Consider an economy in which the CAPM holds. The market portfolio (M) offers an

Question

Consider an economy in which the CAPM holds. The market portfolio (M) offers an expected return of 10% and a standard deviation of 12%. The risk-free rate (F) is equal to 4%. You have the following information about portfolio (P) composed of 3 stocks:

a) Compute the beta of the three stocks.

b) Compute the expected return of the three stocks.

c) Compute the expected return and beta of portfolio P.

d) Find an efficient portfolio that has the same expected return as P. What is the beta of this portfolio? Compute its standard deviation and correlation with the market.

Stock Portfolio Weight Standard Deviation Correlation with M A 0.24 0.15 0.4 B 0.36 0.09 0.2 C 0.40 0.24 0.8

Explanation / Answer

(.24*.5)x.36*.15)X(.40*1.6) =.184

Beta =Covim/Varim   = standard deviationi X standard deviationm X Covim/standard diviationm2 = standard deviationi X Covim/standard deviation m a) stock standard deviationi Covim standard deviationm beta A 0.15 0.4 0.12 0.5 B 0.09 0.2 0.12 0.15 C 0.24 0.8 0.12 1.6 B)                 expected Return of stocks E(R)=Rf+(Rm-Rf) stocks Rf Rm (Rm-Rf) ecpected return A 0.04 0.5 0.1 0.06 0.07 B 0.04 0.15 0.1 0.06 0.049 C 0.04 1.6 0.1 0.06 0.136 c) Expected return of portfolio P (.24*.07)X(.36*.049)X(.40*.136)=.08884 that rounded in to .089 Expected beta of portfolio P d) efficient portfolio that has almost same expecter return is stock A beta of this portfolio is 0 .5 standerd deviatin is .15 &correlation with market is .4

(.24*.5)x.36*.15)X(.40*1.6) =.184

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