(Computing the standard deviation for a portfolio of two risky investments) Mary

Question

(Computing the standard deviation for a portfolio of two risky investments) Mary Guilott recently graduated from Nichols State University and is anxious to begin investing her meager savings as a way of applying what she has learned in business school. Specifically, she is evaluating an investment in a portfolio comprised of two firms' common stock. She has collected the following information about the common stock of Firm A and Firm B a. If Mary invests half her money in each of the two common stocks, what is the portfolio's expected rate of return and standard deviation in port olio return? Answer part a where the correlation between the two common stock investments is equal to zero. c. Answer part a where the correlation between the two common stock investments is equal to 1 d. Answer part a where the correlation between the two common stock investments is equal to -1 e. Using your responses to questions a d, describe the relationship between the correlation and the risk and return of the portfolio in Firm B's common stock and the co relation between the two stocks is 0.70 then the expected rate o return in the portfolio is Round to two a. lf Mary decides to invest 50% o her money n Fim As common stock and 50 decimal places.) %

Explanation / Answer

a)

E(P) = Wa * Ra + Wb * Rb

   = 0.5*0.13 + 0.5*0.17 = 0.15 = 15%

Variance = w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*(RA)*(RB)

   = 0.52*0.192 + 0.52*0.222 + 2*0.5*0.5*0.7*0.19*0.22 = 0.05857

SD = sqrt(Variance) = sqrt(0.05857) = 0.2420 = 24.20%

Expected return is constant from a-d

b)

Variance = w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*(RA)*(RB)

   = 0.52*0.192 + 0.52*0.222 + 2*0.5*0.5*0.0*0.19*0.22 = 0.04394

SD = sqrt(Variance) = sqrt(0.05857) = 0.2096 = 20.96%

c)

Variance = w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*(RA)*(RB)

   = 0.52*0.192 + 0.52*0.222 + 2*0.5*0.5*1.0*0.19*0.22 = 0.06484

SD = sqrt(Variance) = sqrt(0.05857) = 0.2546 = 25.46%

d)

Variance = w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*(RA)*(RB)

   = 0.52*0.192 + 0.52*0.222 + 2*0.5*0.5*(-1.0)*0.19*0.22 = 0.02304

SD = sqrt(Variance) = sqrt(0.05857) = 0.1518 = 15.18%

e)

As corelation coefficient is getting lower risk is getting lower, expeced return will be constant as weights are same

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