State of Economy Probability of State of Economy Rate of Return if State Occurs Recession .32 − .11 Boom .68 .23 Calculate the expected return. 2) You own a stock portfolio invested 33 percent in Stock Q, 20 percent in Stock R, 37 percent in Stock S, and 10 percent in Stock T. The betas for these four stocks are 1.02, 1.08, 1.48, and 1.93, respectively. What is the portfolio beta

1) Expected return is 12.12%

2) Portfolio beta is 1.2932

Explanation:

1)

The expected return can be calculated by multiplying the return in a particular state of economy by the probability of that state occuring.

The expected return = (0.32 * -0.11) + 0.68 * 0.23

Expected return = 0.1212 or 12.12%

b)

The portfolio beta is the the systematic riskiness of the portfolio that is unavoidable. The portfolio beta is the weighted average of the individual stock betas that form up the portfolio.

Thus the portfolio beta will be,

Portfolio beta = 0.33 * 1.02 + 0.2 * 1.08 + 0.37 * 1.48 + 0.1 * 1.93

Portfolio beta = 1.2932

a) Expected Return 12.12% b) Portfolio Beta 1.29

Explanation:

Expected return is calculated by sum of expected returns and the probability of the outcome

E(R) = (0.32*-0.11) + (0.68*0.23)

       =-0.0352 + 0.1564

        =0.1212/12.12%

The beta of a portfolio equals the sum of weighted average of the beta for all individual stocks held in the portfolio

Pβ =(Wq*βq)+(Wr*βr)+(Ws*βs)+(Wt*βt)

      =(0.33*1.02)+(0.20*1.08)+(0.37*1.48)+(0.10*1.93)

       =1.29

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