McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved. 9-0 CHAPTER 9 Capital Market Theory: An Overview

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McGraw-Hill/IrwinCorporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights

Reserved.

CHAPTER

9Capital Market

Theory: An Overview


Reserved.

Chapter Outline

9.1 Returns

9.2 Holding-Period Returns

9.3 Return Statistics

9.4 Average Stock Returns and Risk-Free Returns

9.5 Risk Statistics

9.6 Summary and Conclusions

9.1 Returns



9.4 Average Stock Returns and Risk-Free Returns

9.5 Risk Statistics


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9.1 Returns

Dollar Returnsthe sum of the cash received and the change in value of the asset, in dollars.

Dollar Returnsthe 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.


Reserved.

Dollar Return = Dividend + Change in Market Value

9.1 Returns

yield gains capitalyield dividend

uemarket val beginning

uemarket valin change dividend

uemarket val beginning

returndollar return percentage

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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

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 20.8% = $2,500$520

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9.1 Returns: Example

Dollar Return:$520 gain

Dollar Return:$520 gain

Time 0 1

-$2,500

$3,000

$20

Percentage Return:

20.8% = $2,500$520

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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:

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:

1)1()1()1(

return period holding

21

nrrr

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Holding Period Return: Example

Suppose your investment provides the following returns over a four-year period: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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So, our investor made 9.58% on his money for four years, realizing a holding period return of 44.21%So, our investor made 9.58% on his money for four years, realizing a holding period return of 44.21%


An investor who held this investment would have actually realized an annual return of 9.58%: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

4)095844.1(4421.1

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Note that the geometric average is not the same thing as the arithmetic average: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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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 StocksSmall-company Common StocksLong-Term Corporate BondsLong-Term U.S. Government BondsU.S. Treasury Bills

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 StocksSmall-company Common StocksLong-Term Corporate BondsLong-Term U.S. Government BondsU.S. Treasury Bills

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The Future Value of an Investmentof $1 in 1925

0.1

10

1000

1930 1940 1950 1960 1970 1980 1990 2000

Common StocksLong T-BondsT-Bills

$59.70

$17.48

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.

$1,775.34

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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.

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, 1926-2002


– 90% + 90%0%

Average Standard Series Annual Return Deviation Distribution

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

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9.4 Average Stock Returnsand 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 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%

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 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%

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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 13.2%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%

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 13.2%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%

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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 1926-2002

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95 2000

Common Stocks

Long T-Bonds

T-Bills


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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.”

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


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

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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.

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 DistributionA large enough sample drawn from a normal distribution looks like a bell-shaped curve.A large enough sample drawn from a normal distribution looks like a bell-shaped curve.

Probability

Return onlarge company commonstocks

99.74%

– 3 – 49.3%

– 2 – 28.8%

– 1 – 8.3%

012.2%

+ 1 32.7%

+ 2 53.2%

+ 3 73.7%

The probability that a yearly return will fall within 20.1 percent of the mean of 13.3 percent will be approximately 2/3.

68.26%

95.44%

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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.

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%


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This chapter presents returns for four asset classes:

Large Company StocksSmall Company StocksLong-Term Government BondsTreasury Bills

Stocks have outperformed bonds over most of the twentieth century, although stocks have also exhibited more risk.

This chapter presents returns for four asset classes:

Large Company StocksSmall Company StocksLong-Term Government BondsTreasury Bills

Stocks have outperformed bonds over most of the twentieth century, although stocks have also exhibited more risk.

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The stocks of small companies have outperformed the stocks of small 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.

The stocks of small companies have outperformed the stocks of small 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.

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McGraw-Hill/Irwin Corporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights Reserved. 9-0 CHAPTER 9 Capital Market Theory: An Overview