An investor owns a two-security portfolio consisting of stocks A and B. Stock A\

Question

An investor owns a two-security portfolio consisting of stocks A and B. Stock A's weight is four times that of stock B. There is a 68.26% chance that stock A will exhibit a return between 1.48% and 20.52%, and there is a 95.44% chance that stock B will exhibit a return between -27.6% and 53.6%. Given that the mean returns for stocks A and B are 11% and 13%, respectively, and the portfolio's covariance is -.001, what is the standard deviation of this two-stock portfolio?

(Hints Given: Stock A’s standard deviation = 9.52% --- Stock B’s standard deviation = 20.3%)

Please give a step by step model of how you complete the problem. Thanks!

Explanation / Answer

E(RP) = expected return on the portfolio E(RA) = expected return on Stock A = 0.11 E(RB) = expected return on Stock B =0.13 WA = weight of Stock A in the portfolio WB = weight of Stock B in the portfolio Given, WA = 4WB and we know that WA+WB = 1 => WA = 4/5 =.80 and WB = 0.20 STDA = Standard Deviation of Stock A = 9.52% STDB = Standard Deviation of StockB = 20.3% STDP = Standard Deviation of Portfolio Covariance = -0.001 E(RP) = (WA)*[E(RA)] + (WB)*[E(RB)] = = (0.80)*(0.11) + (0.20)*(0.13) = 0.088 + 0.026 = 0.114 or 11.4% Variance = (WA)^2*(STDA)^2 + (WB)^2*(STDB)^2 + + 2*(WA)*(WB)*(STDA)*(STDB)*[Covariance(RA, RB)] = = (0.80)^2*(0.0952)^2 + (0.20)^2*(0.203)^2 + + 2*(0.80)*(0.20)*(0.0952)*(0.203)*(- 0.001) = = 0.0058 + 0.001648 - 0.00000618 = 0.007441 STDP = sqrt(Variance) = sqrt(0.007441) = 0.086265 or 8.63%

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