Corporate Finance Ronald F. Singer FINA 4330 Risk and Return Lecture 11 Fall 2010.
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Transcript of Corporate Finance Ronald F. Singer FINA 4330 Risk and Return Lecture 11 Fall 2010.
![Page 1: Corporate Finance Ronald F. Singer FINA 4330 Risk and Return Lecture 11 Fall 2010.](https://reader036.fdocuments.in/reader036/viewer/2022070401/56649f1e5503460f94c3647c/html5/thumbnails/1.jpg)
Corporate FinanceRonald F. Singer
FINA 4330
Risk and Return Lecture 11Fall 2010
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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
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The Future Value of an Investment of $1 in 1926Geometric Average Return
0.1
10
1000
1930 1940 1950 1960 1970 1980 1990 2000
Common StocksLong T-BondsT-Bills
$40.22
$15.64
63.845,2$)1()1()1(1$ 199919271926 rrr
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.
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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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Historical Returns, 1926-2005
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.
– 90% + 90%0%
Arithmatic Average Standard Series Annual Return Deviation Distribution
Large Company Stocks 12.3% 20.2%
Small Company Stocks 17.4 32.9
Long-Term Corporate Bonds 6.2 8.5
Long-Term Government Bonds 5.8 9.2
U.S. Treasury Bills 3.8 3.1
Inflation 3.1 4.3
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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 risk-free return.– The average excess return from large company
common stocks for the period 1926 through 1999 was 9.2% = 13.0% – 3.8%
– The average excess return from small company common stocks for the period 1926 through 1999 was 13.9% = 17.7% – 3.8%
– The average excess return from long-term corporate bonds for the period 1926 through 1999 was 2.3% = 6.1% – 3.8%
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Risk Premia• Suppose that The Wall Street Journal announced
that the current rate for on-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 13.9%
• Given a risk-free rate of 5%, we have an expected return on the market of small-company stocks of 18.9% = 13.9% + 5%
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The Risk-Return Tradeoff
2%
4%
6%
8%
10%
12%
14%
16%
18%
0% 5% 10% 15% 20% 25% 30% 35%
Annual Return Standard Deviation
Ann
ual R
etur
n A
vera
ge
T-Bonds
T-Bills
Large-Company Stocks
Small-Company Stocks
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Rates of Return 1926-1999
-60
-40
-20
0
20
40
60
26 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Common Stocks
Long T-Bonds
T-Bills
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.
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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.”
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Stock Market Volatility
0
10
20
30
40
50
60
1926
1935
1940
1945
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
1998
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.
The volatility of stocks is not constant from year to year.
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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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Normal Distribution
• A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
Probability
Return onlarge company commonstocks
68%
95%
> 99%
– 3 – 47.9%
– 2 – 27.6%
– 1 – 7.3%
013.0%
+ 1 33.3%
+ 2 53.6%
+ 3 73.9%
the probability that a yearly return will fall within 20.1 percent of the mean of 13.3 percent will be approximately 2/3.
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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.
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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 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.
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Summary and Conclusions
• This chapter presents returns for four asset classes:– Large Company Stocks– Small Company Stocks– Long-Term Government Bonds– Treasury Bills
• Stocks have outperformed bonds over most of the twentieth century, although stocks have also exhibited more risk.
• The stocks of small companies have outperformed the stocks of small companies over most of the twentieth century, again with more risk.