You have decided to invest 30 percent in X; 30 percent in Y; and 40 percent in Z

Question

You have decided to invest 30 percent in X; 30 percent in Y; and 40 percent in Z. The probability of the state of the economy is Boom 20%; Normal 55%; and, Bust 25%. The rate of return for stock X is Boom .15; Normal .10; and, Bust .00. The rate of return for stock Y is Boom .35; Normal .10; and, Bust -.30. The rate of return for stock Z is Boom .60; Normal .05; Bust -.40.
   A] What is the portfolio expected return?

   B] If the expected T-bill rate is .75 percent, what is the expected risk premium on the portfolio?

Explanation / Answer

A] Investment In X =0.3(30%) , Y =0.3(30%) and Z =0.4(40%)

Portfolio return in boom= 0.3(0.15)+0.3(0.35)+0.4(0.60) = 0.045+0.105+0.24 =0.39

Portfolio return in Normal = 0.3(0.10)+0.3(0.10)+0.4(0.05) = 0.03+0.03+0.02 =0.08

Portfolio return in Bust = 0.3(0.25)+0.3(0.00)+0.4(-0.04) = 0.075+0.00 - 0.016 =0.059

Portfolio expected return = 0.20(0.39)+0.55(0.08)+0.25(0.059) =0.078+0.044+0.01475 =0.13675

Portfolio Expected Return is 13.675%

B] If T-bill rate is 0.75, which means risk free rate is 0.75% or 0.0075

Risk Premium = Expected Return - Risk free Rate

Risk Premium = 13.675 % -0.75% or (0.13675 - 0.0075)

Risk Premium = 12.925%

State Probabilty x (30%) Y(30%) Z(40%) Boom 0.20 0.15 0.35 0.60 Normal 0.55 0.10 0.10 0.05 Bust 0.25 0.00 -0.30 -0.04

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