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Capital Asset Pricing and Arbitrage Pricing Theory Department of Banking and Finance SPRING 2007-08 by Asst. Prof. Sami Fethi

Capital Asset Pricing and Arbitrage Pricing Theory

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Department of Banking and Finance. SPRING 200 7 -0 8. Capital Asset Pricing and Arbitrage Pricing Theory. by Asst. Prof. Sami Fethi. Capital Asset Pricing Model (CAPM). - PowerPoint PPT Presentation

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Page 1: Capital Asset Pricing and Arbitrage Pricing Theory

Capital Asset Pricing and Arbitrage Pricing Theory

Department of Banking and Finance

SPRING 2007-08

by

Asst. Prof. Sami Fethi

Page 2: Capital Asset Pricing and Arbitrage Pricing Theory

2 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)

The asset pricing models aim to use the concepts of portfolio valuation and market equilibrium in order to determine the market price for risk and appropriate measure of risk for a single asset.

Capital Asset Pricing Model (CAPM) has an observation that the returns on a financial asset increase with the risk. CAPM concerns two types of risk namely unsystematic and systematic risks. The central principle of the CAPM is that, systematic risk, as measured by beta, is the only factor affecting the level of return.

Page 3: Capital Asset Pricing and Arbitrage Pricing Theory

3 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) was developed independently by Sharpe (1964), Lintner (1965) and Mossin (1966) as a financial model of the relation of risk to expected return for the practical world of finance.

CAPM is originally depending on the mean variance theory which was demonstrated by Markowitz’s portfolio selection model (1952) aiming higher average returns with lower risk.

Page 4: Capital Asset Pricing and Arbitrage Pricing Theory

4 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)

Equilibrium model that underlies all modern financial theory

Derived using principles of diversification with simplified assumptions

Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

Page 5: Capital Asset Pricing and Arbitrage Pricing Theory

5 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM) From the point that most of the investors think that the

variance or standard deviation of their portfolio’s return will enable them to quantify the risk, portfolio selection model is used in order to find the efficient portfolios and secondly to generate an equation that relates the risk of an asset to its expected return.

The reason for this is that portfolios are expected to have maximum return given the variance of future returns. Therefore, Mean Variance Analysis is one of the tools for achieving higher average returns with lower risk and as a second tool Capital Asset Pricing Model’s main parameters are depending on mean and variance of returns.

Page 6: Capital Asset Pricing and Arbitrage Pricing Theory

6 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)

Moreover, CAPM requires that in the equilibrium the market portfolio must be an efficient portfolio. One way to establish its efficiency is to argue that if investors have homogenous expectations, the set of optimal portfolios they would face would be using the same values of expected returns, variances and co variances.

Therefore, the efficiency of the market portfolio and the CAPM are joint hypothesis and it is not possible to test the validity of one without the other (Roll, 1977).

Page 7: Capital Asset Pricing and Arbitrage Pricing Theory

7 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

CAPM Assumptions-SummaryCAPM Assumptions-Summary

Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes, and transaction costs Information is costless and available to all

investors Investors are rational mean-variance optimizers Homogeneous expectations

Page 8: Capital Asset Pricing and Arbitrage Pricing Theory

8 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

AssumptionsAssumptions

Asset markets are frictionless and information liquidity is high.

All investors are price takers; so that, they are not able to influence the market price by their actions.

All investors have homogenous expectations about asset returns and what the uncertain future holds for them.

All investors are risk averse and they operate in the market rationally and perceive utility in terms of expected return.

Page 9: Capital Asset Pricing and Arbitrage Pricing Theory

9 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Assumptions (cont.)Assumptions (cont.)

All investors are operating in perfect markets which enables them to operate without tax payments on returns and without cost of transactions entailed in trading securities.

All securities are highly divisible for instance they can be traded in small parcels (Elton and Gruber, 1995, p.294).

All investors can lend and borrow unlimited amount of funds at the risk-free rate of return.

All investors have single period investment time horizon in means of different expectations from their investments leads them to operate for short or long term returns from their investments.

Page 10: Capital Asset Pricing and Arbitrage Pricing Theory

10 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Resulting Equilibrium ConditionsResulting Equilibrium Conditions

All investors will hold the same portfolio for risky assets – market portfolio

Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

Risk premium on the market depends on the average risk aversion of all market participants

Risk premium on an individual security is a function of its covariance with the market

Page 11: Capital Asset Pricing and Arbitrage Pricing Theory

11 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

E(r)E(r)

E(rE(rMM))

rrff

MMCMLCML

mm

Capital Market LineCapital Market Line

Page 12: Capital Asset Pricing and Arbitrage Pricing Theory

12 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Capital Market LineCapital Market Line

If a fully diversified investor is able to invest in the market portfolio and lend or borrow at the risk free rate of return, the alternative risk and return relationships can be generally placed around a market line which is called the Capital Market Line (CML).

Page 13: Capital Asset Pricing and Arbitrage Pricing Theory

13 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Capital Market LineCapital Market Line

CML: E(rp)= rF+ λσp

 E(rp): Expected return on portfolio

rF : Return on the risk free assetλ : Market price riskσp : Market portfolio risk

Page 14: Capital Asset Pricing and Arbitrage Pricing Theory

14 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

M = Market portfoliorf = Risk free rate

E(rM) - rf = Market risk premium

E(rM) - rf = Market price of risk

= Slope of the CAPM

Slope and Market Risk PremiumSlope and Market Risk Premium

MM

Page 15: Capital Asset Pricing and Arbitrage Pricing Theory

15 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Expected Return and Risk on Individual Expected Return and Risk on Individual SecuritiesSecurities

The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio

Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio

Page 16: Capital Asset Pricing and Arbitrage Pricing Theory

16 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Security Market LineSecurity Market Line

The SML shows the relationship between risk measured by beta and expected return. The model states that the stock’s expected return is equal to the risk-free rate plus a risk premium obtained by the price of the risk multiplied by the quantity of the risk.

Page 17: Capital Asset Pricing and Arbitrage Pricing Theory

17 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

E(r)E(r)

E(rE(rMM))

rrff

SMLSML

MMßßßß = 1.0= 1.0

Security Market LineSecurity Market Line

Page 18: Capital Asset Pricing and Arbitrage Pricing Theory

18 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

SML RelationshipsSML Relationships

= [COV(ri,rm)] / m

2

Slope SML = E(rm) - rf

= market risk premium

SML = rf + [E(rm) - rf]

(σSpS,M) is the market price of risk

SML: E(rS)=rF+ λσSpS,M

Page 19: Capital Asset Pricing and Arbitrage Pricing Theory

19 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Sample Calculations for SMLSample Calculations for SML

E(rm) - rf = .08 rf = .03

x = 1.25

E(rx) = .03 + 1.25(.08) = .13 or 13%

y = .6

e(ry) = .03 + .6(.08) = .078 or 7.8%

Page 20: Capital Asset Pricing and Arbitrage Pricing Theory

20 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

E(r)E(r)

RRxx=13%=13%

SMLSML

mm

ßß

ßß1.01.0

RRmm=11%=11%RRyy=7.8%=7.8%

3%3%

xxßß1.251.25

yyßß.6.6

.08.08

Graph of Sample CalculationsGraph of Sample Calculations

Page 21: Capital Asset Pricing and Arbitrage Pricing Theory

21 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Disequilibrium ExampleDisequilibrium Example

Suppose a security with a beta of 1.25 is offering expected return of 15%

According to SML, it should be 13%Underpriced: offering too high of a rate of

return for its level of risk

Page 22: Capital Asset Pricing and Arbitrage Pricing Theory

22 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

E(r)E(r)

15%15%

SMLSML

ßß1.01.0

RRmm=11%=11%

rrff=3%=3%

1.251.25

Disequilibrium ExampleDisequilibrium Example

Page 23: Capital Asset Pricing and Arbitrage Pricing Theory

23 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Security Characteristic LineSecurity Characteristic LineExcessExcess Returns (i) Returns (i)

SCLSCL

..

..

........

.. ..

.. ....

.. ....

.. ..

.. ....

......

.. ..

.. ....

.. ....

.. ..

.. ....

.. ....

.. ..

..

.. ...... .... .... ..

ExcessExcess returns returnson market indexon market index

RRii = = ii + ß + ßiiRRmm + e + eii

Page 24: Capital Asset Pricing and Arbitrage Pricing Theory

24 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Using the Text Example p. 231, Table 7.5Using the Text Example p. 231, Table 7.5

Jan.Jan.Feb.Feb.....DecDecMeanMeanStd DevStd Dev

5.415.41-3.44-3.44

..

..2.432.43-.60-.604.974.97

7.247.24.93.93

..

..3.903.901.751.753.323.32

ExcessExcessMkt. Ret.Mkt. Ret.

ExcessExcessGM Ret.GM Ret.

Page 25: Capital Asset Pricing and Arbitrage Pricing Theory

25 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Estimated coefficientEstimated coefficientStd error of estimateStd error of estimateVariance of residuals = 12.601Variance of residuals = 12.601Std dev of residuals = 3.550Std dev of residuals = 3.550R-SQR = 0.575R-SQR = 0.575

ßß

-2.590-2.590(1.547)(1.547)

1.13571.1357(0.309)(0.309)

rrGMGM - r - rf f = + ß(r= + ß(rmm - r - rff))

Regression Results:Regression Results:

Page 26: Capital Asset Pricing and Arbitrage Pricing Theory

26 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Arbitrage Pricing TheoryArbitrage Pricing Theory

Arbitrage Pricing Theory was developed by Stephen Ross (1976). His theory begins with an analysis of how investors construct efficient portfolios and offers a new approach for explaining the asset prices and states that the return on any risky asset is a linear combination of various macroeconomic factors that are not explained by this theory namely.

Similar to CAPM it assumes that investors are fully diversified and the systematic risk is an influencing factor in the long run. However, unlike CAPM model APT specifies a simple linear relationship between asset returns and the associated factors because each share or portfolio may have a different set of risk factors and a different degree of sensitivity to each of them.

Page 27: Capital Asset Pricing and Arbitrage Pricing Theory

27 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

The Assumptions of APTThe Assumptions of APT Capital asset returns’ properties are consistent

with a linear structure of the factors. The returns can be described by a factor model.

Either there are no arbitrage opportunities in the capital markets or the markets have perfect competition.

The number of the economic securities are either inestimable or so large that the law of large number can be applied that makes it possible to form portfolios that diversify the firm specific risk of individual stocks.

Lastly, the number of the factors can be estimated by the investor or known in advance (K. C. John Wei, 1988)

Page 28: Capital Asset Pricing and Arbitrage Pricing Theory

28 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

The Model of APTThe Model of APT

k Ri= E( Ri )+ ∑ δj βij+ εi

j=1 where,  R i : The single period expected rate on

security i , i =1,2….,n δj : The zero mean j factor common to the

all assets under consideration βij : The sensitivity of security i’s returns to

the fluctuations in the j th common factor portfolio

εi : A random of i th security that constructed to have a mean of zero.

Page 29: Capital Asset Pricing and Arbitrage Pricing Theory

29 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Arbitrage Pricing Theory-brieflyArbitrage Pricing Theory-briefly

• Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit

Since no investment is required, an investor can create large positions to secure large levels of profit

In efficient markets, profitable arbitrage opportunities will quickly disappear

Page 30: Capital Asset Pricing and Arbitrage Pricing Theory

30 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Arbitrage Example Arbitrage Example

Current Expected Standard

Stock Price$ Return% Dev.%

A 10 25.0 29.58

B 10 20.0 33.91

C 10 32.5 48.15

D 10 22.5 8.58

Page 31: Capital Asset Pricing and Arbitrage Pricing Theory

31 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Arbitrage PortfolioArbitrage Portfolio

Mean Stan. Correlation

Return Dev. Of Returns

Portfolio

A,B,C 25.83 6.40 0.94

D 22.25 8.58

Page 32: Capital Asset Pricing and Arbitrage Pricing Theory

32 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Arbitrage Action and ReturnsArbitrage Action and Returns

E. Ret.E. Ret.

St.Dev.St.Dev.

* * PP* * DD

Short 3 shares of D and buy 1 of A, B & C to form Short 3 shares of D and buy 1 of A, B & C to form PP

You earn a higher rate on the investment than You earn a higher rate on the investment than you pay on the short saleyou pay on the short sale

Page 33: Capital Asset Pricing and Arbitrage Pricing Theory

33 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

APT and CAPM ComparedAPT and CAPM Compared

APT applies to well diversified portfolios and not necessarily to individual stocks

With APT it is possible for some individual stocks to be mispriced - not lie on the SML

APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio

APT can be extended to multifactor models

Page 34: Capital Asset Pricing and Arbitrage Pricing Theory

34 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-market riskExample-market risk

Suppose the risk free rate is 5%, the average investor has a risk-aversion coefficient of A* is 2, and the st. dev. Of the market portfolio is 20%.

A) Calculate the market risk premium. B) Find the expected rate of return on the market. C) Calculate the market risk premium as the risk-

aversion coefficient of A* increases from 2 to 3. D) Find the expected rate of return on the market

referring to part c.

Page 35: Capital Asset Pricing and Arbitrage Pricing Theory

35 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-market riskAnswer-market risk

A) E(rm-rf)=A*σ2m

Market Risk Premium =2(0.20)2=0.08B) E(rm) = rf +Eq. Risk prem

= 0.05+0.08=0.13 or 13%

C) Market Risk Premium =3(0.20)2=0.12D) E(rm) = rf +Eq. Risk prem

= 0.05+0.12=0.17 or 17%

Page 36: Capital Asset Pricing and Arbitrage Pricing Theory

36 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-risk premiumExample-risk premium

Suppose an av. Excess return over Treasury bill of 8% with a st. dev. Of 20%.

A) Calculate coefficient of risk-aversion of the av. investor.

B) Calculate the market risk premium as the risk-aversion coefficient is 3.5

Page 37: Capital Asset Pricing and Arbitrage Pricing Theory

37 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-risk premiumAnswer-risk premium

A) A*= E(rm-rf)/ σ2m =0.085/0.202=2.1

B) E(rm)-rf =A*σ2m =3.5(0.20)2=0.14 or 14%

Page 38: Capital Asset Pricing and Arbitrage Pricing Theory

38 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-ERORExample-EROR

Suppose the risk premium of the market portfolio is 9%, and the estimated beta is 1.3. The risk premium for stock is 1.3 times the market risk premium.

A) Calculate expected ROR if T-bill rate is 5%. B) Calculate ROR and the risk premium if the

estimated of the beta is 1.2 for the company. C) Find the company’s risk premium if market

risk premium and beta are 8% and 1.3 respectively.

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39 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-ERORAnswer-EROR

A) E(rc)=rf+βc[E(rm-rf)]

=5%+1.3(9%)=16.7%B) E(rc)=rf+βc[E(rm-rf)]

=5%+1.2(9%)=15.8% 1.2(9%)=10.8% risk premium C) 1.3(8%)=10.4%

Page 40: Capital Asset Pricing and Arbitrage Pricing Theory

40 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-Portfolio beta and risk premiumExample-Portfolio beta and risk premium

Consider the following portfolio:

A) Calculate the risk premium on each portfolio

B) Calculate the total portfolio if Market risk premium is 7.5%.

Asset BetaRisk

prem.Portfolio Weight

X 1.2 9% 0.5

Y 0.8 6 0.3

Z 0.0 0 0.2

Port. 0.84 1.0

Page 41: Capital Asset Pricing and Arbitrage Pricing Theory

41 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-Portfolio beta and risk premiumAnswer-Portfolio beta and risk premium

A) (9%) (0.5)=4.5 (6%) (0.3)=1.8 =6.3%B) 0.84(7.5)=6.3%

Page 42: Capital Asset Pricing and Arbitrage Pricing Theory

42 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-risk premiumExample-risk premium

Suppose the risk premium of the market portfolio is 8%, with a st. dev. Of 22%.

A) Calculate portfolio’s beta. B) Calculate the risk premium of the portfolio

referring to a portfolio invested 25% in x motor company with beta 0f 1.15 and 75% in y motor company with a beta of 1.25.

Page 43: Capital Asset Pricing and Arbitrage Pricing Theory

43 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-risk premiumAnswer-risk premium

A) βy= 1.25, βx= 1.15

βp=wy βy+ wx βx

=0.75(1.25)+0.25(1.15)=1.225

B) E(rp)-rf=βp[E(rm)-rf]

=1.225(8%)=9.8%

Page 44: Capital Asset Pricing and Arbitrage Pricing Theory

44 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-SMLExample-SML

Suppose the return on the market is expected to be 14%, a stock has a beta of 1.2, and the T-bill rate is 6%.

A) Calculate the expected return of the SML B) If the return is 17%, calculate alpha of the

stock

Page 45: Capital Asset Pricing and Arbitrage Pricing Theory

45 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-SMLAnswer-SML A) E(rp)=rf+β[E(rm)-rf]

=6+1.2(14-6)=15.6%E(r)E(r)

17%17% SMLSML

ßß1.01.0

15.6%15.6%

14%14%

6%6%

1.21.2

MM

StockStock

α=α= 17-15.6=1.417-15.6=1.4

Page 46: Capital Asset Pricing and Arbitrage Pricing Theory

46 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-SMLExample-SML Stock xyz has an expected return of 12% and risk of

beta is 1.5. Stock ABC is expected to return 13% with a beta of 1.5. The market expected return is 11% and rf=5%.

A) Based on CAPM, which stock is a better buy? B) What is the alpha of each stock? C) Plot the relevant SML of the two stocks D) rf is 8% ER on the market portfolio is 16%, and

estimated beta is 1.3, what is the required ROR on the project?

E) If the IRR of the project is 19%, what is the project alpha?

Page 47: Capital Asset Pricing and Arbitrage Pricing Theory

47 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-SMLAnswer-SML

A and B) α=E(r)-{rf+β[E(rm)-rf]}

αXYZ= 12-{5+1.0[11-5]}=1– UNDERVALUED

αABC= 13-{5+1.5[11-5]}= -1– OVERVALUED

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Ch 7: CAPM and APT

Answer-SML-CAnswer-SML-C

E(r)E(r)

14%14% SMLSML

ßß1.01.0

13%13%

12%12%

5%5%

1.51.5

xyzxyz

StockStock

α=α= 13-14=-113-14=-1

ααABCABC

=13-12=1=13-12=1

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49 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-SMLAnswer-SML

D) E(r)={rf+β[E(rm)-rf]}

= 8+1.3[16-8]=18.4%E) If the IRR of the project is 19%, it is

desirable. However, any project with an IRR by using similar beta is less than 18.4% should be rejected.

Page 50: Capital Asset Pricing and Arbitrage Pricing Theory

50 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-SMLExample-SML

Consider the following table:

Market Return

Aggressive stock

Defensive stock

5% 2% 3.5%

20 32 14

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51 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Example-SML cont..Example-SML cont..

A) What are the betas of the two stock? B) What is the E(ROR) on each stock if Market

return is equally likely to be 5% or 20%? C) If T-bill rate is 8% and Market return is equally

likely to be 5% or 20%, draw SML for the economy?

D) Plot the two securities on the SML graph and show the alphas

Page 52: Capital Asset Pricing and Arbitrage Pricing Theory

52 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

Answer-SMLAnswer-SML

A) βA=2-32/5-20=2 βB=3.5-14/5-20=0.7

B) E(rA)={rf+β[E(rm)-rf]}

=0.5(2%+32%)=17% =0.5(3.5%+14%)=8.75%

Page 53: Capital Asset Pricing and Arbitrage Pricing Theory

53 Investment Management © 2005, Sami Fethi, EMU, All Right Reserved.

Ch 7: CAPM and APT

The EndThe End

Thanks