corporate finance ronald f. singer fina 4330 risk and return lecture 11 fall 2010

Corporate FinanceRonald F. Singer

FINA 4330

Risk and Return Lecture 11Fall 2010

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

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.

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

Historical Returns, 1926-2005


– 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

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%

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%

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

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


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.”

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


The volatility of stocks is not constant from year to year.

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.

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.

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.

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%


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.

corporate finance ronald f. singer fina 4330 risk and return lecture 11 fall 2010

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