Question

you are considering investing in two securities. Security 1 has a expected return of 12% and a standard deviation of return of 10%. Security 2 has an expected return of 9%and a standard deviation of returns of 8%. The correlation coefficient of returns for the two securities is 0.3.

1. What would the weights be for each of the two securities in the minimum variance portfolio?

W₁=

W₂=

2. Given the weights computed in (a), compute the expected return and standard deviation of this minimum variance portfolio.

Expected return:

Standard deviation:

3. Would you recommend this minimum variance portfolio to an investor who would like to maximize the Sharpe ratio of his investment? Briefly Explain.

please type out answer

Answer 1

Minimum variance portfolio can be found easily using the variance-covariance matrix, with Solver:

a). Weights for the minimum variance portfolio:

W1 = 34.48%; W2 = 65.52%

b). Expected return = 10.03%; standard deviation = 7.09%

Calculations:

C. D К L Security 1 Security 2 Weight 36 Stock fund Bond fund Covariance matrix 12% Stock fund 37 Expected return 0.0100 9% 0.0024 34.48% 65.52% 10% 8% 38 Standard deviation Bond fund 0.0024 0.0064 39 Correlation 0.3000 40 Return 12% 9% 41 Portfolio: Expected return Variance 42 10.03% 43 0.0050 7.09% Standard deviation 44

Formulas:

В C D K L M Security 1 Security 2 36 Stock fund Bond fund Weight Covariance matrix 0.344827586206897 37 Expected return 0.12 0.1 0.3 Stock fund Bond fund 0.09 K38 Ес38^2 C39*C38 *D38 - 1 -N37 38 Standard deviation -D38 2 0.08 39 Correlation D37 40 ЕС37 Return 41 Portfolio: Expected return Variance Standard deviation -SQRT(K43) MMULT ( K40:L40,N37:N38) 42 EMMULT(MMULT(TRANSPOSENS7NS8),N ,NS7.N38) 43 44 45 Solver Parameters X 46 47 Set Objective: 48 SK$43 49 50 To: O Max O Min Value Of: 0 51 52. By Changing Variable Cells: 53 SNS37 54

c). No, a minimum variance portfolio is not the same as a portfolio with maximum Sharpe ratio. A minimum variance portfolio only minimizes risk without taking into consideration, the effect on portfolio return. A portfolio with maximum Sharpe ratio will focus on maximizing return per unit of risk.