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Transcript of Fm Risk Return 2
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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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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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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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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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Annualized R:(1 .00 42) 12 - 1 = .0 52 = 5.2%
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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
Tbill, 1 month holding period
buy for $9478,sell for $9628
1 month R:
Annualized R
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Class work 2: Calculating R
Tbill, 1 month holding period
buy for $9408,sell for $9828
1 month R:
Annualized R
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Class work 3: Calculating R
100 shares MSFT, 6 months
buy for $24.125, sell for $25.875$.00 dividends
6 month R:
Annualized R
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Class work 4: Calculating R
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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Visual description of variance betweenactual and forecasted returns
But what is the variance?Umbrellas
Cider
ER
ER
ER
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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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Probability distribution
Rate of return (%)50150-20
Stock X
Stock Y
Which stock is riskier? Why?
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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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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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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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The History of Returns: Real ReturnsThe Real Value of $1 Invested in Stocks, Treasury Bonds, and
B ills
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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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Percentage Returns on B ills, Bonds, andStocks, 19002006
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Table 6 .2 Risk Premiums for Stocks,Bonds, and B ills, 19002006
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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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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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Portfolio Risk and Return
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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Portfolio Risk and Return
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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Portfolio Risk and Return
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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Portfolio Risk and Return
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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Portfolio Risk and Return
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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Portfolio Risk and Return
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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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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Portfolio Risk and Return
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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Portfolio Risk and Return
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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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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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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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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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 .
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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
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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
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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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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
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Risk Premiums Around the World
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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
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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
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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 .
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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?
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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.^
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Large
0 15
Prob .
2
1
W1 } 35% ; WLarge } 20% .Return
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# Stocks in Portfolio
10 20 30 40 2,000+
Company Specific(Diversifiable) Risk
Market Risk
20
0
Stand-Alone Risk, Wp
Wp (%)35
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2 - 81Ex ample
Choose stocks from NYSElistings
Go from 1 stock to 20 stocks
Reduce risk by 40-50%
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# assets
systematicrisk
unsystematicrisk
totalrisk
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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= +.
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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 .
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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?
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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
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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
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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
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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?
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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 )
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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.
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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%
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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
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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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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
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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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113
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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114
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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115
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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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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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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127
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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128
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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129
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