Chapter 11 Risk, Return, and Capital Budgeting. Topics Covered Measuring Market Risk Measuring Market Risk Portfolio Betas Portfolio Betas Risk and Return.

Chapter 11Chapter 11

Risk, Return, and Capital Risk, Return, and Capital BudgetingBudgeting

Topics CoveredTopics Covered

Measuring Market RiskMeasuring Market RiskPortfolio BetasPortfolio BetasRisk and ReturnRisk and ReturnCAPM and Expected ReturnCAPM and Expected ReturnSecurity Market LineSecurity Market LineCapital Budgeting and Project RiskCapital Budgeting and Project Risk

Chapter 11 ObjectivesChapter 11 Objectives

To be able to measure and interpret the To be able to measure and interpret the market risk, or beta of a security.market risk, or beta of a security.

To relate the market risk of a security to To relate the market risk of a security to the rate of return that investors demand the rate of return that investors demand and apply this rate to stock valuation.and apply this rate to stock valuation.

To calculate the opportunity cost of capital To calculate the opportunity cost of capital for a project.for a project.

Some risk can be diversified Some risk can be diversified away and some cannot.away and some cannot.

Market riskMarket risk (systematic risk) is (systematic risk) is nondiversifiable. This type of risk cannot nondiversifiable. This type of risk cannot be diversified away. Macroeconomic be diversified away. Macroeconomic factors that affect all companies.factors that affect all companies.

Unique riskUnique risk (unsystematic risk) is (unsystematic risk) is diversifiable. This type of risk can be diversifiable. This type of risk can be reduced through diversification. Specific reduced through diversification. Specific (microeconomic) factors that affect (microeconomic) factors that affect individual firms or industries.individual firms or industries.

As you add stocks to your portfolio, As you add stocks to your portfolio, unique risk is reduced.unique risk is reduced.

portfoliorisk

number of stocks

Market risk

uniquerisk

Note:Note:

The market compensates investors for accepting The market compensates investors for accepting risk - but only for risk - but only for market riskmarket risk. Unique risk can . Unique risk can and should be diversified away.and should be diversified away.

So - we need to be able to measure market risk. So - we need to be able to measure market risk. We use We use betabeta as a measure of market risk. as a measure of market risk.

The Concept of BetaThe Concept of Beta

Beta(Beta()) measures how the return of an individual measures how the return of an individual asset (or even a portfolio) varies with the market asset (or even a portfolio) varies with the market portfolio (a stock index like the S&P 500).portfolio (a stock index like the S&P 500).

= 1.0 : same risk as the market (average stock)= 1.0 : same risk as the market (average stock) < 1.0 : less risky than the market (defensive < 1.0 : less risky than the market (defensive

stock)stock) > 1.0 : more risky than the market (aggressive > 1.0 : more risky than the market (aggressive

stock)stock) Beta is the slope of the regression line (y = a + Beta is the slope of the regression line (y = a + x) x)

between a stock’s return(y) and the market between a stock’s return(y) and the market return(x) over time, return(x) over time, from simple linear regression. from simple linear regression.

ii = Covariance = Covariancei,mi,m/Mkt. Var. =/Mkt. Var. =imimiimm//mm22

Measuring Market RiskMeasuring Market Risk

ExampleExample - Turbo Charged Seafood has the - Turbo Charged Seafood has the following % returns on its stock, relative to following % returns on its stock, relative to the listed changes in the % return on the the listed changes in the % return on the market portfolio. The beta of Turbo market portfolio. The beta of Turbo Charged Seafood can be derived from this Charged Seafood can be derived from this information.information.

Measuring Market RiskMeasuring Market Risk

Month Market Return % Turbo Return %

1 + 1 + 0.8

2 + 1 + 1.8

3 + 1 - 0.2

4 - 1 - 1.8

5 - 1 + 0.2

6 - 1 - 0.8

ExampleExample - continued - continued

Measuring Market RiskMeasuring Market Risk

B = = 0.81.62

When the market was up 1%, Turbo average % change was +0.8%When the market was up 1%, Turbo average % change was +0.8% When the market was down 1%, Turbo average % change was -0.8% When the market was down 1%, Turbo average % change was -0.8% The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8.The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8.

Example - continued

Measuring Market RiskMeasuring Market RiskExampleExample - continued - continued

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Market Return %

Turbo return %

Portfolio BetaPortfolio Beta

The The for a portfolio of stocks is the weighted for a portfolio of stocks is the weighted average of the individual stock average of the individual stock s.s. pp = = wwjjjj

ExampleExample: What is the portfolio beta for a : What is the portfolio beta for a portfolio consisting of 40% Dell with b = 2.14, portfolio consisting of 40% Dell with b = 2.14, 30% General Electric with b = 1.18, and 30% 30% General Electric with b = 1.18, and 30% PepsiCo. with b = 0.67.PepsiCo. with b = 0.67.

Bp = .4(2.17)+.3(1.18)+.3(0.67) = 1.423Bp = .4(2.17)+.3(1.18)+.3(0.67) = 1.423

Relating Market Risk and Expected Relating Market Risk and Expected Return: the CAPMReturn: the CAPM

Here’s the word story: a stock’s expected Here’s the word story: a stock’s expected rate of return = risk-free rate + the rate of return = risk-free rate + the (stock’s) risk premium.(stock’s) risk premium.

The main assumption is investors hold The main assumption is investors hold well diversified portfolios = only concerned well diversified portfolios = only concerned with market risk. with market risk.

A stock’s risk premium = measure of A stock’s risk premium = measure of market risk X market risk premium.market risk X market risk premium.

CAPM EquationCAPM Equation

market risk premium = rmarket risk premium = rmm - r - rff

risk premium = risk premium = (r(rmm-r-rff)) r = rr = rff + + (r(rmm - r - rf f ))

Example: Example: What is Yahoo’s expected return if its b = What is Yahoo’s expected return if its b = 1.75, the current 3-mo. T-bill rate is 1%, and the 1.75, the current 3-mo. T-bill rate is 1%, and the historical market risk premium of 8% is historical market risk premium of 8% is demanded?demanded?

Yahoo k = 1% + 1.75(8%) = 15%Yahoo k = 1% + 1.75(8%) = 15%

The Security Market Line (SML)The Security Market Line (SML) A graphical representation of the CAPM equation.A graphical representation of the CAPM equation. Gives expected returns for investments with different Gives expected returns for investments with different

betas.betas. Y axis = expected return, X axis = betaY axis = expected return, X axis = beta Intercept = risk-free rate = 3-month T-bill rate (B = 0)Intercept = risk-free rate = 3-month T-bill rate (B = 0) Slope of SML = market risk premiumSlope of SML = market risk premium For the following SML graph, let’s use the current 3-For the following SML graph, let’s use the current 3-

month T-bill rate of 1% and assume investors expect a month T-bill rate of 1% and assume investors expect a market risk premium equal to the historical market risk market risk premium equal to the historical market risk premium of 8%.premium of 8%.

Graph r = 1% + B(8%)Graph r = 1% + B(8%) Expected market return (B=1) = 1+1(8%) = 9%Expected market return (B=1) = 1+1(8%) = 9%

Our SML: rOur SML: rff = 1%, r = 1%, rmm = 9% = 9%

0.00%

5.00%

10.00%

15.00%

20.00%

0 0.5 1 1.5 2 2.5

Beta

Exp

ecte

d

Ret

urn

Application of CAPM to Stock Application of CAPM to Stock ValuationValuation

Can use CAPM to calculate a stock’s Can use CAPM to calculate a stock’s expected return for valuation purposes.expected return for valuation purposes.

Also, our previous expected return Also, our previous expected return formulas should equal CAPM expected formulas should equal CAPM expected return.return.

Expected Dividend Yield + Expected Expected Dividend Yield + Expected Capital Gains Yield = CAPM expected Capital Gains Yield = CAPM expected returnreturn

(Div(Div11 + P + P11 – P – P00)/P)/P00 or Div or Div11/P/P00 + g = CAPM + g = CAPM

CAPM and Stock Valuation: PepsiCAPM and Stock Valuation: Pepsi

Pepsi’s B = 0.67, assume rPepsi’s B = 0.67, assume rff = 1%, r = 1%, rmm = 9%.Pepsi’s = 9%.Pepsi’s stock price today is $48 and it’s expected dividend is stock price today is $48 and it’s expected dividend is $0.68. What price do investors expect Pepsi’s stock $0.68. What price do investors expect Pepsi’s stock to sell for a year from now?to sell for a year from now?

From CAPM: r = 1% + 0.67(9%-1%) = 6.36%From CAPM: r = 1% + 0.67(9%-1%) = 6.36% 6.36% = Exp. Dividend Yld. + Exp. Capital Gains Yld.6.36% = Exp. Dividend Yld. + Exp. Capital Gains Yld. PP00 = $48, Div = $48, Div1 1 = $0.68: Div1/P0 = $0.68/$48 = 1.42%= $0.68: Div1/P0 = $0.68/$48 = 1.42% 1.42% + Exp. Capital Gain Yld = 6.36%1.42% + Exp. Capital Gain Yld = 6.36% Exp Capital Gain Yld = 4.94% = (PExp Capital Gain Yld = 4.94% = (P11-P-P00)/P)/P0 0 or gor g Exp. PExp. P1 1 = P= P00(1+g) = $48(1.0494) = $50.37(1+g) = $48(1.0494) = $50.37

What about this Pepsi?What about this Pepsi?

Pepsi’s B = 0.67, assume rPepsi’s B = 0.67, assume rff = 1%, r = 1%, rmm = = 9%.Pepsi’s stock price today is $48 and 9%.Pepsi’s stock price today is $48 and it’s expected dividend is $0.68. Analysts it’s expected dividend is $0.68. Analysts now expect a constant growth rate of now expect a constant growth rate of 5.25% for Pepsi? Would you want to buy 5.25% for Pepsi? Would you want to buy Pepsi today for $48?Pepsi today for $48?

Pepsi’s CAPM return = 1% + 0.67(9%-1%) Pepsi’s CAPM return = 1% + 0.67(9%-1%) = 6.36%= 6.36%

DivDiv11/P/P00 + g = $0.68/$48 + .0525 = 6.67% + g = $0.68/$48 + .0525 = 6.67%

Pepsi: Analyst Expected Return vs. Pepsi: Analyst Expected Return vs. CAPMCAPM

Investors would want to buy Pepsi and will drive up the Investors would want to buy Pepsi and will drive up the price until its expected return = CAPM return of 6.36%.price until its expected return = CAPM return of 6.36%.

New Price = DivNew Price = Div11/(CAPM r – g) = $0.68/(.0636 -.0525) = /(CAPM r – g) = $0.68/(.0636 -.0525) =

$61.26$61.26

6.67%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

0 0.2 0.4 0.6 0.8 1 1.2

Beta

Ex

pecte

d

Retu

rn

Capital Budgeting & Project RiskCapital Budgeting & Project Risk

The project cost of capital depends on the use to The project cost of capital depends on the use to which the capital is being put. Therefore, it which the capital is being put. Therefore, it depends on the risk of the project and not the depends on the risk of the project and not the risk of the company. risk of the company.

For now, we can assume a firm uses only equity For now, we can assume a firm uses only equity financing. (We’ll relax this assumption in Chapter financing. (We’ll relax this assumption in Chapter 12.)12.)

Given this assumption, we can use the market Given this assumption, we can use the market risk of the project and the CAPM to find the risk of the project and the CAPM to find the opportunity cost of capital. opportunity cost of capital.

Capital Budgeting & Project RiskCapital Budgeting & Project Risk

Example Example - Based on the CAPM with r- Based on the CAPM with rff = 3% and market risk = 3% and market risk premium of 9% , MAD-Doctor Inc. (insert maniacal laughter here) premium of 9% , MAD-Doctor Inc. (insert maniacal laughter here) has a cost of capital of 3% + 2.1(9%) = 21.9%. A breakdown of has a cost of capital of 3% + 2.1(9%) = 21.9%. A breakdown of the company’s investment projects is listed below. When the company’s investment projects is listed below. When evaluating a new tissue re-animation investment, which cost of evaluating a new tissue re-animation investment, which cost of capital should be used?capital should be used?

1/3 Lightning Power Generation B=1.61/3 Lightning Power Generation B=1.6

1/3 Surgical Equipment B=2.01/3 Surgical Equipment B=2.0

1/3 Tissue Re-animation B=2.71/3 Tissue Re-animation B=2.7

AVG. B of assets = 2.1AVG. B of assets = 2.1

Capital Budgeting & Project RiskCapital Budgeting & Project Risk

Example Example - Based on the CAPM with r- Based on the CAPM with rff = 3% and market = 3% and market risk premium of 9% , MAD-Doctor Inc. (insert maniacal risk premium of 9% , MAD-Doctor Inc. (insert maniacal laughter here) has a cost of capital of 3% + 2.1(9%) = laughter here) has a cost of capital of 3% + 2.1(9%) = 21.9%. A breakdown of the company’s investment 21.9%. A breakdown of the company’s investment projects is listed below. When evaluating a new tissue projects is listed below. When evaluating a new tissue re-animation investment, which cost of capital should be re-animation investment, which cost of capital should be used?used?

Re-animation r = 3% + 2.7 (9% ) = 27.3% Re-animation r = 3% + 2.7 (9% ) = 27.3%

27.3% reflects the opportunity cost of capital on an investment 27.3% reflects the opportunity cost of capital on an investment given the unique risk of the project.given the unique risk of the project.