The following are estimates for two stocks. The market index has a standard devi

Question

The following are estimates for two stocks. The market index has a standard deviation of 25% and the risk-free rate is 9%. What are the standard deviations of stocks A and 8? (Do not round intermediate calculations. Enter your responses as decimal numbers rounded to 2 decimal places). Suppose that we were to construct a portfolio with proportions: Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio. (Do not round intermediate calculations. Enter your answer for Beta in numbers, not in percentage. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

Standard deviation of Stock A = 28% (given)
Standard deviation of Stock B = 40%

Expected Return of Portfolio => (0.25 x 0.08) + (0.50 x 0.16) + (0.25 x 0.09) = 0.1225 or 12.25%

Beta of Portfolio => (0.25 x 1) + (0.50 x 1.6) + (0.25 x 0) = 1.05

Standard Deviation of Portfolio:
Variance of this portfolio = sP2= bP2sM2+ s2(eP)
where bP2sM2 is the systematic component and s2(eP) is the non-systematic component. Since the residuals, ei are uncorrelated, the non-systematic variance is:

s2(eP) = wA2s2 (eA) +wB2s2(eB) + wf2s2(ef)

Systematic risk = b*sM

Systematic risk of Stock A = 1 x 0.25 = 0.25
Non-systematic variance of Stock A = (0.282 – 0.252) = 0.0159

Systematic risk of Stock B = 1.6 x 0.25 = 0.4
Non-systematic variance of Stock B = (0.42 -0.42) = 0

s2(eP) = (0.252 x 0.0159) + (0.52 x 0) + (0.252 x 0) = 0.00099375
s(eP) = (0.00099375)1/2 = 0.031523801 (Non-Systematic Standard Deviation)

sP2= bP2sM2+ s2(eP)
=> (1.052 x 0.252) + 0.00099375 = 0.0699

Standard Deviation of Portfolio = (0.0699)1/2 = 0.264386081 or 26.44%

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