1

Ch 10 and Ch 11

Risk and Return

2Ch 10 and 11 Dollar return and Percentage Return Measuring Return and Risk

Historical returns and risk Expected returns and risk

Capital market history Understanding Risk

Systematic risk vs. Unsystematic risk Diversification Capital Asset pricing Model (CAPM)

Security Market Line (SML) Beta

Stock Market Efficiency

3

4Return: Capital Market History

Dollars

$10,000

$1,000

$100

$10

$1

$0.1

1925 1935 1945 1955 1965 1975

Year-end

1985 1995 1999

Small-companystocks

Large-companystocks

Inflation

Treasury bills

Long-termgovernment bonds

$6,640.79

$2,845.63

$40.22

$15.64

$9.39

6Risk: The Great Bull Market of 1982 – 1999, “Bumps Along the Way”

Period % Decline in S&P 500

Oct. 10, 1983 – July 24, 1984 -14.4%

Aug. 25, 1987 – Oct. 19, 1987 -33.2%

Oct. 21, 1987 – Oct. 26, 1987 -11.9%

Nov. 2, 1987 – Dec. 4, 1987 -12.4%

Oct. 9, 1989 – Jan. 30, 1990 -10.2%

July 16, 1990 – Oct. 11, 1990 -19.9%

Feb. 18, 1997 – Apr. 11, 1997 -9.6%

July 19, 1999 – Oct. 18, 1999 -12.1%

7

Calculating returns

Dollar return = dividend income + capital gain (or loss)

Percentage return = dividend yield + capital gains yield

where, dividend yield

= dividend income / beginning price capital gains yield

= (ending price – beginning price) / beginning price.

8Example: $ Return, % Return

-$10

$14

$1

$13

9Measuring Return and Risk

Historical return and risk Expected return and risk

10Historical returns

Example: Find the average returns and standard deviation of the stock for given four years data. Assume that at Year 0, the price was $100.

Year Actual Return Price1 15% $115.002 9% $125.353 -6% $117.834 12% $131.97

11Historical return and risk

Historical average return

r = ri / N = (15 + 9 + (-6) + 12 ) / 4 = 30 / 4= 7.5%

¯

12What is investment risk?

Typically, investment returns are not known with certainty.

Investment risk pertains to the probability of earning a return less than that expected.

The greater the chance of a return far below the expected return, the greater the risk.

Risk = volatility of returns = standard deviation of returns

13Standard Deviation: “Rolling a Dice” Suppose Michelle, Jennifer, and Christine

play at the Rolling Dice Contest. Each contestant rolls a dice four times. Michelle: 1, 6, 6, 1 Jennifer: 3, 4, 4, 3 Christine: 2, 5, 5, 2

Which contestant’s outcomes shows the highest standard deviation?

14Picturing Risk: Frequency distribution of returns on common stocks

1936 193719741930

1973196619571941

199019811977196919621953194619401939193419321929

19941993199219871984197819701960195619481947

1988198619791972197119681965196419591952194919441926

199919981996198319821976196719631961195119431942

1997199519911989198519801975195519501945193819361927

195619351928

19541933

1 12

4

12 1211

13 13

23

0-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90

Return (%)

Risk can be pictured by constructing frequency distribution. The flatter the distribution is, the greater the risk.

15Picturing Risk: Normal Distribution

-3-47.0%

-2-26.9%

-1-6.8%

013.3%

+133.4%

+253.5%

+373.6%

Probability

Return onlarge commonstocks

68%

95%>99%

High Risk

Low Risk

Suppose average return on large common stocks is 13.3%, and standard deviation of returns is 20.1%

16Normal Distribution

Of all observed values, 68.3 percent will occur within plus/minus one standard deviation of the mean

Of all observed values, 95.7 percent will occur within plus/minus one standard deviation of the mean

Of all observed values, 99.7 percent will occur within plus/minus one standard deviation of the mean

17Historical return and risk

Historical risk We measure risk by calculating

standard deviation of returns. The greater the standard deviation,

the greater the risk. Standard deviation = risk = volatility

Measuring Risk

Variance - Average value of squared deviations from mean. A measure of volatility. We square them to give equal weights to negative returns.

Standard Deviation – Standardized average value of squared deviations from mean. A measure of volatility.

19Historical return and risk

2

2

2 2 2

2

Variance, 1

(.15 .075) (.09 .075) ( .06 .075) .......

4 1.0261

3.0087

,

.0087

.0933 9.33%

ir r

N

SD

or

20Historical returns and risks of various instruments

90%

Large-companystocks 13.3% 20.1%

Small-companystocks 17.6 33.6

Long-termcorporate bonds 5.9 8.7

Long-termgovernment 5.5 9.3

Intermediate-termgovernment 5.4 5.8

U.S. Treasurybills 3.8 3.2

Inflation 3.2 4.5

-90% 0%

*

Series AverageReturn

StandardDeviation

Distribution

21Lesson from capital market history

There is a reward for bearing risk The greater the potential reward, the

greater the risk This is called the risk-return trade-off

22Risk Premium

Definition: The “extra” return earned for taking on risk

The return on Treasury bills are considered to be risk-free rate

The risk premium is the return over and above the risk-free rate

23Historical Risk Premiums

Large stocks: 13.3 – 3.8 = 9.5% Small stocks: 17.6 – 3.8 = 13.8% Long-term corporate bonds: 5.9 – 3.8 =2.1% Long-term government bonds: 5.5 – 3.8 = 1.7%

24Expected returns: Using forecasted returns with probability

A stock analyst projects the future performance of a company XYZ’s stock. A today’s price is $100.00

State of Economy Probability

Rate of Return Price

Recession 30% -13% $87.00Boom 70% 15% $115.00

25

Calculating the Expected Rate of Return

r = expected rate of return.

r = -13% (0.3) + 15% (0.7) = 6.6%

^

^

. n

1=iiiPr = r

26

Calculating Standard Deviation using Probability Distribution

2

2

1

2 2

Standard deviation

Variance

( .13 .066) .3 (.15 .066) .7

.0165

.128 12.8%

n

i ii

r r P

or

27Calculating return and risk of portfolio

A portfolio is a collection of assets An asset’s risk and return is important in how

it affects the risk and return of the portfolio The risk-return trade-off for a portfolio is

measured by the portfolio expected return and standard deviation, just as with individual assets

28Calculating return and risk of portfolio Example: Suppose you had $1 million to invest

on stocks. You bought stock A for $500,000, stock B for $250,000, and stock C for $250,000, respectively. Your brokerage firm sent the following projections on these stocks. What are the portfolio’s expected returns and standard deviations?

State of Economy Probability Stock A Stock B Stock C

Boom 0.4 10% 15% 20%Bust 0.6 8% 4% 0%

Returns

29Calculating returns and risk of portfolio Step One: Calculate the weighted average of

returns for each of given economy status Expected Return of portfolio for “Boom” Economy

= (500K/1,000K)10% + (250K/1,000K)15% + (250K/1,000K)20%

= 13.75% Expected Return of portfolio for “Bust” Economy

= 5% Step Two: Compute the expected return of

portfolio as we did for the single stock

30Calculating Return and Risk: Portfolio Case

State of Economy Probability

Rate of Return Product

Expected Return

Return Deviation from Expected

ReturnSquared Deviation Product

Boom 0.4 13.75% 0.055 8.50% 0.0525 0.002756 0.001103Bust 0.6 5.00% 0.03 8.50% -0.035 0.001225 0.000735

1 8.50% 0.0018384.29%

31Diversification Portfolio diversification is the investment in

several different asset classes or sectors Diversification can substantially reduce the variability of

returns This reduction in risk arises because worse than

expected returns from one asset are offset by better than expected returns from another

Diversification is not just holding a lot of assets For example, if you own 50 internet stocks, you are not

diversified However, if you own 50 stocks that span 20 different

industries, then you are diversified

Microsoft Excel Worksheet

32Correlation

Returns Distributions for Two Perfectly Positively Correlated Stocks (correlation = +1.0) and for Portfolio MM’

Stock M

0

15

25

-10

0

15

25

-10

Stock M’

0

15

25

-10

Portfolio MM’

33Correlation Returns Distribution for Two Perfectly Negatively

Correlated Stocks (Correlation = -1.0) and for Portfolio WM

25

15

0

-10 -10 -10

0 0

15 15

25 25

Stock W Stock M Portfolio WM

.

. .

. .

.

.

..

.. . . . .

34

Correlation

36Total Risk

Total risk can be decomposed into Unsystematic Risk Systematic Risk

37Systematic Risk

Risk factors that affect a large number of assets

Also known as non-diversifiable risk or market risk

Includes such things as changes in GDP, inflation, interest rates, etc.

38Unsystematic Risk

Risk factors that affect a limited number of assets

Also known as unique risk, asset-specific risk, diversifiable risk, and company-specific risk

Includes such things as labor strikes, part shortages, etc.

39Pop Quiz:Systematic Risk or Unsystematic Risk? The government announces that inflation

unexpectedly jumped by 2 percent last month. Systematic Risk

One of Big Widget’s major suppliers goes bankruptcy.Unsystematic Risk

The head of accounting department of Big Widget announces that the company’s current ratio has been severely deteriorating.Unsystematic Risk

Congress approves changes to the tax code that will increase the top marginal corporate tax rate.Systematic Risk

40Risk Reduction

1 49.24 1.00

2 37.36 .76

4 29.69 .60

6 26.64 .54

8 24.98 .51

10 23.93 .49

20 21.68 .44

30 20.87 .42

40 20.46 .42

50 20.20 .41

100 19.69 .40

200 19.42 .39

300 19.34 .39

400 19.29 .39

500 19.27 .39

1,000 19.21 .39

(2)Average Standard

Deviation of AnnualPortfolio Returns

(3)Ratio of Portfolio

Standard Deviation toStandard Deviationof a Single Stock

(1)Number of Stocks

in Portfolio

%

41

Risk Reduction

Average annualstandard deviation (%)

Diversifiable risk

Nondiversifiablerisk

Number of stocksin portfolio

49.2

23.9

19.2

1 10 20 30 40 1,000

42The Principle of Diversification Diversification can substantially reduce the variability

of returns This reduction in risk arises because worse than

expected returns from one asset are offset by better than expected returns from another

However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

43Diversifiable Risk

Often considered the same as unsystematic, unique or asset-specific risk

If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

Diversifiable Risk = Unsystematic Risk

44Total Risk

Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of

total risk For well diversified portfolios, unsystematic risk is

very small Consequently, the total risk for a diversified portfolio

is essentially equivalent to the systematic risk.

Conclusion: The reward for bearing risk depends only on the systematic risk of an investment.

4545

So, the important question is how to So, the important question is how to measure systematic risk of a stock (or measure systematic risk of a stock (or

portfolio)?portfolio)?

The answer is a beta.The answer is a beta. This is where Capital Asset Pricing This is where Capital Asset Pricing

Model and Security Market Line Model and Security Market Line come in.come in.

46What is a beta? (the Greek Symbol )

A beta coefficient (or a beta shortly): the amount of systematic risk present in a particular risky asset relative to that in an average risky asset.

47What does a beta tell us?

A beta of 1 implies the asset has the same systematic risk as the overall market portfolio (or average asset)

A beta < 1 implies the asset has less systematic risk than the overall market portfolio

A beta > 1 implies the asset has more systematic risk than the overall market portfolio

Note: A beta of the market portfolio (or average portfolio) is 1. Typically, we use S&P 500 Index as a proxy portfolio to represent the market portfolio.

48

Company Beta Coefficient

McDonalds .85

Gillette .90

IBM 1.00

General Motors 1.05

Microsoft 1.10

Harley-Davidson 1.20

Dell Computer 1.35

America Online 1.75

(I)

49Beta and the Risk Premium Remember

risk premium = expected return – risk-free rate The higher the beta, the greater the risk

premium should be. Can we define the relationship between the

return and beta (or risk)? YES! Capital Pricing Asset Model (CAPM)

50Capital Asset Pricing Model (CAPM)

Created by William F. Sharpe and others A Nobel Prize winner idea Widely used by Wall Street professionals Describes the relationship between return

and risk (i.e., systematic risk) A beta (the Greek symbol, β) measures

systematic risk of a stock or portfolio.

51Capital Asset Pricing Model (CAPM)

E(Ri) = Rf + (E(Rm) – Rf)i

Rf = Risk-free rate, or Treasury bill return

E(Rm) = Expected return on the market portfolio, often S & P 500 index return is used as a proxy.

i = Beta

52Security Market Line (SML)

0%

5%

10%

15%

20%

25%

30%

0 0.5 1 1.5 2 2.5 3

Beta

Exp

ecte

d R

etur

n

Rf

E(RA)

A

(E(RA) – Rf)/ A

E(Ri) = Rf + (E(Rm) – Rf)i

53Example - CAPM

Consider the betas for each of the assets given earlier. If the risk-free rate is 6.15% and the market risk premium is 9.5%, what is the expected return for each?

Security Beta Expected Return DCLK 4.03 6.15 + 4.03(9.5) = 44.435% KO 0.84 6.15 + .84(9.5) = 14.13% INTC 1.05 6.15 + 1.05(9.5) = 16.125% KEI 0.59 6.15 + .59(9.5) = 11.755%

54Example: Portfolio Betas “What if we want to invest on many stocks, instead of single stock? “ Suppose you have $1 million to invest. You allocated your

money as follows:

Stocks Allocations Beta

CIN $300,000 0.47

MOT $500,000 1.69

CAG $200,000 0.62

What is the portfolio beta?

=(0.3)(0.47)+(0.5)(1.69)+(0.2)(0.62) = 1.11

55What’s the Efficient Market Hypothesis (EMH)? Stock prices reflect new events efficiently. Therefore, securities are normally in

equilibrium and are “fairly priced.” Stock prices follows “random” process. Therefore, one cannot “beat the market”

except through good luck or inside information. If this is true, then you should not be able to

earn “abnormal” or “excess” returns consistently.

.

56Common Misconceptions about EMH

Efficient markets DO NOT imply that you can’t make money from stock market

They do imply that, on average, you will earn a return that is appropriate for the risk undertaken There is not a bias in prices that can be exploited

to earn excess returns

57What Makes Markets Efficient? There are many investors out there doing

research 100,000 or so trained analysts--MBAs, CFAs, and

PhDs--work for firms like Fidelity, Merrill, Morgan, and Prudential.

These analysts have similar access to data and megabucks to invest.

Thus, news is reflected in stock price (P0) almost instantaneously.

Therefore, prices should reflect all available public information

58

59

60

61

An Example of Diversification If you invest

individually,

Avg R of Starcents = 10%

SD of Starcents = 20%

Avg R of jPhone = 40%

SD of jPhone = 60%

If you invest collectively, i.e., investing on 50-50 portfolio,

Avg R of 50-50 P = 25%

However, it is possible that

SD of 50-50 P can be smaller than the avg of two SDs (40%) or even smaller than the smaller of two SDs (20%) !!!

62