Download Ch 9

9-0
Chapter Nine
Capital Market
Theory:
Corporate
Finance
Ross Westerfield Jaffe
An Overview


9
Seventh Edition
Seventh Edition
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-1
Chapter Outline
9.1
9.2
9.3
9.4
9.5
9.6
Returns
Holding-Period Returns
Return Statistics
Average Stock Returns and Risk-Free Returns
Risk Statistics
Summary and Conclusions
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-2
9.1 Returns
• Dollar Returns
– the sum of the cash received and
the change in value of the asset, in
dollars.
Dividends
Ending
market value
Time
0
Initial
investment
McGraw-Hill/Irwin
1
•Percentage Returns
–the sum of the cash received and the
change in value of the asset divided by
the original investment.
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-3
9.1 Returns
Dollar Return = Dividend + Change in Market Value
dollar return
percentage return 
beginning market val ue
dividend  change in market val ue

beginning market val ue
 dividend yield  capital gains yield
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-4
9.1 Returns: Example
• Suppose you bought 100 shares of Wal-Mart
(WMT) one year ago today at $25. Over the last
year, you received $20 in dividends (= 20 cents per
share × 100 shares). At the end of the year, the stock
sells for $30. How did you do?
• Quite well. You invested $25 × 100 = $2,500. At
the end of the year, you have stock worth $3,000
and cash dividends of $20. Your dollar gain was
$520 = $20 + ($3,000 – $2,500).
• Your percentage gain for the year is
$520
20.8% =
$2,500
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-5
9.1 Returns: Example
Dollar Return:
$520 gain
$20
$3,000
Time
0
-$2,500
McGraw-Hill/Irwin
1
Percentage Return:
$520
20.8% =
$2,500
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-6
9.2 Holding-Period Returns
• The holding period return is the return that an
investor would get when holding an investment over
a period of n years, when the return during year i is
given as ri:
holding period return 
 (1  r1 )  (1  r2 )   (1  rn )  1
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-7
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%
McGraw-Hill/Irwin
Your holding period return 
 (1  r1 )  (1  r2 )  (1  r3 )  (1  r4 )  1
 (1.10)  (.95)  (1.20)  (1.15)  1
 .4421  44.21%
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-8
Holding Period Return: Example
• An investor who held this investment would have
actually realized an annual return of 9.58%:
Year Return Geometric average return 
1
10% (1  r ) 4  (1  r )  (1  r )  (1  r )  (1  r )
g
1
2
3
4
2
-5%
4 (1.10)  (.95)  (1.20)  (1.15)  1
r

g
3
20%
4
15%  .095844  9.58%
• So, our investor made 9.58% on his money for four
years, realizing a holding period return of 44.21%
1.4421  (1.095844) 4
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-9
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%
r1  r2  r3  r4
Arithmetic average return 
4
10%  5%  20%  15%

 10%
4
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-10
Holding Period Returns
• A famous set of studies dealing with the rates of returns on
common stocks, bonds, and Treasury bills was conducted by
Roger Ibbotson and Rex Sinquefield.
• They present year-by-year historical rates of return starting
in 1926 for the following five important types of financial
instruments in the United States:
– Large-Company Common Stocks
– Small-company Common Stocks
– Long-Term Corporate Bonds
– Long-Term U.S. Government Bonds
– U.S. Treasury Bills
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-11
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.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-12
9.3 Return Statistics
• The history of capital market returns can be summarized by
describing the
– average return
( R1    RT )
R
T
– the standard deviation of those returns
( R1  R) 2  ( R2  R) 2   ( RT  R) 2
SD  VAR 
T 1
– the frequency distribution of the returns.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-13
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.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-14
9.4 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 market
data is this long-run excess of stock return over the riskfree return.
– The average excess return from large company
common stocks for the period 1926 through 1999 was
8.4% = 12.2% – 3.8%
– The average excess return from small company
common stocks for the period 1926 through 1999 was
13.2% = 16.9% – 3.8%
– The average excess return from long-term corporate
bonds for the period 1926 through 1999 was
2.4% = 6.2% – 3.8%
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-15
Risk Premia
• Suppose that The Wall Street Journal announced that the
current rate for one-year Treasury bills is 5%.
• What is the expected return on the market of small-company
stocks?
• Recall that the average excess return from small company
common stocks for the period 1926 through 1999 was 13.2%
• Given a risk-free rate of 5%, we have an expected return on
the market of small-company stocks of:
18.2% = 13.2% + 5%
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-16
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
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-17
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.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-18
Risk Premiums
• Rate of return on T-bills is essentially risk-free.
• Investing in stocks is risky, but there are
compensations.
• The difference between the return on T-bills and
stocks is the risk premium for investing in stocks.
• An old saying on Wall Street is “You can either
sleep well or eat well.”
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-19
Stock Market Volatility
60
The volatility of stocks is not constant from year to year.
50
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.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-20
9.5 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.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-21
Normal Distribution
• A large enough sample drawn from a normal distribution
looks like a bell-shaped curve.
Probability
– 3s
– 49.3%
– 2s
– 28.8%
– 1s
– 8.3%
0
12.2%
68.26%
The probability that a yearly return
will fall within 1 standard deviation
of the mean will be approximately
⅔ (67%).
+ 1s
32.7%
+ 2s
53.2%
+ 3s
73.7%
Return on
large company common
stocks
95.44%
99.74%
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-22
Normal Distribution
• The 20.1-percent standard deviation we found for
stock returns from 1926 through 1999 can now be
interpreted in the following way: if stock returns are
approximately normally distributed, the probability
that a yearly return will fall within 20.1 percent of
the mean of 13.3 percent will be approximately 2/3.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-23
Normal Distribution
S&P 500 Return Frequencies
16
16
Normal
approximation
Mean = 12.8%
Std. Dev. = 20.4%
14
12
12
11
10
9
8
6
5
Return frequency
12
4
2
1
1
2
2
1
0
0
0
-58% -48% -38% -28% -18%
-8%
2%
12%
22%
32%
42%
52%
62%
Annual returns
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.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-24
9.6 Summary and Conclusions
• This chapter presents returns for four asset classes:
– Large Company Stocks: 12.2%
– Small Company Stocks: 16.9%
– Long-Term Government Bonds: 5.8%
– Treasury Bills: 3.8%
• Stocks have outperformed bonds over most of the
twentieth century, although stocks have also
exhibited more risk.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
9-25
9.6 Summary and Conclusions
• The stocks of small companies have outperformed
the stocks of large companies over most of the
twentieth century, again with more risk.
• The statistical measures in this chapter are
necessary building blocks for the material of the
next three chapters.
McGraw-Hill/Irwin
Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.