You have just invested in a portfolio of three stocks. The amount of money that you invested in each stock and its beta are summarized below. Stock Investment Beta A $220,000 1.49 B 330,000 0.61 C 550,000 1.35 Calculate the beta of the portfolio and use the Capital Asset Pricing Model (CAPM) to compute the expected rate of return for the portfolio. Assume that the expected rate of return on the market is 14 percent and that the risk-free rate is 6 percent.

Beta of portfolio=1.16

Expected return=15.28%

Explanation:

Total investment=$220,000+$330,000+$550,000=$1,100,000

Beta of portfolio=(220,000/1,100,00)*1.49+(330,000/1,100,000)*.61+(550,000/1,100,000)*1.35=1.16

Ra=Rf+(Rm-Rf)*Beta of securities

Ra=Expected return?

Rf=risk free return=6%

Rm=Market return=14%

Ba=1.16

Ra=6%+(14%-6%)*1.16

Ra=15.28%    

a) Beta is 1.16 B)The expected return of the portfolio is 15.28%

Explanation:

Beta of a portfolio is given by the weighted sum of individual asset betas

We know the investment in each assets so we need to find the weights of each asset in the portfolio

Total invested= 220000+330000+550000=$1100000

Proportions in each

A = 220000/1100000=0.2, B =330000/1100000=0.3, C=550000/110000=0.5

Beta of the portfolio

= Wa *Ba+Wb*Bb+Wc*Bc

=0.2*1.49+0.3*0.61+0.5*1.35

=1.156/1.16

B ) Use the capital asset pricing model to calculate the expected rate of return

RM=14%, RF=6% Beta= 1.16

ER= RF+B(RM-RF)

    =6%+1.16(14%-6%)

     =15.28

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