Consider the following information about three stocks; If your portfolio is inve

Question

Consider the following information about three stocks; If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return? The variance? The standard deviation? If the expected T-bill rate is 3.80 percent, what is the expected risk premium o the portfolio? If the expected inflation rate is 3.50 percent, what are the approximate and exa expected real returns on the portfolio? What are the approximate and exact expected real risk premiums on the portfolio?

Explanation / Answer

A)

E(A) = .35*24 + .5*17 + 0 = 16.9%

E(B) = .35*36+.5*13 - .15*28 = 14.9%

E(C) = .35*55+.5*9 - .15*45 = 17%

E(Rportfolio) = .4*16.9 + .4*14.9 + .2*17 = 16.12%

boom: R(P) = .4*24+.4*36+.2*55 = 35%

normal: R(P) = .4*17 + .4*13 + .2*9 = 13.8%

bust: R(P) = .4*0 -.4*28 - .2*45 = -20.2%

hence E(Rportfolio) = .35*35 + .5*13.8 - .15*20.2 = 16.12%

variance = (.35*(35-16.12)^2 + .5*(13.8-16.12)^2 + .15*(-20.2-16.12)^2) = 325.32%

SD = sqrt(varince) = 18.04%

B)expected T-bill rate = 3.80%

expected risk premium of the portfolio = E(Rportfolio) - 3.80

= 16.12 - 3.80 = 12.32%

C) expected inflatoin rate = 3.5%

approximate expected real return on portfolio = 16.12-3.5 = 12.62%

exact expected real return = (1+.16.12)/(1+.035) - 1 = 12.19%

approximate expected real risk premium on portfolio = 16.12-3.8 = 12.32%

exact expected real risk premium on portfolio =  (1+.16.12)/(1+.038) - 1 = 11.87%

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