An investor invests 35% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 65% in a T-bill that pays 4%. His portfolio's expected return and standard deviation are and , respectively.

A) 0.089; 0.111
B) 0.087; 0.063
C) 0.096; 0.126
D) 0.087; 0.144

Question

An investor invests 35% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 65% in a T-bill that pays 4%. His portfolio's expected return and standard deviation are __________ and __________, respectively.

A) 0.089; 0.111
B) 0.087; 0.063
C) 0.096; 0.126
D) 0.087; 0.144

Muhammad Haris · Accepted Answer

Final Answer : A, Explanation :  The expected return is the weighted average of the expected returns of the two assets. The weight of the risky asset is 35%, and its expected return is 0.18. The weight of the T-bill is 65%, and its expected return is 0.04. Therefore, the expected return of the portfolio is 0.35 * 0.18 + 0.65 * 0.04 = 0.089.The variance of the portfolio is the weighted average of the variances of the two assets, plus the covariance between the two assets. The covariance is zero because the two assets are uncorrelated. Therefore, the variance of the portfolio is 0.35 * 0.10 + 0.65 * 0 = 0.035. The standard deviation is the square root of the variance, so the standard deviation of the portfolio is 0.187.

An investor invests 35% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 65% in a T-bill that pays 4%. His portfolio's expected return and standard deviation are and , respectively.

A) 0.089; 0.111
B) 0.087; 0.063
C) 0.096; 0.126
D) 0.087; 0.144

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