9
Long-Term Corporate Bonds
6.1
8.7
Long-Term Government Bonds
5.6
9.2
U.S. Treasury Bills
3.8
3.2
Inflation
3.2
4.5
– 90%
Distribution
0%
+ 90%
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
Chhachhi/519/Ch. 9
10
The Risk-Return Tradeoff
18%
Small-Company Stocks
Annual Return Average
16%
14%
Large-Company Stocks
12%
10%
8%
6%
T-Bonds
4%
T-Bills
2%
0%
5%
10%
15%
20%
25%
30%
35%
Annual Return Standard Deviation
Chhachhi/519/Ch. 9
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Rates of Return 1926-2002
60
40
20
0
-20
Common Stocks
Long T-Bonds
T-Bills
-40
-60 26
30
35
40
45
50
55
60
65
70
75
80
85
90
95 2000
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
Chhachhi/519/Ch. 9
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Stock Market Volatility
60
50
The volatility of stocks is not constant from year to year.
40
30
20
10
19
26
19
35
19
40
19
45
19
50
19
55
19
60
19
65
19
70
19
75
19
80
19
85
19
90
19
95
19
98
0
Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by
Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
Chhachhi/519/Ch. 9
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Small-Cap Effect?
$1
1926-1996
excluding 1974-1983
Large
$1,370
$368
Small
$3,990
$263
Is the whole “small-cap” effect a result of a
“freakish” 9-year period?
What about risk of small-caps??
Can you eliminate that by diversification?
H.W. 2, 4, 6-9, 12, 14, 16, 19
Chhachhi/519/Ch. 9
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