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10-1
McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Chapter Outline
10.1 Returns
10.2 Holding-Period Returns
10.3 Return Statistics
10.4 Average Stock Returns and Risk-Free Returns
10.5 Risk Statistics
10.6 Summary and Conclusions
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
10.1 Returns
• Dollar Returns– the sum of the cash received and
the change in value of the asset, in dollars.
Time 0 1
Initial investment
Ending market value
Dividends
•Percentage Returns
– the sum of the cash received and the change in value of the asset divided by the original investment.
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Dollar Return = Dividend + Change in Market Value
10.1 Returns
yield gains capitalyield dividend
uemarket val beginning
uemarket valin change dividend
uemarket val beginning
returndollar return percentage
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
10.1 Returns: Example
• Dollar Returns– $520 gain
Time 0 1
-$2,500
$3,000
$20
•Percentage Returns
500,2$
520$%8.20
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Holding Period Return: Example
• Suppose your investment provides the following returns over a four-year period:
Year Return
1 10%2 -5%3 20%4 15% %21.444421.
1)15.1()20.1()95(.)10.1(
1)1()1()1()1(
return period holdingYour
4321
rrrr
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Holding Period Return: Example
• An investor who held this investment would have actually realized an annual return of 9.58%:
Year Return
1 10%2 -5%3 20%4 15% %58.9095844.
1)15.1()20.1()95(.)10.1(
)1()1()1()1()1(
return average Geometric
4
43214
g
g
r
rrrrr
• So, our investor made 9.58% on his money for four years, realizing a holding period return of 44.21%
4)095844.1(4421.1
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Holding Period Return: Example
• Note that the geometric average is not the same thing as the arithmetic average:
Year Return
1 10%2 -5%3 20%4 15%
%104
%15%20%5%104
return average Arithmetic 4321
rrrr
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
0.1
10
1000
1957 1962 1967 1972 1977 1982 1987 1992 1997 2002
The Future Value of an Investment of $1 in 1957
$42.91
$20.69
17.86$)1()1()1(1$ 200319581957 rrr
Common StocksLong BondsT-Bills
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
10.3 Return Statistics
• The history of capital market returns can be summarized by describing the
– average return
– the standard deviation of those returns
– the frequency distribution of the returns.
T
RRR T )( 1
1
)()()( 222
21
T
RRRRRRVARSD T
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Average Standard Investment Annual Return Deviation Distribution
Canadian common stocks 10.64% 16.41%
Long Bonds 8.96 10.36
Treasury Bills 6.80 4.11
Inflation 4.29 3.63
Historical Returns, 1957-2003
– 60% + 60%0%
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
10.4 Average Stock Returns and Risk-Free Returns
• The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk.
• One of the most significant observations of stock and bond market data is this long-run excess of security return over the risk-free return.
– The average excess return from Canadian large-company common stocks for the period 1957 through 2003 was
3.84% = 10.64% – 6.80%
– The average excess return from Canadian long-term bonds for the period 1957 through 2003 was
2.16% = 8.96% – 6.80%
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Risk Premia
• Suppose that The National Post announced that the current rate for one-year Treasury bills is 5%.
• What is the expected return on the market of Canadian large-company stocks?
• Recall that the average excess return from Canadian large-company common stocks for the period 1957 through 2003 was 3.84%
• Given a risk-free rate of 5%, we have an expected return on the market of Canadian large-company common stocks of 8.84% = 3.84% + 5%
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
0.00 5.00 10.00 15.00 20.00 25.00
Annual Return Standard Deviation
Ann
ual R
etur
n A
vera
ge
The Risk-Return Tradeoff (1957-2003)
Long Bonds
T-Bills
Large-Company Stocks
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
10.5 Risk Statistics
• There is no universally agreed-upon definition of risk.
• The measures of risk that we discuss are variance and standard deviation.
– The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time.
– Its interpretation is facilitated by a discussion of the normal distribution.
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Normal Distribution
• A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
The probability that a yearly return will fall within 16.41-percent of the mean of 10.64-percent will be approximately 2/3.
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Normal Distribution
• A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
The probability that a yearly return will fall within 32.82-percent (2×16.41) of the mean of 10.64-percent will be 0.9544.
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Normal Distribution
• A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
The probability that a yearly return will fall within 49.23-percent (3×16.41) of the mean of 10.64-percent will be 0.9974.
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McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
Normal Distribution S&P 500 Return Frequencies
0
2
5
11
16
9
1212
1
2
110
0
2
4
6
8
10
12
14
16
62%52%42%32%22%12%2%-8%-18%-28%-38%-48%-58%
Annual returns
Ret
urn
fre
qu
ency
Normal approximationMean = 12.8%Std. Dev. = 20.4%
Source: © Stocks, Bonds, Bills, and Inflation 2002 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
