Introduction to risk, return, and the opportunity

cost of capital

So, don't ask me no questions And I won't tell you no lies So, don't ask me about my business And I won't tell you goodbye - Rossington, VanZant

Stock market indexes

DOW JONES INDUSTRIAL AVERAGE (The Dow)

Value of a portfolio holding one share

in each of 30 large industrial firms.

STANDARD & POOR'S COMPOSITE INDEX (The S&P 500)

Value of a portfolio holding shares in 500

major firms. Holdings are proportional to

the number of shares in issue.

$0.10

$1.00

$10.00

$100.00

$1,000.00

$10,000.00

$100,000.00

Large Company StocksSmall Company StocksGovernment BondsTreasury BillsInflation

Stocks, Bonds, Bills, and Inflation

Hypothetical value of $1 invested at year-end 1925. Assumes reinvestment of income and no transaction costs or taxesThis is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2010. Copyright © 2010 Ibbotson Associates, Inc.

1925 - 2009

AverageReturn

EndingWealth

1925

1935

1945

1955

1965

1975

1985

1995

2009

$12,233$2,587

$84.39 $20.53$12.14

Volatility of Stock and Bond Returns1926 - 2006

Mon

thly

Ret

urns

Monthly returns in percent from 1926-2006.This is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2006. Copyright © 2006 Ibbotson Associates, Inc..

Stocks

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

1926 1946 1966 1986 2006

Bonds

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

1926 1946 1966 1986 2006

Rates of Return 1926-2009

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

Common Stocks

Long T-Bonds

T-Bills

Year

Per

cent

age

Ret

urn

Stocks, Bonds, Bills, and Inflation

CompoundAnnualReturn

ArithmeticAnnualReturn

Risk(StandardDeviation)

*The 1933 Small Company Stock total return was 142.9%.This is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2010. Copyright © 2010 Ibbotson Associates, Inc.

Summary Statistics 1926 - 2009

Distribution of Annual Returns

LargeCompanyStocks

9.66% 11.8% 20.5%

Small CompanyStocks

*11.7% 16.5% 33.0%

GovernmentBonds 5.7% 6.1% 9.4%

Inflation 2.9% 3.1% 4.2%

Treasury Bills 3.7% 3.8% 3.1%

Large Company Stocks Histogram1926-2009

Source: Ibbotson Associates 2010

Risk Premiums 1926-2009 Average Risk Portfolio Premium

Small-firm stocks 12.24%

Common stocks 7.71 (S&P 500)

Long-term govt 2.22bonds

Treasury bills 0

Average Market Risk Premia (by country)Risk premium, %

Country

Expected return on market portfolio(= expected return on average-risk US

stock)

current expectedrm = interest + market risk rate (rf) premium

If expected risk premium = long-run average*

rm = interest rate (rf) + 7.71%*

* Note: This can change a little bit from year to year.

Risk and Return

• Expected ReturnPrefer more to less.

• Variance and Standard Deviation (Risk)Prefer less to more.

Measuring Risk

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

Standard Deviation – square root of variance.

Calculating standard deviation of returns

Deviation Rate of from Squared Year return average deviation

1988 16.8 .1 .01

1989 31.5 14.8 219.04

1990 - 3.2 -19.9 396.01

1991 30.6 13.9 193.21

1992 7.7 - 9.0 81.0

Total 83.4 889.27

Average rate of return = 83.4/5 = 16.68 = 16.7

Variance = average of squared deviations = 889.27/5 = 177.854

Std deviation = square root of variance = 177.854 = 13.34%

Calculating variance and standard deviation

of Merck returns from past monthly data Deviation from mean Squared Month Return return deviation

1 5.4% 2.6% 6.76 2 1.7 - 1.1 1.21 3 - 3.6 - 6.4 40.96 4 13.6 10.8 116.64 5 - 3.5 - 6.3 39.69 6 3.2 0.4 0.16

Total 16.8 205.41

Mean: 16.8/6 = 2.8% Variance: 205.41/6 = 34.235 Std dev: Sq root of 34.235 = 5.85% per month

Total risk (standard deviation)for common stocks, 1989 -

1994

Standard StandardStock deviation Stock deviation

AT&T 21.4% Exxon 12.1%

Biogen 51.5 Ford Motor 28.0

Bristol-Myers Squibb 18.6 General Electric 19.6

Coca Cola 21.6 McDonald’s 21.7

Compaq 43.5 Microsoft 53.6

Risk and Diversification

Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.

Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”

Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

Diversification eliminates unique risk

deviationstandardPortfolio

Unique risk

Market risk

Number ofsecurities

5 10

Number of Randomly Selected Assets in Portfolio

Ris

kReduction of Portfolio Risk

Risk is measured by standard deviation.This is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2000. Copyright © 2000 Ibbotson Associates, Inc.

0%

5%

10%

15%

20%

25%

30%

35%

40%

1 2 3 4 5 6 7 8

Stock Diversification

1 2 4 6 8 16 30 50 100 1000Number of Stocks in Portfolio

Ris

k

Market Risk

Diversifiable Risk

This is for illustrative purposes only and not indicative of any investment.

Past performance is no guarantee of future results. 3/1/2000. Copyright © 2000 Ibbotson Associates, Inc.

Where do Diversification Benefits Come from?

• Concepts of Correlation and Covariance

• Expected Return on portfolio

• Standard Deviation of Portfolio Returns

Portfolio Risk and Return

)rx()r(x Return Portfolio Expected 2211

)σσρxx(2σxσxVariance Portfolio 21122122

22

21

21

Portfolio ReturnExample

Suppose you invest 60% of your portfolio in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The expected return on your portfolio is:

%12)1540(.)1060(. ReturnExpected

Portfolio RiskExample

Suppose you invest 60% of your portfolio in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The standard deviation of their annualized daily returns are 19.8% and 29.7%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.

% 23.8 5.564 Deviation Standard

5.56419.8x29.7)2(.40x.60x

]x(29.7)[(.40)

]x(19.8)[(.60) Variance Portfolio22

22

To calculate portfolio variance add up the boxes The shaded boxes contain variance terms; the

remainder contain covariance terms.

1

2

3

4

5

6

N

1 2 3 4 5 6 NSTOCK

STOCK

Beta and Unique RiskMarket Portfolio - Portfolio of all assets in the

economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.

How can we measure exposure to market risk?

Beta - Sensitivity of a stock’s return to the return on the market portfolio. Beta is a measure of sensitivity to market movements.

Beta Computation

2m

imiB

Covariance with the market

Variance of the market

Beta

(1) (2) (3) (4) (5) (6) (7)Product of

Deviation Squared deviationsDeviation from average deviation from average

Market Anchovy Q from average Anchovy Q from average returnsMonth return return market return return market return (cols 4 x 5)

1 -8% -11% -10% -13% 100 1302 4 8 2 6 4 123 12 19 10 17 100 1704 -6 -13 -8 -15 64 1205 2 3 0 1 0 06 8 6 6 4 36 24

Average 2 2 Total 304 456

Variance = σm2 = 304/6 = 50.67

Covariance = σim = 456/6 = 76

Beta (β) = σim/σm2 = 76/50.67 = 1.5

Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of

the variance to the covariance (i.e., β = σim/σm2)

Market risk (beta) for common stocks1994

Stock Beta Stock Beta

AT&T .92 Exxon .51Biogen 2.20 Ford Motor Co. 1.12Bristol Myers Squibb .97 General Electric 1.22Coca Cola 1.12 McDonald’s 1.07Compaq 1.18 Microsoft 1.23

Market risk (beta) for common stocks2010*

Stock Beta Stock Beta

AT&T .63 Exxon .39Biogen .68 Ford Motor Co. 2.79Bristol Myers Squibb .59 General Electric 1.72Coca Cola .51 McDonald’s .52Hewlett-Packard 1.03 Microsoft 1.06

* Source: Finance.yahoo.com, which is based on 36 months of data and S&P500 as market index.

Firm Goals to Diversify?

Since diversification reduces risk, should

firms be concerned about diversification?

• Investors may diversify more easily.

• Value Additivity