Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom .15 .39 .49 .29 Good .55 .15 .20 .08 Poor .25 –.01 –.09 –.07 Bust .05 –.20 –.24 –.10 Your portfolio is invested 24 percent each in A and C, and 52 percent in B. What is the expected return of the portfolio?

15.68%

Explanation:

Now to get the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the expected return in an equally weighted portfolio, we can sum the returns of each asset and the we divide it by the number of assets, so the expected return of the portfolio in each state of the economy will be :

Boom: RP= (.13 + .21 + .39) / 3 = .2433, or 24.33%

Bust: RP= (.15 + .05 −.06) / 3 = .0467, or 4.67%

Now to get the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum. In so doing, we get

E(RP) = .56(.2433) + .44(.0467)

=.1568, or 15.68%

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