Introduction to Risk

The pricing of Risky Assets

Required return depends on the risk of the investment

The Greater the risk the greater the return

Do all risks result in higher return?

Look at the history of Capital Market returns

Returns from non-financial investments have to be comparable with returns from financial investments of similar risk

What determines the required rate of return of an investment?

Market Indexes

Summarize the performance of different classes of securities

Most well known: Dow Jones Industrial Average Standard & Poor’s Composite Index

Indexes are portfolios of various stocks DJIA: 30 stocks SP500: 500 stocks

Different types of Indexes

Equally Weighted portfolios (DJIA) Each asset is represented in the portfolio by 1

share, no matter what the price of the share and the total value of the firm

If you are using 30 firms in your index, you will include a stock of each in it

Value weighted portfolios(SP500) Stocks in the portfolio are weighted by their

relative weight on the market. The bigger the company, the higher it’s weight

Market Capitalization

Total number of stocks * price of stock This is the measure of size that is used when

building value weighted portfolios.

The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

0.1

10

1000

1925 1940 1955 1970 1985 2000

S&PSmall CapCorp BondsLong BondT Bill

Inde

x

Year End

1

6402

2587

64.1

48.9

16.6

0.1

10

1000

1925 1940 1955 1970 1985 2000

S&PSmall CapCorp BondsLong BondT Bill

Source: Ibbotson Associates

Inde

x

Year End

1

660

267

6.6

5.0

1.7

Real returns

The Value of an Investment of $1 in 1926

Value in 1994 of $1 invested in 1926

$7 in 1994 had the same purchasing power as $1 in 1926.

NOMINAL REAL

1994 2000 1994 2000

SMALL CAP $2,843 $6402 $340 $660

S&P500 $811 $2587 $97 $267

CORPORATE BONDS

$38 $64.1 $4.5 $6.6

TREASURY BONDS

$26 $48.9 $3.1 $5

T-BILLS $12 $16.6 $1.5 $1.7

INFLATION $7

Risk of different Asset Classes

Security Risk

Treasury Bills Inflation Risk

Treasury Bonds + Interest Risk

Corporate Bonds + Default Risk

Common Stocks + Market Risk

+ Unsystematic Risk

Average Return 1926-1994

Average Nominal Return

Average Real Return

Average Risk Premium

Treasury bills 3.7% 0.6% 0 %

Government bonds

5.2 2.1 1.4

Corporate bonds

5.7 2.7 2.0

Common stocks

12.2 8.9 8.4

Small-firm stocks

17.4 13.9 13.7

Rates of Return 1926-2000

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 9520

00

Common Stocks

Long T-Bonds

T-Bills

Year

Per

cent

age

Ret

urn

-60

-40

-20

0

20

40

60

19

26

19

29

19

32

19

35

19

38

19

41

19

44

19

47

19

50

19

53

19

56

19

59

19

62

19

65

19

68

19

71

19

74

19

77

19

80

19

83

19

86

Year

Return %

US Stock Market

0

2

4

6

8

10

12

14

Number of

years

-50% -30% -10% 10% 30% 50%

Return, percent

Annual Market Returns in the US 1926-1994

Measuring Risk

Variance (σ2) and Standard Deviation (σ)

Average value of squared deviations from mean. A measure of volatility.

N

ii

N

ii

N

ii

RRN

RRN

RN

R

1

2

2

1

2

1

1

1

1

Deviation from mean Squared Month Return return deviation

1 5.4% 2.6% 6.8 2 1.7 - 1.1 1.2 3 - 3.6 - 6.4 41.0 4 13.6 10.8 116.6 5 - 3.5 - 6.3 39.7 6 3.2 0.4 0.2

Total 16.8 205.4

Mean: 16.8/6 = 2.8% Variance: 205.4/6 = 34.2 Standard deviation: 34.2 = 5.9% per month Annualized standard deviation 5.9 x (12) = 20.3%

Merck’s historical Mean and Standard Deviation

Average Return 1926-1994

Average Nominal Return

Average Risk Premium

Standard Deviation

Treasury bills 3.7% 0 % 3.3 %

Government bonds

5.2 1.4 8.7

Corporate bonds

5.7 2.0 8.3

Common stocks

12.2 8.4 20.2

Small-firm stocks

17.4 13.7 34.3

Brief periods of extremely high volatility

October 19, 1987, market fell 23% in one day

VARIABILITY IN STOCK MARKET RETURNS

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.

– 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

Historical returns 1926 to Today

Normal Distribution

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

Return onlarge company commonstocks

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

Probability

99.74%

– 3 – 49.3%

– 2 – 28.8%

– 1 – 8.3%

012.2%

+ 1 32.7%

+ 2 53.2%

+ 3 73.7%

68.26%

95.44%

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.

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.

Normal Distribution

Calculated over recent five-year period Firm faces changing business risks over 70-year

period Calculate monthly variance and multiply by twelve,

assuming successive monthly returns are independent Standard deviation increases with the square root of

the length of time over which it is being measured Most stocks more variable than market Diversification reduces variability

Changes in the price of different stocks are not perfectly correlated

Tend to offset each other

Variability In Returns Of Individual Stocks

PortfolioStandardDeviation

UNIQUE RISK

MARKET RISK

Number of securities5 10

Diversification Eliminates Unique Risk

MARKET RISK

Or Systematic Risk Or Undiversifiable Risk

Affects All Stocks UNIQUE RISK

Or Unsystematic Risk Or Diversifiable Risk Or Specific Risk Or Residual Risk

Affects Individual Stocks Or Small Groups Of Stocks

Unique Risk Of Different Firms Unrelated

Eliminated By Diversification

Individual Stocks Have Two Kinds Of Risk

A drug trial showing that beta blockers increase risk of cancer in older people will affect Pfizer’s stock But has no effect on shares of GM or IBM

A strike at a single GM plant will affect only GM and perhaps its suppliers and competitors

A hot summer will increase demand for air conditioners But won’t affect the demand for computers

Unique Or Unsystematic Risk

All firms affected by economy and exposed to market risk Example: surprise in rate of growth in GNP

Market risk cannot be diversified away

Market Or Systematic Risk

Risk of a well-diversified portfolio depends only

on the market or systematic risk of the securities

in the portfolio

Risk of a non- diversified portfolio depends on

the market risk and the unique risk of the

securities in the portfolio

Portfolio Risk

The market or an average stock has =1

A stock with =2 has twice as much systematic risk as the market

An investor in a high beta stock will expect to earn a higher return than an investor in a low beta stock

Systematic Risk Of A Stock Measured By Its Beta

The return on a portfolio, diversified or not, depends only on the market risk of the portfolio

The market doesn’t reward us for taking unique risks we can avoid at very little cost by diversification otherwise mutual funds would always sell at a

premium to the value of their underlying shares

Major Investors Hold Diversified Portfolios, With Little Or No Diversifiable Or Unique Risk

Market risk (beta) for common stocks1989 - 1994

Stock Beta Stock Beta

AT&T .92 Exxon .51

Biogen 2.2 Ford Motor 1.12

Bristol Myers .97 General Electric 1.22

Coca Cola 1.12 McDonald’s 1.32

Compaq 1.18 Microsoft 1.23

= 2.2

Biogen has 2.2 times as much market risk as the

market

relation between and actual returns not precise

because of biogen’s unique risk actual returns scattered about fitted line

BIOGEN

1. TOTAL RISK = DIVERSIFIABLE RISK + MARKET RISK2. MARKET RISK IS MEASURED BY BETA, THE SENSITIVITY TO MARKET CHANGES

beta

EXPECTED

RETURN

EXPECTEDMARKETRETURN

STOCK

Risk Of Individual Stocks

Diversification makes sense for investors Does it also make sense for a firm?

If diversification makes sense for the firm, each new project has to be analyzed in the context of the firm’s portfolio of existing projects

Value of the diversified portfolio of projects would be greater than the sum of the projects considered separately

No. Investors can easily diversify by holding different securities; they will not pay more for firms that diversify In countries with efficient capital markets, diversification

does not increase or decrease a firm’s value Total value of a firm is the sum of its parts

Diversification And Value Additivity

r = rf + (rm - rf)

EXPECTEDRETURN

Expectedmark

etreturn

Riskfreerate

0 .5 1.0 BETA

MARKET PORTFOLIO

Security market line

rm - rf

Rate of return on market - t-bill rate

Has averaged 8.4% over 69 years

Market risk premium

f

m Xr

r

EXPECTED RETURN

BETA1.0

X

SML and investments

Investments lying below the security market line are dominated by a mixture of the market portfolio and the riskless asset

Investments lying below the security market line are dominated by a mixture of the market portfolio and the riskless asset

= 0.92 Interest rate on t-bills rf = 6% Market risk premium rm - rf = 8.4% Expected return on AT&T

r = rf + (rm - rf)

= 6 + .92 X 8.4 = 13.7%

Expected Return On AT&T Stock At Beginning Of 1995