State of probability of economy 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 a. your portfolio is invested 24 percent each in a and c, and 52 percent in b. what is the expected return of the portfolio? (do not round intermediate calculaitons. ent

0.12392 or 12.39%

Explanation:

Expected return (Boom):

= Sum of (Probability × Rate of return) of all the stocks

= 0.24(0.39) + 0.52(0.49) + 0.24(0.29)

= 0.418 or 41.80%

Expected return (Good):

= Sum of (Probability × Rate of return) of all the stocks

= 0.24(0.15) +0 .52(0.20) + 0.24(0.08)

= 0.1592 or 15.92%

Expected return (Poor):

= Sum of (Probability × Rate of return) of all the stocks

= 0.24(-0.01) +0 .52(–0.09) +0.24(–0.07)

= -0.066 or -6.60%

Expected return (Bust):

= Sum of (Probability × Rate of return) of all the stocks

= 0.24(–0.20) + 0.52(–0.24) + 0.24(–0.10)

= -0.1968 or -19.68%

Hence,

The expected return of the portfolio is as follows:

E(Rp) = Sum of (Probability of state of economy × Expected return) of all the state of economy

         = 0.15(0.418) + 0.55(0.1592) + 0.25(-0.066) + 0.05(-0.1968)

         = 0.12392 or 12.39%