1 b280f introduction to financial management lecture 5 risk and rates of return

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B280F Introduction to Financial ManagementB280F Introduction to Financial Management

Lecture 5Lecture 5

Risk and Rates of ReturnRisk and Rates of Return

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ObjectivesObjectives Inflation and rates of returnInflation and rates of return How to How to measuremeasure risk risk

(variance, standard deviation, beta)(variance, standard deviation, beta) How to How to reducereduce risk risk

(diversification)(diversification) How to How to priceprice risk risk

(security market line, Capital Asset (security market line, Capital Asset Pricing Model)Pricing Model)

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Conceptually:

Nominalrisk-freeInterest

Rate

krf

=

Realrisk-freeInterest

Rate

k*

+

Inflationrisk

premium

IRP

Mathematically:

(1 + krf) = (1 + k*) (1 + IRP)

This is known as the “Fisher Effect”

Interest RatesInterest Rates

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Suppose the real rate is 3%, and the nominal Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation risk rate is 8%. What is the inflation risk premium?premium?

(1 + k(1 + krfrf) = (1 + k*) (1 + IRP)) = (1 + k*) (1 + IRP)

(1.08) = (1.03) (1 + IRP)(1.08) = (1.03) (1 + IRP)

(1 + IRP) = (1.0485),(1 + IRP) = (1.0485), so so

IRP = 4.85%IRP = 4.85%

Interest RatesInterest Rates

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Term Structure of Interest RatesTerm Structure of Interest Rates The pattern of rates of return for debt The pattern of rates of return for debt

securities that differ only in the length of securities that differ only in the length of time to maturity.time to maturity.

yieldto

maturity(YTM)

time to maturity (years)

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Term Structure of Interest RatesTerm Structure of Interest Rates

yieldto

Maturity(YTM)

time to maturity (years)

The yield curve may be downward The yield curve may be downward sloping or “inverted” if rates are sloping or “inverted” if rates are expected to fall.expected to fall.

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For a Treasury security, what is For a Treasury security, what is the required rate of return?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-freerisk-free”” rate of return. rate of return.

RequiredRequired

rate of rate of

returnreturn==

Risk-freeRisk-free

rate of rate of

returnreturn

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

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ReturnsReturns

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

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

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State of Probability ReturnState of Probability Return

Economy (P) Economy (P) Orl. Utility Orl. TechOrl. Utility Orl. Tech

Recession .20 4% -10%Recession .20 4% -10%

Normal .50 10% 14%Normal .50 10% 14%

Boom .30 14% 30%Boom .30 14% 30%

For each firm, the expected return on the For each firm, the expected return on the stock is just a stock is just a weighted averageweighted average::

kk = P( = P(kk11)*)*kk11 + P( + P(kk22)*)*kk22 + ...+ P( + ...+ P(kknn)*)*kknn

Expected ReturnExpected Return

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Normal .50 10% 14%Normal .50 10% 14%

Boom .30 14% 30%Boom .30 14% 30%


kk (OU) (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%= .2 (4%) + .5 (10%) + .3 (14%) = 10%

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Normal .50 10% 14%Normal .50 10% 14%

Boom .30 14% 30%Boom .30 14% 30%


kk (OT) (OT) = = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%.2 (-10%)+ .5 (14%) + .3 (30%) = 14%

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Portfolio Expected Returns

Weighted average of the expected return of each individual stock with the weights being equal to the proportion of the portfolio invested in each security

j

jjp kwk

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Portfolio Expected Returns

Assume you wish to hold a portfolio consisting of Assume you wish to hold a portfolio consisting of

asset A and a riskless asset. Given the following asset A and a riskless asset. Given the following

information, information, calculate portfolio expected returns and calculate portfolio expected returns and

portfolio betasportfolio betas, letting the proportion of funds , letting the proportion of funds

invested in asset A range from 0 to 125%. Asset A invested in asset A range from 0 to 125%. Asset A

has an expected return of 18%. The risk-free rate is has an expected return of 18%. The risk-free rate is

7%. Asset A weights: 0%, 25%, 50%, 75%, 100%, 7%. Asset A weights: 0%, 25%, 50%, 75%, 100%,

and 125%.and 125%.

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Proportion Proportion Portfolio Invested in Invested in Expected Asset A Riskless Asset Return

00% 100% 7.00% 25% 75% 9.75% 50% 50% 12.50% 75% 25% 15.25% 100% 0% 18.00% 125% -25% 20.75%

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PPt+1t+1 60 60

PPtt 50 50

Holding Period Return CalculationsHolding Period Return Calculations

= = = 20% = 20%PPt+1t+1 - P - Pt t 60 - 50 60 - 50

PPtt 50 50

- 1- 1 = = -1-1 = 20% = 20%

t t+1

$50 $60

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(a) (b)monthly expected

month price return return (a - b)2

Dec $50.00Jan $58.00 0.160 0.049 0.012321Feb $63.80 0.100 0.049 0.002601Mar $59.00 -0.075 0.049 0.015376Apr $62.00 0.051 0.049 0.000004May $64.50 0.040 0.049 0.000081Jun $69.00 0.070 0.049 0.000441Jul $69.00 0.000 0.049 0.002401Aug $75.00 0.087 0.049 0.001444Sep $82.50 0.100 0.049 0.002601Oct $73.00 -0.115 0.049 0.028960Nov $80.00 0.096 0.049 0.002090Dec $86.00 0.075 0.049 0.000676

0.0781St. Dev: sum, divided by (n-1), and take sq root:

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What is Risk?What is Risk?

The possibility that an The possibility that an actualactual return will return will differ from our differ from our expectedexpected return. return.

Uncertainty in the distribution of Uncertainty in the distribution of possible outcomes.possible outcomes.

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What is Risk?What is Risk?

Uncertainty in the distribution of Uncertainty in the distribution of possible outcomes.possible outcomes.

returnreturn

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-10 -5 0 5 10 15 20 25 30

Company B

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

4 8 12

Company A

returnreturn

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How do We Measure Risk?How do We Measure Risk?

To get a general idea of a stock’s To get a general idea of a stock’s price variability, we could look at price variability, we could look at the the stock’s price rangestock’s price range over the over the past year.past year.

52 weeks Yld Vol NetHi Lo Sym Div % PE 100s Hi Lo Close Chg134 80 IBM .52 .5 21 143402 98 95 9549 -3

115 40 MSFT … 29 558918 55 52 5194 -475

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How do We Measure Risk?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.

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Standard DeviationStandard Deviation

= (k= (kii - k) - k)22 P(k P(kii)) n

i=1

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Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8Variance = 12Variance = 12

Stand. dev. = 12 = Stand. dev. = 12 = 3.46%3.46%

Orlando Utility, Inc. Orlando Utility, Inc.

( 4% - 10%)( 4% - 10%)22 (.2) = 7.2 (.2) = 7.2

(10% - 10%)(10% - 10%)22 (.5) = 0 (.5) = 0

(14% - 10%)(14% - 10%)22 (.3) (.3) = = 4.84.8Variance = 12Variance = 12


= (kii - k)2 P(kii) n

i=1

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Orlando Technology, Inc. Orlando Technology, Inc.

(-10% - 14%)(-10% - 14%)22 (.2) = 115.2 (.2) = 115.2

(14% - 14%)(14% - 14%)22 (.5) = 0 (.5) = 0

(30% - 14%)(30% - 14%)22 (.3) (.3) = = 76.8 76.8Variance = 192Variance = 192


= (kii - k)2 P(kii) n

i=1

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Which stock would you prefer?Which stock would you prefer?

How would you decide?How would you decide?

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Orlando OrlandoOrlando Orlando

UtilityUtilityTechnologyTechnology

Expected ReturnExpected Return 10% 14% 10% 14%

Standard DeviationStandard Deviation 3.46% 13.86% 3.46% 13.86%

SummarySummary

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It depends on your tolerance for risk! It depends on your tolerance for risk!

Remember, there’s a tradeoff between Remember, there’s a tradeoff between risk and return.risk and return.

Return

Risk

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PortfoliosPortfolios

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?

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Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated).

rateof

return

time

kA

kB

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rateof

return

time

kpkA

kB

What has happened to the variability of returns for the

portfolio?

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DiversificationDiversification

Investing in Investing in more than onemore than one security security to to reduce riskreduce risk..

If two stocks are If two stocks are perfectly perfectly positivelypositively correlatedcorrelated, diversification has , diversification has no no effecteffect on risk. on risk.

If two stocks are If two stocks are perfectly perfectly negativelynegatively correlatedcorrelated, the portfolio is , the portfolio is perfectlyperfectly diversified.diversified.

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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.

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

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

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Market RiskMarket Risk

Unexpected changes in interest Unexpected changes in interest rates.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 competition, and the overall business cycle.business cycle.

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Company-unique RiskCompany-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.

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

portfoliorisk

number of stocks

Market risk

company-unique

risk

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Do some firms have more Do some firms have more market risk than others?market risk than others?

YesYes.. For example: For example:

Interest rate changes affect all firms, but Interest rate changes affect all firms, but which of the following would be which of the following would be moremore affected?affected?

a) Retail food chaina) Retail food chain

b) Commercial bankb) Commercial bank

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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.

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This is why we have This is why we have Beta.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.

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A firm that has a A firm that has a beta = 1beta = 1 has has average average market riskmarket risk. The stock is as volatile as the . The stock is as volatile as the market.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 the than the market.market.– (ex: utilities)(ex: utilities)

The market’s beta is The market’s beta is 11

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Calculating BetaCalculating Beta

-5-15 5 10 15

-15

-10

-10

-5

5

10

15

XYZ Co. returns

S&P 500returns

. . . .

. . . .. . . .

. . . .

. . . .

. . . .

. . . .

. . . .

. . .

. . . .

. . . .

Beta = slope = 1.20

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Summary:Summary:

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

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.

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What is the Required Rate of What is the Required Rate of Return?Return?

The return on an investment The return on an investment requiredrequired by an investor given by an investor given market interest rates and the market interest rates and the investment’s investment’s riskrisk..

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marketrisk

company-unique risk

can be diversifiedaway

Required

rate of

return= +

Risk-free

rate of

return

Risk

premium

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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).

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rrjj = r = rrfrf + + jj ( (rrmm - - rrrfrf ))

where:where:

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

rrrfrf = 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

rrmm = the return on the market index. = the return on the market index.

The CAPM equation:The CAPM equation:

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RequiredRequired

rate of rate of

returnreturn

Beta

12%

0

Is there a riskless(zero beta) security?

Treasurysecurities are

as close to risklessas possible.

Risk-freerate ofreturn(6%)

.

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RequiredRequired

rate of rate of

returnreturn

Beta

12%

10

How to find the return of the market portfolio?

Stock marketindex could be used to approximate the market portfolio.


.

.

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RequiredRequired

rate of rate of

returnreturn

.


Beta

12%

1

SecurityMarket

Line (SML)

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What does beta tell us? A beta of 1 implies the asset has the A beta of 1 implies the asset has the

same systematic risk as the overall same systematic risk as the overall marketmarket

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

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

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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)

Estimates of Estimates of for Selected Stocks for Selected Stocks

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RequiredRequired

rate of rate of

returnreturn

.

Beta

12%

1

SML

UtilityStocks


0

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RequiredRequired

rate of rate of

returnreturn .

Beta

12%

1

SMLHigh-techstocks


0

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Example: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?

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rrjj = = rrrfrf + ( + (rrmm - - rrrfrf ))

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

rrjj = .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.

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RequiredRequired

rate of rate of

returnreturn

Beta

12%

1

SML

0

Theoretically, every security should lie on the SML

If every stock is on the SML,

investors are being fully compensated for risk.Risk-free

rate ofreturn(6%)

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RequiredRequired

rate of rate of

returnreturn

.

Beta

12%

1

SML

0

If a security is abovethe SML, it isunderpriced.

If a security is below the SML, it

is overpriced.Risk-freerate ofreturn(6%)

.

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Total versus Systematic Risk

Consider the following information:Consider the following information:

Standard DeviationStandard Deviation BetaBeta– Security CSecurity C 20%20% 1.251.25– Security KSecurity K 30%30% 0.950.95

Which security has more total risk?Which security has more total risk? Which security has more systematic risk?Which security has more systematic risk? Which security should have the higher expected Which security should have the higher expected

return?return?

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Question for Discussion 1Question for Discussion 1 Consider the following stocks. If the risk-free

rate is 6.15% and the market risk premium is 9.5%, what is the required rate of return for each?

Stock Beta Required Return– DCLK 4.03 ?– KO 0.84 ?– INTC 1.05 ?– KEI 0.59 ?

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Portfolio BetaPortfolio Beta

Weighted average of the individual stock betas with the weights being equal to the proportion of the portfolio invested in each security

Portfolio beta indicates the percentage change on average of the portfolio for every 1 percent change in the general market

j

jjp w

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Question for Discussion 2Question for Discussion 2

Consider the a portfolio consisting of the Consider the a portfolio consisting of the following four securities following four securities

SecuritySecurity WeightWeight BetaBeta– DCLKDCLK 0.1330.133 4.034.03– KOKO 0.20.2 0.840.84– INTCINTC 0.2670.267 1.051.05– KEIKEI 0.40.4 0.590.59

What are the portfolio beta and portfolio required What are the portfolio beta and portfolio required rate of return?rate of return?

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Diversification and BetaDiversification and Beta

Beta measures systematic riskBeta measures systematic risk Diversification does Diversification does notnot mean to reduce betamean to reduce beta Investors differ in the extent to which they Investors differ in the extent to which they

will take risk, so they choose securities with will take risk, so they choose securities with different betasdifferent betas– E.g., an E.g., an aggressiveaggressive investor could choose a investor could choose a

portfolio with a beta of 2.0portfolio with a beta of 2.0– E.g., a E.g., a conservativeconservative investor could choose a investor could choose a

portfolio with a beta of 0.5portfolio with a beta of 0.5

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Answer 1 Answer 1

SecuritySecurity Required Rate of Return Required Rate of Return– DCLKDCLK 6.15% + 4.03(9.5%) = 44.435%6.15% + 4.03(9.5%) = 44.435%– KOKO 6.15% + 0.84(9.5%) = 14.130%6.15% + 0.84(9.5%) = 14.130%– INTCINTC 6.15% + 1.05(9.5%) = 16.125%6.15% + 1.05(9.5%) = 16.125%– KEIKEI 6.15% + 0.59(9.5%) = 11.755%6.15% + 0.59(9.5%) = 11.755%

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Answer 2 Answer 2

Portfolio betaPortfolio beta

= 0.133(4.03)+0.2(0.84)+0.267(1.05)+0.4(0.59) = 0.133(4.03)+0.2(0.84)+0.267(1.05)+0.4(0.59)

= 1.22= 1.22

Portfolio required rate of returnPortfolio required rate of return =6.15%+1.22(9.5%)=6.15%+1.22(9.5%)

=17.74%=17.74%

1 b280f introduction to financial management lecture 5 risk and rates of return

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