Fm Risk Return 2

8/8/2019 Fm Risk Return 2

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2 - 1

Ri$k

Re

turn


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$ R tu 2 - 2

Risk and Return

Basic return conceptsBasic risk concepts

Stand-alone riskPortfolio (market) risk

Risk and return: CAPM/SML


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4

Ex pected Return

The future is uncertain.

Investors do not know with certainty whether the economywill be growing rapidly or be in recession.

Investors do not know what rate of return theirinvestments will yield.Therefore, they base their decisions on their expectationsconcerning the future.The expected rate of returnon a stock represents themean of a probability distribution of possible futurereturns on the stock.


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I. Portfolio Theory

how does investor decide among group ofassets?

assume: investors are risk averseadditional compensation for risk

tradeoff between risk and expected return


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2 - 6

What are investment returns?

Investmentreturnsmeasure the financial resultsof an investment.

Returns may behistoricalor prospective(anticipated).

Returns can be expressed in:

Dollar terms.Percentage terms.

Return can be seen as the reward for investing


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What is the return on an investment that costs$1,000 and is sold

after 1 year for $1,100?

Dollar return:

Percentage return:

$ Received - $ Invested$1,100 - $1,000 =$100.

$ Return/$ Invested$100/$1,000 =0.10=10%.


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2 - 9

e xample 1

Tbill, 1 month holding period

buy for $9488,sell for $9528

1 month R:9528 - 9488

9488= .00 42 = . 42%


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2 - 10

Annualized R:(1 .00 42) 12 - 1 = .0 52 = 5.2%


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2 - 11

e xample 2

100 shares IBM, 9 months

buy for $62, sell for $101.50

$.80 dividends

9 month R:1

01

.5

0- 62

+ .8

062

= .65 =65%


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Annualized R:(1 .65) 12/9 - 1 = . 95 = 95%

Measuring Return -> R


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Class work 1: Calculating R



1 month R:

Annualized R


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2 - 14




1 month R:

Annualized R


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2 - 15


100 shares MSFT, 6 months

buy for $24.125, sell for $25.875$.00 dividends

6 month R:

Annualized R


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100 shares F, 3 months

buy for $ 11.0625, sell for $ 13.125$ 0.125 dividends

3 month R:

Annualized R


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Ex pected Return -> E (R)

measuring likely future return

based on probability distributionrandom variable

E (R ) = SUM (R i x Prob (R i))


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18

Visual description of variance betweenactual and forecasted returns

But what is the variance?Umbrellas

Cider

ER

ER

ER


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2 - 19

G iven the following information,

calculate the e xpected return:

Return Probability

-30% .03

-20% .06

-10% .080% .15

Return Probability

10% .18

20% .20

30% .1340% .12

50% .05


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Calculating e xpected return

EV = (-30)(.03) + (-20)(.06) + (-10)(.08)+ (0)(.15) + (10)(.18) + (20)(.20)+ (30)(.13) + (40)(.12) + (50)(.05)

EV = 14.1%

EV =7

R iP ii=1


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What is investment risk?

Typically, investment returns are not knowwith certainty.Investment riskpertains to the probabilityofearning a return less than that expected.Th

e greater the c

hance of a return far belowthe expected return, the greater the risk.


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Sources of Risk

Business Risk

Financial RiskPurchasing Power RiskInterest Rate RiskLiquidity RiskMarket Risk


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2 - 23

Probability distribution

Rate of return (%)50150-20

Stock X

Stock Y

Which stock is riskier? Why?


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2 - 24

less risky more risky

Probability distribution - Risk


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symmetric asymmetric

E (R )R

prob (R )

R

prob (R )

E (R )


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Assume the FollowingInvestment Alternatives

Economy Prob . T-B ill Alta Repo Am F. MP

Recession 0 .10 8 .0% -22 .0% 28 .0% 10 .0% -13 .0%

Below avg . 0.20 8 .0 -2 .0 14 .7 -10 .0 1 .0

Average 0 .40 8 .0 20 .0 0 .0 7. 0 15 .0

Above avg . 0.20 8 .0 35 .0 -10 .0 45 .0 29 .0

Boom 0 .10 8 .0 50 .0 -20 .0 30 .0 43 .0

1.00


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What is unique aboutthe T-bill return?

The T-bill will return 8% regardless

of the state of the economy.Is the T-bill riskless?Explain.


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2 - 28

Do the returns of Alta Inds . and Repo

Men move with or counter to theeconomy?

Alta Inds . moves with the economy, so itis positively correlated with theeconomy . This is the typical situation .

Repo Men moves counter to theeconomy . Such negative correlation isunusual .


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2 - 29

Calculate the e xpected rate of returnon each alternative .

.n

1=i

iiPr=r

r = e xpected rate of return .

r Alta = 0 .10(-22%) + 0 .20(-2%)+ 0 .40(20%) + 0 .20(35%)+ 0 .10(50%) = 17. 4% .

^

^Where:E[R] = the expected return on the

stockN = the number of statespi = the probability of state iRi = the return on the stock in state i.


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Class work 5 Ex pected rate of return

Calculate the expected rate of return for:

T-BillsRepo

Am.FMP


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Altahas the highest rate of return.Does that make it best?

r Alta 1 7. 4%Market 15 .0

Am . Foam 13 .8T-bill 8 .0Repo Men 1 .7

^


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Risk

Risk is the chance that the actual return from aninvestment may differ from its expected value.

Risk is not knowing what you are doing.Warren Buffett

Statistically, risk is measured by calculating the totalvariation from the expected value.

The common measure used is the standard deviation.


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What is the standard deviationof returns for each alternative?

.

ariance

deviationStandard

1

2

2

!

!

!!

!

n

i

ii P r r

W W

W


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Calculating Risk-stand alone

W = 7 ((R i - EV) )P iW !(-30 - 14 .1)2 (.03) + (-20 14) 2 (.06)

+ (10 - 14 .1)2(.08) + (0 - 14 .1)2(.15)+ (10 -14 .1)2(.18) + (20 - 14 .1)2(.20)+ (30 - 14 .1 ) 2(.13) + (40 - 14 .1)2(.12)+ (50 - 14 .1)2(.05)


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WT-bills = 0 .0% .WAlta = 20 .0% .

WRepo = 13 .4% .WAm Foam = 18 .8% .

WMarket = 15 .3% .

.1

2

!

!

n

i

ii r r W

Alta Inds:

W= ((-22 - 1 7. 4)20 .10 + (-2 - 1 7. 4)20 .20+ (20 - 1 7. 4)20 .40 + (35 - 1 7. 4)20 .20+ (50 - 1 7. 4)20 .10) 1/2 = 20 .0% .


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Class work 6-standard deviation

Calculate the standard deviation for:

T-BillsRepo

Am.FMP


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Prob .

Rate of Return (%)

T-bill

Am . F.

Alta

0 8 13 .8 1 7. 4


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Standard deviationmeasures the stand-alonerisk of an investment.The larger the standard deviation, the

higher the probability that returns will befar below the expected return.Coefficient of variationis an alternativemeasure of stand-alone risk.


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Ex pected Return versus Risk

Ex pectedSecurity return Risk, W

AltaInds

.1

7.4% 20

.0%Market 15 .0 15 .3

Am . Foam 13 .8 18 .8T-bills 8 .0 0 .0Repo Men 1 .7 13 .4


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Coefficient of Variation:

CV = Ex pected return/standard deviation

CVT-B ILLS = 0 .0%/8 .0% = 0 .0 .

CVAlta Inds = 20 .0%/1 7. 4% = 1 .1 .CVRepo Men = 13 .4%/1 .7 % = 7. 9 .

CVAm

. Foam

= 18 .8%/13 .8% = 1 .4 .

CVM = 15 .3%/15 .0% = 1 .0 .


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Ex pected Return versus

Coefficient of VariationEx pected Risk: Risk:

Security return W CVAlta Inds 1 7. 4% 20 .0% 1 .1Market 15 .0 15 .3 1 .0Am . Foam 13 .8 18 .8 1 .4T-bills 8 .0 0 .0 0 .0Repo Men 1 .7 13 .4 7. 9


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T-bills

Coll.

MU

lta

0.0%2.0%

4.0%6.0%8.0%

10.0%12.0%14.0%

16.0%18.0%20.0%

0.0% 5.0% 10.0% 15.0% 20.0% 25.0%

Risk (Std. ev.)

R e

t u r n

Return vs. Risk (Std. ev.) :

Wh ich invest ment is best ?


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2 - 43The Trade-off Between Risk and Return


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2 - 44The History of Returns: Nominal ReturnsThe Value of $1 Invested in Stocks, Treasury Bonds, and

B ills


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45

The History of Returns: Real ReturnsThe Real Value of $1 Invested in Stocks, Treasury Bonds, and

B ills


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46

Risk premium : the additional return that an investment mustoffer, relative to some alternative, because it is more risky

than the alternative.

The Risk Dimension

Percentage Returns on Bills, Bonds, and tocks, 1900 - 2006


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47

Percentage Returns on B ills, Bonds, andStocks, 19002006


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48

Table 6 .2 Risk Premiums for Stocks,Bonds, and B ills, 19002006


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49

Asset classes with greater volatility payhigher average returns.Average return on stocks is more than double the average

return on bonds, but stocks are 2.5 times more vola.

Volatility and Risk

A verage Returns and tandard Deviation for Equities, Bonds, and Bills, 1900 -2006


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F ig . 6 .6 The Relationship Between Average (Nominal)Return and Standard Deviation for Stocks, Treasury

Bonds, and B ills, 1900 - 2006

Investors who want higher returns have to take more risk .

The incremental reward from accepting more risk is constant .


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2 - 51II. Managing risk

Diversification

holding a group of assets

lower risk w/out lowering E (R)Is it always possible?


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2 - 52

52

Portfolio Risk and Return

Most investors do not hold stocks in isolation .Instead, they choose to hold a portfolio of severalstocks .

When this is the case, a portion of an individualstock's risk can be eliminated, i.e., diversifiedaway .

F rom our previous calculations, we know that:the e xpected return on Stock A is 12 .5%

the e xpected return on Stock B is 20%the variance on Stock A is .00263

the variance on Stock B is .04200

the standard deviation on Stock A is 5 .12%

the standard deviation on Stock B is 20 .49%


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Assume a two-stock portfolio with$50,000 in Alta Inds . and $50,000 inRepo Men .

Calculate r p and Wp .^


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Portfolio Return, r p

r p is a weighted average:

r p = 0 .5(1 7. 4%) + 0 .5(1 .7 %) = 9 .6% .

r p is between r Alta and r Repo .

^

^

^

^

^ ^

^ ^

r p = 7 w ir in

i = 1


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The Ex pected Return on a Portfolio is computed as theweighted average of the e xpected returns on the stockswhich comprise the portfolio .

The weights reflect the proportion of the portfolioinvested in the stocks .

This can be e xpressed as follows:N

E[ Rp] = 7 w iE[ R i]i=1

Where:E[ Rp] = the e xpected return on the portfolio

N = the number of stocks in the portfolio

w i = the proportion of the portfolio invested in stock i

E[ R i] = the e xpected return on stock i


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56


For a portfolio consisting of two assets, theabove equation can be e xpressed as:

E[ Rp] = w

1E[ R

1] + w

2E[ R

2]

If we have an equally weighted portfolio of stockA and stock B (50% in each stock), then theexpected return of the portfolio is:

E[ Rp] = .50( .125) + .50( .20) = 16 .25%


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The variance/standard deviation of a portfolio reflectsnot only the variance/standard deviation of the stocksthat make up the portfolio but also how the returns onthe stocks which comprise the portfolio vary together .

Two measures of how the returns on a pair of stocksvary together are the covariance and the correlationcoefficient .

Covariance is a measure that combines the variance of a stocksreturns with the tendency of those returns to move up or downat the same time other stocks move up or down .

Since it is difficult to interpret the magnitude of the covarianceterms, a related statistic, the correlation coefficient, is oftenused to measure the degree of co-movement between twovariables . The correlation coefficient simply standardizes the

covariance .


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58


The Covariance between the returns on two stocks canbe calculated as follows:

N

Cov(R A,RB) = WA,B = 7 p i(RAi - E[ RA])(RB i - E[ RB])i=1

Where:W% &= the covariance between the returns on stocks A and B

N = the number of states

p i = the probability of state iRAi = the return on stock A in state i

E[ RA] = the e xpected return on stock A

RB i = the return on stock B in state i

E[ RB] = the e xpected return on stock B


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59


The Correlation Coefficient between the returns on twostocks can be calculated as follows:

WA,B Cov(R A,RB)

Corr(R A,RB) = VA,B = WAWB = S D(RA)SD(RB)

Where:VA,B=the correlation coefficient between the returns on stocks Aand BWA,B=the covariance between the returns on stocks A and B ,

WA=the standard deviation on stock A, and

WB=the standard deviation on stock B


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60

Ex pected Return

The table below provides a probability distribution for t

he returns on stocksA& B

State Probability Return On Return On

StockA Stock B

1 20% 5% 50%

2 30% 10% 30%3 30% 15% 10%

4 20% 20% -10%

The state represents the state of the economy one period in the future i.e. state

1 could represent a recession and state 2 a growth economy.The probability reflectshow likely it is that the state will occur.The sum of theprobabilities must equal 100%.The last two columns present the returns or outcomes for stocksAand B that

will occur in each

of the four states.


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61


The covariance between stock A and stock B is asfollows:

WA,B = .2( .05- .125)( .5- .2) + .3( .1- .125)( .3- .2) +.3( .15- .125)( .1- .2) + .2( .2- .125)(- .1- .2) = - .0105

The correlation coefficient between stock A and stock B is as follows:

-.0105

VA,B = ( .0512)( .2049) = -1 .00


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63


Lets calculate the variance and standard deviation of aportfolio comprised of 7 5% stock A and 25% stock B :

W2p =(.7 5)2 2+(.25) 2(.2049) 2+2( .7 5)( .25)(-1)( .0512)( .2049)= .00016

Wp = .00016 = .0128 = 1 .28%

Notice that the portfolio formed by investing 7 5% inStock A and 25% in Stock B has a lower variance andstandard deviation than either Stocks A or B and theportfolio has a higher e xpected return than Stock A .

This is the purpose of diversification; by formingportfolios, some of the risk inherent in the individual

stocks can be eliminated .

The Power of Diversification


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64

F rom 1994 2006 , the standard deviation of the typical stock in the U .S. wasabout 60% per year, while the standard deviation of the entire stock market

was only19 .8%!

The Power of DiversificationAverage Returns and Standard Deviations for 11

Stocks, 1994-2006


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65

M ost individual stock prices show higher volatility than the pricevolatility of a portfolio of all common stocks .

How can the standard deviation for individual stocks be higher than thestandard deviation of the portfolio?

Diversification: T he act of investing in many different assetsrather than just a few, so as to reduce volatility .

The ups and downs of individual stocks partially cancel eachother out.

The Power of Diversification


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66

Annual Returns onCoca-Cola and Wendys International

The two stocks did not always move in sync . The net effect is that the portfolio is less volatile than either stock held in isolation .

The Relationship Between Portfolio Standard


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67

The Relationship Between Portfolio StandardDeviation and the Number of Stocks in the

Portfolio

The risk that diversification eliminates is called unsystematicrisk .The risk that remains, even in a diversified portfolio, is calledsystematic risk .

2 68


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68

Diversification reduces portfolio volatility, but only up to apoint. Portfolio of all stocks still has a volatility of 19.8% .

Systematic risk: the volatility of the portfolio that cannot beeliminated through diversification.

Unsystematic risk: the proportion of risk of individual assets

that can be eliminated through diversification

What really matters is systematic risk.how a group of assets move together.

Systematic and nsystematic Risk

2 69


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Two types of risk

Unsystematic riskspecific to a firm

can be eliminated through diversificationexamples:

-- Safeway and a strike

-- Microsoft and antitrust cases

2 70


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Systematic risk

market risk

cannot be eliminated through diversification

due to factors affecting all assets

-- energy prices, interest rates, inflation,business cycles


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2 72


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72

A nheuser-Busch had a higher average return than A rcher DanielsM idland, and with smaller volatility .

A merican A irlines had a much smaller average return than Wal-M art, with similar volatility .

T he tradeoff between standard deviation and average returns thatholds for asset classes does not hold for individual stocks !

Because investors can eliminate unsystematic risk throughdiversification, market rewards only systematic risk .

S tandard deviation contains both systematic and unsystematicrisk .

Risk and Return Revisited

2 73


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73

Risk Premiums Around the World

2 74


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74

Investment performance is measured by totalreturn.Trade-off between risk and return for assets:historically, stockshavehigher returns and

volatility than bonds and bills.

One measure of volatility: standard deviationSystematic risk: risk that cannot be eliminatedthrough diversification

The Trade-off Between Risk and Return

2 75


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Alternative Method: 2 stock portfolio

r p = (3 .0%)0 .10 + (6 .4%)0 .20 + (10 .0%)0 .40+ (12 .5%)0 .20 + (15 .0%)0 .10 = 9 .6% .

^

Estimated Return

(More ... )

Economy Prob . Alta Repo Port .

Recession 0 .10 -22 .0% 28 .0% 3 .0%

Below avg . 0 .20 -2 .0 14 .7 6 .4Average 0 .40 20 .0 0 .0 10 .0Above avg . 0 .20 35 .0 -10 .0 12 .5Boom 0 .10 50 .0 -20 .0 15 .0

2 76


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Wp = ((3 .0 - 9 .6)20 .10 + (6 .4 - 9 .6)20 .20 +(10 .0 - 9 .6)20 .40 + (12 .5 - 9 .6)20 .20+ (15 .0 - 9 .6)20 .10) 1/2 = 3 .3% .

Wp is much lower than:either stock (20% and 13 .4%) .

average of Alta and Repo (16 .7 %) .

The portfolio provides average returnbut much lower risk . The key here isnegative correlation .

2 77


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Two-Stock Portfolios

Two stocks can be combined to forma riskless portfolio if V = -1 .0 .

Risk is not reduced at all if the twostocks have V = +1 .0 . In general, stocks have V } 0 .65, sorisk is lowered but not eliminated .Investors typically hold many stocks .

What happens when V = 0?

2 78


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What would happen to therisk of an average 1-stockportfolio as more randomly

selected stocks were added?

Wp would decrease because the addedstocks would not be perfectly correlated,

but r p would remain relatively constant.^

2 79


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Large

0 15

Prob .

2

1

W1 } 35% ; WLarge } 20% .Return

2 - 80


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2 - 80

# Stocks in Portfolio

10 20 30 40 2,000+

Company Specific(Diversifiable) Risk

Market Risk

20

0

Stand-Alone Risk, Wp

Wp (%)35

2 - 81


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2 - 81Ex ample

Choose stocks from NYSElistings

Go from 1 stock to 20 stocks

Reduce risk by 40-50%

2 - 82


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2 82W

# assets

systematicrisk

unsystematicrisk

totalrisk

2 - 83


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2 83

Stand-alone Market Diversifiable

Market risk is that part of a securitys

stand-alone risk that cannot beeliminated by diversification .

F irm-specific , or diversifiable , risk isthat part of a securitys stand-alone riskthat can be eliminated bydiversification .

risk risk risk= +.

2 - 84


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2 84

Conclusions

As more stocks are added, each newstock has a smaller risk-reducingimpact on the portfolio .

Wp falls very slowly after about 40stocks are included . The lower limitfor Wp is about 20% = WM .

By forming well-diversified portfolios,investors can eliminate about half theriskiness of owning a single stock .

2 - 85


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2 85

No. Rational investors will minimize riholding portfolios.They bear only market risk, so prices andreturns reflect this lower risk.

The one-stock investor bearshigher (stand-alone) risk, so the return is less than thatrequired by the risk.

Can an investor holding one stock earna return commensurate with its risk?

2 - 86


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2 86

measuring relative risk

If some risk is diversifiable,

then Wis not the best measure of risk

is an absolute measure of risk Need a measure just for the systematiccomponent

2 - 87

B F


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2 87Beta, F

Variation in asset/portfolio returnrelative to return of market portfolio

mkt. portfolio = mkt. index

-- S&P 500 or NYSEindex

F =

% change in asset return

% change in market return

2 - 88


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2 88interpreting F

if F !

asset is risk free

if F !

asset return = market returnif F "

asset is riskier than market inde x

Fasset is less risky than market inde x

2 - 89


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Market risk, which is relevant for stocksheld in well-diversified portfolios, is

defined as the contribution of a securityto the overall riskiness of the portfolio .It is measured by a stocks betacoefficient . For stock i, its beta is:

b i = ( ViM Wi) / WM

How is market risk measured for

individual securities?

2 - 90


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Sample betas

ma .e se B s . 7

s t .F .Ge e al Ele t .

Wal a t .(monthly returns, 5 years back )

2 - 91


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How are betas calculated?

In addition to measuring a stockscontribution of risk to a portfolio,

beta also which measures the stocksvolatility relative to the market.

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Measuring F

Estimated by regression

data on returns of assets

data on returns of market index

estimate

IE! m

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U sing a Regression to Estimate Beta

Run aregressionwith returns on the stockin question plotted on the Y axis andreturns on the market portfolio plotted onthe X axis.The slope of the regression line, which measures relative volatility, is defined asthe stocksbeta coefficient, orb.

2 - 94


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U se the historical stock returns tocalculate the beta for PQ U .

Year Market PQ U1 25 .7 % 40 .0%2 8 .0% -15 .0%

3 -11.0% -15

.0%4 15 .0% 35 .0%

5 32 .5% 10 .0%6 13 .7 % 30 .0%7 40 .0% 42 .0%8 10 .0% -10 .0%9 -10 .8% -25 .0%

10 -13 .1% 25 .0%

2 - 95


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Calculating Beta for PQ U

r PQ U = 0 .83r M + 0 .03R2 = 0 .36

-40%

-20%

0%

20%

40%

-40% -20% 0% 20% 40%r M

r K WE

2 - 96


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What is beta for PQ U ?

The regression line, andhence beta, can be foundusing a calculator with aregression function or aspreadsheet program . Inthis e xample, b = 0 .83 .

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Calculating Beta in Practice

Many analysts use the S&P 500 tofind the market return .

Analysts typically use four or fiveyears of monthly returns toestablish the regression line .

Some analysts use 52 weeks of

weekly returns .


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F inding Beta Estimates on the Web

Go to www .bloomberg .com .

Enter the ticker symbol for aStock Quote, such as IBMor Dell .

When the quote comes up,look in the section onFundamentals .

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Ex pected Return versus Market Risk

Which of the alternatives is best?

Ex pectedSecurity return Risk, b

HT 17. 4% 1 .29Market 15 .0 1 .00U SR 13 .8 0 .68

T-bills 8.0 0

.00Collections 1 .7 -0 .86


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2 - 102


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Required Rates of Return

r Alta = 8 .0% + ( 7 %)(1 .29)= 8 .0% + 9 .0% = 1 7. 0% .

r M = 8 .0% + ( 7 %)(1 .00) =15 .0% .

r Am . F. = 8 .0% + ( 7 %)(0 .68) =

12 .8% .r T-bill = 8 .0% + ( 7 %)(0 .00) = 8 .0% .

r Repo = 8 .0% + ( 7 %)(-0 .86) = 2 .0% .

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Ex pected versus Required Returns

^r r Alta 1 7. 4% 1 7. 0% U ndervalued

Market 15 .0 15 .0 Fairly valued

Am . F. 13 .8 12 .8 U ndervalued

T-bills 8 .0 8 .0 Fairly valuedRepo 1 .7 2 .0 Overvalued

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.

.Repo

.Alta

T-bills

.Am . Foam

r M = 15

r RF = 8

-1 0 1 2

.

SML: r i = r RF + (RP M) b ir i = 8% + ( 7 %) b ir i (%)

Risk, b i

SML and Investment Alternatives

Market

2 - 105


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Calculate beta for a portfolio with 50%

Alta and 50% Repo

b p = Weighted average= 0 .5(b Alta ) + 0 .5(b Repo )= 0 .5(1 .29) + 0 .5(-0 .86)= 0 .22 .

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What is the required rate of return

on the Alta/Repo portfolio?

r p = Weighted average r

= 0 .5(1 7 %) + 0 .5(2%) = 9 .5% .

Or use SML:

r p = r RF + (RP M) b p= 8 .0% + 7 %(0 .22) = 9 .5% .

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SML1

Original situation

Required Rateof Return r (%)

SML2

0 0 .5 1 .0 1 .5 2 .0

181511

8

New SML( I = 3%

Impact of Inflation Change on SML

2 - 108Impact of Risk Aversion Change


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r M = 18%r M = 15%

SML1

Original situation

Required Rateof Return (%)

SML2

After increasein risk aversion

Risk, b i

18

15

8

1 .0

( RP M = 3%

p g

2 - 109III. Asset Pricing Models


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Asset Pricing Models

CAPM

Capital Asset Pricing Model

1964, Sharpe, Linter quantifies the risk/return tradeoff


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2 - 111implication


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implication

expected return is a function of

beta

risk free returnmarket return

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Has the CAPM been completely confirmed

or refuted through empirical tests?No . The statistical tests haveproblems that make empiricalverification or rejection virtuallyimpossible .

Investors required returns arebased on future risk, but betas arecalculated with historical data .Investors may be concerned aboutboth stand-alone and market risk .

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CAPM


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CAPM

Security Market Line

Rm Market Portfolio

Rf

0 1 .0 2 .0 Beta

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Capital Asset Pricing Model (CAPM)


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If investors are mainly concerned with the risk of their portfoliorather than the risk of the individual securities in the portfolio,how should the risk of an individual stock be measured?

In important tool is the CAPM .

CAPM concludes that the relevant risk of an individual stock is itscontribution to the risk of a well-diversified portfolio .

CAPM specifies a linear relationship between risk and requiredreturn .

The equation used for CAPM is as follows:K i = K rf + Fi(K m - K rf )

Where:K i = the required return for the individual securityK

rf = the risk-free rate of returnFi = the beta of the individual securityK m = the e xpected return on the market portfolio(K m - K rf ) is called the market risk premium

This equation can be used to find any of the variables listed

above, given the rest of the variables are known.

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CAPM E l


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CAPM Ex ample

F ind the required return on a stock given that the risk-free rate is 8%, the e xpected return on the marketportfolio is 12%, and the beta of the stock is 2 .

K i = K rf + Fi(K m - K rf )K i = 8% + 2(12% - 8%)K i = 16%

Note that you can then compare the required rate of return to the e xpected rate of return . You would onlyinvest in stocks where the e xpected rate of returnexceeded the required rate of return .


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2 - 117


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CAPM tells us size of risk/returntradeoff

CAPM tells use the price of risk

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T i h CAPM


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Testing the CAPM

CAPM overpredicts returns

return under CAPM > actual return

relationship between and return?some studies it is positive

some recent studies argue norelationship (1992 Fama & F rench)

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bl / t ti CAPM


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problems w/ testing CAPM

Roll critique (19 77 )

CAPM not testable

do not observe E (R), only Rdo not observe true R mdo not observe true R f results are sensitive to the sampleperiod

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APT


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APT

Arbitrage Pricing Theory

19 7 6, Ross

assume:several factors affect E (R)

does not specify factors

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i li i


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implications

E (R) is a function of several factors,F

each with its own F

N N332211f ....FFFR )R ( F F F F!


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2 - 125

testing the APT


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testing the APT

how many factors?what are the factors?

1980 Chen, Roll, and Ross

industrial production

inflation

yield curve slopeother yield spreads

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summary


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summary

known risk/return tradeoff

how to measure risk?

how to price risk?neither CAPM or APT are perfect or free of testing problems

both have shown value in asset pricing

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Risk and Return


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Cost of EquityOther models

Gordon Dividend G rowth

ER = D1 + g

P 0E .g . Share price = 2 7 5 pence

Current Div = 8 .25 pence

Historic growth = 9 %8 .99 + .09 = 12 .27

27 5

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Fama- F rench


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3 Factor ModelTo estimate the e xpected returns under APT

Ex pected risk premium, r - r f =b 1 (r factor1 -r f ) + b 2(r factor2 -r f ) +b 3 (r factor3 -r f ) etc

etcSo all we have to do is

Step 1 . Identify a reasonably short list of macroeconomicfactors that could affect stock returns

Step 2. Estimate the e xpected risk premium on each of thesefactors

Step 3 . Measure the sensitivity of each stock to the factors

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Fama- F rench


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3 Factor ModelAbove average returns on

Small sized companies and

High book to market value

R r f = b market (r market factor )+b size (r size factor )

+b book too market (r book to market factor )

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Assignment

Read the article on Investopediaentitled:

Determining Risk and the Risk Pyramid

Terms to K now:

-Risk and Retur n -Ma rgin T r ad ing-S elling Sho rt -Ex-an te

-S ix Func tion s of the $ -Ex-po st

Fm Risk Return 2

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