Ch 6: Risk and Rates of Return

ReturnReturn

RiskRisk 2000, Prentice Hall, Inc.

For a Treasury security, what is the required rate of return?

Since Treasuries are essentially Since Treasuries are essentially free of free of default riskdefault risk, the rate of return on a , the rate of return on a

Treasury security is considered the Treasury security is considered the ““risk-risk-freefree”” rate of return. rate of return.

RequiredRequired

rate of rate of

returnreturn==

Risk-freeRisk-free

rate of rate of

returnreturn

For a corporate stock or bond, what is the required rate of return?

How large of a How large of a risk premiumrisk premium should we should we require to buy a corporate security? require to buy a corporate security?

RequiredRequired

rate of rate of

returnreturn== + +

Risk-freeRisk-free

rate of rate of

returnreturn

RiskRisk

premiumpremium

Returns

Expected ReturnExpected Return - the return that an - the return that an investor expects to earn on an asset, investor expects to earn on an asset, given its price, growth potential, etc.given its price, growth potential, etc.

Required ReturnRequired Return - the return that an - the return that an investor requires on an asset given investor requires on an asset given itsits riskrisk and market interest rates.and market interest rates.

How do we Measure Risk?

A more scientific approach is to A more scientific approach is to examine the stock’s examine the stock’s standard standard deviationdeviation of returns. of returns.

Standard deviation is a measure of Standard deviation is a measure of the the dispersion of possible outcomesdispersion of possible outcomes. .

The greater the standard deviation, The greater the standard deviation, the greater the uncertainty, and the greater the uncertainty, and therefore , the greater the risk.therefore , the greater the risk.

Portfolios

Combining several securities Combining several securities in a in a portfolioportfolio can actually can actually reduce overall riskreduce overall risk..

How does this work?How does this work?

If you owned a share of every stock If you owned a share of every stock traded on the NYSE and NASDAQ, traded on the NYSE and NASDAQ, would you be diversified?would you be diversified?

YES!YES! Would you have eliminated all of Would you have eliminated all of

your risk?your risk?

NO!NO! Common stock portfolios still Common stock portfolios still have risk. have risk.

Some risk can be diversified away and some can not.

Market riskMarket risk ( (systematic risk)systematic risk) is is nondiversifiable. nondiversifiable. This type of risk This type of risk can not be diversified away.can not be diversified away.

Company-unique riskCompany-unique risk (unsystematic (unsystematic risk)risk) is is diversifiablediversifiable. This type of risk . This type of risk can be reduced through can be reduced through diversification.diversification.

Market Risk

Unexpected changes in interest rates.Unexpected changes in interest rates. Unexpected changes in cash flows Unexpected changes in cash flows

due to tax rate changes, foreign due to tax rate changes, foreign competition, and the overall business competition, and the overall business cycle.cycle.

Company-unique Risk

A company’s labor force goes on A company’s labor force goes on strike.strike.

A company’s top management dies A company’s top management dies in a plane crash.in a plane crash.

A huge oil tank bursts and floods a A huge oil tank bursts and floods a company’s production area.company’s production area.

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

portfolioportfolioriskrisk

number of stocksnumber of stocks

Market riskMarket risk

company-company-uniqueunique

riskrisk

NoteNoteAs we know, the market compensates As we know, the market compensates

investors for accepting risk - but investors for accepting risk - but only for only for market riskmarket risk.. Company- Company-unique risk can and should be unique risk can and should be diversified away.diversified away.

So - we need to be able to So - we need to be able to measuremeasure market risk.market risk.

This is why we have Beta.

Beta: a measure of market risk.Beta: a measure of market risk. Specifically, beta is a measure of how Specifically, beta is a measure of how

an individual stock’s returns vary an individual stock’s returns vary with market returns.with market returns.

It’s a measure of the It’s a measure of the “sensitivity”“sensitivity” of of an individual stock’s returns to an individual stock’s returns to changes in the market.changes in the market.

A firm that has a A firm that has a beta = 1beta = 1 has has average average market riskmarket risk. The stock is no more or less . The stock is no more or less volatile than the market.volatile than the market.

A firm with a A firm with a beta > 1beta > 1 is is more volatilemore volatile than than the market. the market. (ex: technology firms)(ex: technology firms)

A firm with a A firm with a beta < 1beta < 1 is is less volatileless volatile than than the market.the market. (ex: utilities)(ex: utilities)

The market’s beta is 1

Calculating Beta: The Characteristic Line

-5-5-15-15 55 1010 1515

-15-15

-10-10

-10-10

-5-5

55

1010

1515

XYZ Co. returnsXYZ Co. returns

S&P 500S&P 500returnsreturns

. . . .

. . . .. . . .

. . . .. . . .

. . . .

. . . .

. . . .

. . . .

. . .

. . . .

. . . .

Beta = slopeBeta = slope = 1.20= 1.20

Summary:

We know how toWe know how to measuremeasure risk, using risk, using standard deviationstandard deviation for overall risk for overall risk and and betabeta for market risk. for market risk.

We know how to We know how to reducereduce overall risk overall risk to only market risk through to only market risk through diversificationdiversification..

We need to know how to We need to know how to priceprice risk so risk so we will know how much extra return we will know how much extra return we should require for accepting extra we should require for accepting extra risk.risk.

This linear relationship between This linear relationship between risk and required return is risk and required return is known as the known as the Capital Asset Capital Asset

Pricing ModelPricing Model (CAPM). (CAPM).

RequiredRequired

rate of rate of

returnreturn

Beta

12%12% .

11

SMLSML

00

Is there a risklessIs there a riskless(zero beta) security?(zero beta) security?

TreasuryTreasurysecurities aresecurities are

as close to risklessas close to risklessas possible. as possible. Risk-freeRisk-free

rate ofrate ofreturnreturn(6%)(6%)

RequiredRequired

rate of rate of

returnreturn

Beta

12%12% .

1

SMLSMLWhere does the S&P 500Where does the S&P 500fall on the SML?fall on the SML?

The S&P 500 isThe S&P 500 isa good a good

approximationapproximationfor the marketfor the market

Risk-freeRisk-freerate ofrate ofreturnreturn(6%)(6%)

00

The CAPM equation:

kkjj = k = krfrf + + jj (k (kmm - k - krf rf ))

where:where:

kkjj = the required return on security j, = the required return on security j,

kkrfrf = the risk-free rate of interest, = the risk-free rate of interest,

jj = the beta of security j, and = the beta of security j, and

kkmm = the return on the market index. = the return on the market index.

Example:

Suppose the Treasury bond rate is Suppose the Treasury bond rate is 6%6%,, the average return on the the average return on the S&P 500 index is S&P 500 index is 12%12%,, and Walt and Walt Disney has a beta of Disney has a beta of 1.21.2..

According to the According to the CAPMCAPM, what , what should be the should be the required rate of required rate of returnreturn on Disney stock? on Disney stock?

kj = krf + (km - krf )

kkjj = .06 + 1.2 (.12 - .06) = .06 + 1.2 (.12 - .06)

kkjj = .132 = = .132 = 13.2%13.2%

According to the CAPM, Disney According to the CAPM, Disney stock should be priced to give a stock should be priced to give a 13.2%13.2% return. return.