FM Chp 6

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Defining RiskDefining RiskDefining RiskDefining Risk

What rate of return do you expect on yourWhat rate of return do you expect on your

investment (savings) this year?investment (savings) this year?

What rate will you actually earn?What rate will you actually earn?Does it matter if it is a bank CD or a shareDoes it matter if it is a bank CD or a share

of stock?of stock?

What rate of return do you expect on yourWhat rate of return do you expect on your

investment (savings) this year?investment (savings) this year?

What rate will you actually earn?What rate will you actually earn?Does it matter if it is a bank CD or a shareDoes it matter if it is a bank CD or a share

of stock?of stock?

The variability of returns from thoseThe variability of returns from those

that are expected.that are expected.The variability of returns from thoseThe variability of returns from those

that are expected.that are expected.

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Defining ReturnDefining ReturnDefining ReturnDefining Return

Income receivedIncome received on an investmentplus any change in market pricechange in market price,

usually expressed as a percent ofthe beginning market pricebeginning market price of the

investment.

Income receivedIncome received on an investmentplus any change in market pricechange in market price,

usually expressed as a percent ofthe beginning market pricebeginning market price of the

investment.

DDtt+ (PPtt - P- Pt-1t-1 )

PPt-1t-1R =

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Return ExampleReturn ExampleReturn ExampleReturn Example

The stock price for Stock A was $10$10 pershare 1 year ago. The stock is currently

trading at $9.50$9.50 per share, andshareholders just received a $1 dividend$1 dividend.

What return was earned over the past year?

The stock price for Stock A was $10$10 pershare 1 year ago. The stock is currently

trading at $9.50$9.50 per share, andshareholders just received a $1 dividend$1 dividend.

What return was earned over the past year?

$1.00$1.00 + ($9.50$9.50 - $10.00$10.00)

$10.00$10.00RR= = 5%5%

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Using Probability DistributionUsing Probability Distribution

to measure riskto measure riskxWhat is a Probability?

xA chance that a given outcome willoccur.

xFor example:-

xAn investor believed that the possible

one year returns from investing in aparticular common stock are on table.

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Determining Expected ReturnDetermining Expected ReturnDetermining Expected ReturnDetermining Expected Return

R = ( Ri )( Pi )R is the expected return for the asset,

Ri is the return for the ith possibility,

Pi is the probability of that return

occurring,

n is the total number of possibilities.

R = ( Ri )( Pi )R is the expected return for the asset,

Ri is the return for the ith possibility,

Pi is the probability of that return

occurring,

n is the total number of possibilities.

n

i=1

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How to Determine the ExpectedHow to Determine the Expected

Return and Standard DeviationReturn and Standard Deviation



Stock A

Ri

Pi

(Ri)(P

i)

-.15 .10 -.015

-.03 .20 -.006

.09 .40 .036

.21 .20 .042

.33 .10 .033

Sum 1.00 .090.090

Stock A

Ri

Pi

(Ri)(P

i)

-.15 .10 -.015

-.03 .20 -.006

.09 .40 .036

.21 .20 .042

.33 .10 .033

Sum 1.00 .090.090

Theexpectedreturn, R,for Stock

is .09 or9%

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Determining StandardDetermining Standard

Deviation (Risk Measure)Deviation (Risk Measure)



= ( Ri - R )2( Pi )Standard DeviationStandard Deviation, , is a statistical

measure of the variability of a distribution

around its mean.It is the square root of variance

= ( Ri - R )2( Pi )Standard DeviationStandard Deviation, , is a statistical

measure of the variability of a distribution

around its mean.It is the square root of variance

n

i=1

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Stock A Expected return Variance

Ri

Pi

(Ri)(P

i) (R

i- R )2(P

i)

-.15 .10 -.015 .00576

-.03 .20 -.006 .00288

.09 .40 .036 .00000

.21 .20 .042 .00288

.33 .10 .033 .00576

Sum 1.00 .090.090 .01728.01728

Stock A Expected return Variance

Ri

Pi

(Ri)(P

i) (R

i- R )2(P

i)

-.15 .10 -.015 .00576

-.03 .20 -.006 .00288

.09 .40 .036 .00000

.21 .20 .042 .00288

.33 .10 .033 .00576

Sum 1.00 .090.090 .01728.01728

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= ( Ri - R )2( Pi ) = .01728

= .1315.1315 or13.15%13.15%

= ( Ri - R )2( Pi ) = .01728

= .1315.1315 or13.15%13.15%

n

i=1

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Risk PreferencesRisk Preferences

The three basic risk preferencesbehaviors are:

Risk averse

Risk indifferent

Risk seeking

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RP = ( Wj )( Rj )RP is the expected return for the portfolio,

Wj is the weight (investment proportion) for

the jth asset in the portfolio,

Rj is the expected return of the jth asset,

m is the total number of assets in the

portfolio.

RP = ( Wj )( Rj )RPis the expected return for the portfolio,

Wj is the weight (investment proportion) for

thejth asset in the portfolio,

Rj is the expected return of the jth asset,

m is the total number of assets in the

portfolio.

Determining PortfolioDetermining Portfolio

Expected ReturnExpected Return



m

j=1

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You are creating a portfolio ofStock DStock D and StockStock

AA. You are investing $2,000$2,000 in Stock AStock A and $3,000$3,000in Stock DStock D. Remember that the expected return

and standard deviation ofStock AStock A is 9%9% and13.15%13.15%,, respectively. The expected return and

standard deviation ofStock DStock D is 8%8% and 10.65%10.65%,,respectively.

What is the expected return and standardWhat is the expected return and standard

deviation of the portfolio?deviation of the portfolio?

You are creating a portfolio ofStock DStock D and StockStock

AA. You are investing $2,000$2,000 in Stock AStock A and $3,000$3,000in Stock DStock D. Remember that the expected return

and standard deviation ofStock AStock A is 9%9% and13.15%13.15%,, respectively. The expected return and

standard deviation ofStock DStock D is 8%8% and 10.65%10.65%,,respectively.

What is the expected return and standardWhat is the expected return and standard

deviation of the portfolio?deviation of the portfolio?

Portfolio Risk andPortfolio Risk and

Expected Return ExampleExpected Return Example

Portfolio Risk andPortfolio Risk and

Expected Return ExampleExpected Return Example

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WBW

= $2,000 / $5,000 = .4

WWDD = $3,000 / $5,000 = .6.6

RP= (W

BW)(R

BW) + (WW

DD)(RR

DD)

RP= (.4)(9%) + (.6.6)(8%8%)

RP = (3.6%) + (4.8%4.8%) = 8.4%8.4%

WBW

= $2,000 / $5,000 = .4

WWDD= $3,000 / $5,000 = .6.6

RP= (W

BW)(R

BW) + (WW

DD)(RR

DD)

RP= (.4)(9%) + (.6.6)(8%8%)

RP = (3.6%) + (4.8%4.8%) = 8.4%8.4%

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Risk & Return in a Portfolio contextRisk & Return in a Portfolio context

Investors rarely place their entirewealth into a single asset orinvestment , rather they construct aportfolio or a group of investments.

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Combining securities that are not perfectly,

positively correlated reduces risk.

Combining securities that are not perfectly,

positively correlated reduces risk.

DiversificationDiversificationDiversificationDiversification

INVEST

MENTRETUR

N

TIME TIMETIME

SECURITY ESECURITY E SECURITY FSECURITY FCombinationCombination

E and FE and F

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x Correlation is a statistical measurementof the relationship between two variables.

x Possible correlations range from +1 to 1.A zero correlation indicates that there isno relationship between the variables.

x A correlation of 1 indicates a perfectnegative correlation, meaning that as onevariable goes up, the other goes down.

x A correlation of +1 indicates a perfectpositive correlation, meaning that bothvariables move in the same direction

together.

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Systematic RiskSystematic Riskis the variability of returnon stocks or portfolios associated with

changes in return on the market as a whole.

Unsystematic RiskUnsystematic Riskis the variability of returnon stocks or portfolios not explained by

general market movements. It is avoidablethrough diversification.

Systematic RiskSystematic Riskis the variability of returnon stocks or portfolios associated with

changes in return on the market as a whole.

Unsystematic RiskUnsystematic Riskis the variability of returnon stocks or portfolios not explained by

general market movements. It is avoidablethrough diversification.

Total Risk = SystematicTotal Risk = Systematic

Risk + Unsystematic RiskRisk + Unsystematic Risk



Total RiskTotal Risk = SystematicSystematicRiskRisk+

UnsystematicUnsystematicRiskRisk

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TotalTotal

RiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

STD

DE

VO

FP

ORTFOLIO

RETURN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors such as changes in nationseconomy, tax reform by the Congress,or a change in the world situation.

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TotalTotal

RiskRisk

Unsystematic riskUnsystematic risk

Systematic riskSystematic risk

STD

DE

VO

FP

ORTFOLIO

RETURN

NUMBER OF SECURITIES IN THE PORTFOLIO

Factors unique to a particular companyor industry. For example, the death of akey executive or loss of a governmental

defense contract.

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Measuring Market Risk-Measuring Market Risk-

The concept of BetaThe concept of BetaxTo measure a stocks market risk a

statistic known as beta has been

developed.

xBeta captures variation in a

stocksreturn brought along withvariation in the return on the market.

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Developing BetaDeveloping BetaxA stocks beta is developed by plotting the

historical relationship between the return onthe stock and the return on the market.

xA regression line is fitted to these data

points is known as the characteristic line forthe stock.

xThe slope of the line is the measure of

market risk for the stock simply called beta.

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Characteristic LineCharacteristic LineCharacteristic LineCharacteristic Line

RETURNON STOCK

RETURNON MARKET PORTFOLIO

BetaBeta =

RiseRise

RunRun

Narrower spreadNarrower spread

is higher correlationis higher correlation

Characteristic LineCharacteristic Line

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Characteristic LinesCharacteristic Lines

and Different Betasand Different Betas

Characteristic LinesCharacteristic Lines

and Different Betasand Different Betas

RETURNON STOCK

RETURNON MARKET PORTFOLIO

Beta < 1Beta < 1(defensive)(defensive)

Beta = 1Beta = 1

Beta > 1Beta > 1(aggressive)(aggressive)

Each characteristiccharacteristiclineline has a

different slope.

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CAPM is a model that describes therelationship between risk and

expected (required) return; in thismodel, a securitys expected

(required) return is the risk-free raterisk-free rateplus a premiuma premium based on the

systematic risksystematic riskof the security.

CAPM is a model that describes therelationship between risk and

expected (required) return; in thismodel, a securitys expected

(required) return is the risk-free raterisk-free rateplus a premiuma premium based on the

systematic risksystematic riskof the security.

Capital AssetCapital Asset

Pricing Model (CAPM)Pricing Model (CAPM)

Capital AssetCapital Asset

Pricing Model (CAPM)Pricing Model (CAPM)

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RRjj is the required rate of return for stock j,RRff is the risk-free rate of return,

jjis the beta of stock j (measures systematicrisk of stock j),

RRMM is the expected return for the market

portfolio.

RRjj is the required rate of return for stock j,RRff is the risk-free rate of return,

jjis the beta of stock j (measures systematicrisk of stock j),

RRMM is the expected return for the market

portfolio.

Security Market LineSecurity Market LineSecurity Market LineSecurity Market Line

RRjj = RRff + j(RRMM - RRff)

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RRjj = RRff + j(RRMM - RRff)

MM = 1.01.0

Systematic Risk (Beta)

RRff

RRMM

Requ

iredR

eturn

Requ

iredR

eturn

RiskRisk

PremiumPremium

Risk-freeRisk-free

ReturnReturn

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Lisa Miller at Basket Wonders is attemptingto determine the rate of return required by

their stock investors. Lisa is using a 6% R6% Rffand a long-term market expected rate ofmarket expected rate of

returnreturn of10%10%. A stock analyst following

the firm has calculated that the firm betabeta is1.21.2. What is the required rate of returnrequired rate of returnon

the stock ofBasket Wonders?

Lisa Miller at Basket Wonders is attemptingto determine the rate of return required by

their stock investors. Lisa is using a 6% R6% Rffand a long-term market expected rate ofmarket expected rate of

returnreturn of10%10%. A stock analyst following

the firm has calculated that the firm betabeta is1.21.2. What is the required rate of returnrequired rate of returnon

the stock ofBasket Wonders?

Determination of theDetermination of the

Required Rate of ReturnRequired Rate of Return


Required Rate of ReturnRequired Rate of Return

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RRBWBW = RRff + j(RRMM - RRff)RRBWBW = 6%6% + 1.21.2(10%10% - 6%6%)

RRBWBW = 10.8%10.8%

The required rate of return exceeds themarket rate of return as BWs beta

exceeds the market beta (1.0).

RRBWBW = RRff+ j(RRMM - RRff)RRBWBW = 6%6% + 1.21.2(10%10% - 6%6%)

RRBWBW = 10.8%10.8%

The required rate of return exceeds themarket rate of return as BWs beta

exceeds the market beta (1.0).

BWs RequiredBWs Required

Rate of ReturnRate of Return

BWs RequiredBWs Required

Rate of ReturnRate of Return

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Lisa Miller at BW is also attempting todetermine the intrinsic valueintrinsic value of the stock. She

is using the constant growth model. Lisaestimates that the dividend next perioddividend next period will be

$0.50$0.50 and that BW will growgrow at a constant rateof5.8%5.8%. The stock is currently selling for $15.

What is the intrinsic valueintrinsic value of the stock?Is the stock overover orunderpricedunderpriced?

Lisa Miller at BW is also attempting todetermine the intrinsic valueintrinsic value of the stock. She

is using the constant growth model. Lisaestimates that the dividend next perioddividend next period will be

$0.50$0.50 and that BW will growgrow at a constant rateof5.8%5.8%. The stock is currently selling for $15.

What is the intrinsic valueintrinsic value of the stock?Is the stock overoverorunderpricedunderpriced?


Intrinsic Value of BWIntrinsic Value of BW



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The stock is OVERVALUED asthe market price ($15) exceeds

the intrinsic valueintrinsic value ($10$10).

The stock is OVERVALUED asthe market price ($15) exceeds

the intrinsic valueintrinsic value ($10$10).





$0.50$0.5010.8%10.8% - 5.8%5.8%

IntrinsicIntrinsic

ValueValue=

= $10$10

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Systematic Risk (Beta)

RRffRequ

iredRetu

rn

Requ

iredRetu

rn

Direction ofMovement

Direction ofMovement

Stock YStock Y (Overpriced)

Stock X (Underpriced)

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An index ofsystematic risksystematic risk.

It measures the sensitivityof astocks returns to changes inreturns on the market portfolio.

The betabeta for a portfolio is simply aweighted average of the individual

stock betas in the portfolio.

An index ofsystematic risksystematic risk.

It measures the sensitivityof astocks returns to changes inreturns on the market portfolio.

The betabeta for a portfolio is simply aweighted average of the individual

stock betas in the portfolio.

What is Beta?What is Beta?What is Beta?What is Beta?

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Characteristic LineCharacteristic Line

A line that describes the relationshipbetween an individual securitysexcess returns and excess returns on

the market portfolio.Excess return = Expected return Riskfree return

To compare the returns of risky assetsexcess returns are calculated.

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Unsystematic RiskUnsystematic RiskThe dispersion of the data point about the

characteristic line is a measure of theunsystematic risk of the stock.

The wider the relative distance of the points

from the line the greater the unsystematic riskof the stocks, i.e. the stocks return has lowcorrelation with the return on the market

portfolio.The narrower the dispersion, higher thecorrelation and lower the unsystematic risk.

Documents

FM Chp 6