Consider the following information on a portfolio of three stocks: If your portf

Question

Consider the following information on a portfolio of three stocks: If your portfolio is invested 36 percent each in A and B and 28 percent in C, what is the portfolio's expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places (e.g., 32.16161) and input your other answers as a percentage rounded to 2 decimal places (e.g., 32.16).) If the expected T-bill rate is 3.85 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Explanation / Answer

A) p(boom) = 0.13 and p(normal)=0.53 and p(Bust)=0.34 (Note that probabilities always add up to 1)

E(Ra) = 0.13 × 0.04 + 0.53 × 0.12 + 0.34*0.18 = 0.13(13%)
E(Rb) = 0.13 × 0.34 + 0.53 × 0.14 - 0.34*0.13 = 0.0742(7.42%)
E(Rc) = 0.13 × 0.58 + 0.53 × 0.22 - 0.34*0.37 = 0.0662(6.62%)

  SD(RA) = [0.13 × (0.04-0.13)^2 + 0.53 × (0.12-0.13)^2 + 0.34 × (0.18 - 0.13)^2]^0.5= 0.04423(4.423%)
SD(RB) = [0.13 × (0.34-0.0742)^2 + 0.53 × (0.14-0.0742)^2 + 0.34 × (-0.13 - 0.0742)^2]^0.5= 0.1602(16.02%)
SD(RC) = [0.13 × (0.58-0.0662)^2 + 0.53 × (0.22-0.0662)^2 + 0.34 × (-0.37 - 0.0662)^2]^0.5= 0.3340(33.4%)

Portfolio weights: WA=0.36 and WB=0.36 and WC=0.28:
E(RP) = 0.36 × 0.13 + 0.36 × 0.0742 + 0.28 × 0.0662= 0.092048(i.e 9.20%)

COV (RA,RB) = 0.13 × (0.04-0.13)*(0.34-0.0742) + 0.53 × (0.12-0.13)*(0.14-0.0742) + 0.34 × (0.18 - 0.13)*(-0.13 - 0.0742) = 1.0774
COV (RB,RC) = 0.13 × (0.34-0.0742)*(0.58-0.0662) + 0.53 × (0.14-0.0742)*(0.22-0.0662) + 0.34 × (-0.13 - 0.0742)* (-0.37 - 0.0662) = 0.0534
COV (RA,RC) = 0.13 × (0.04-0.13)*(0.58-0.0662) + 0.53 × (0.12-0.13)*(0.22-0.0662) + 0.34 × (0.18 - 0.13)* (-0.37 - 0.0662) = -0.014242

VAR(RP) = (0.36 × 0.04423)^2 + (0.36 × 0.1602)^2+ (0.28 × 0.3340)^2 + 2 × 0.36 × 0.36*(-0.00347) + 2 × 0.36 × 0.28*(0.0534) + 2 × 0.36 × 0.28*(-0.014242)
  =0.29948

SD = square root of Var = 0.29948^0.5 = 0.54724 = 54.72%

B)

Risk premium on the portfolio = Portfolio return - Risk free return(or T bill rate for 1 year) = 9.20- 3.85 = 5.35%

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