An investor invests 40 percent of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 60 percent in a T-bill that pays 4 percent.His portfolio's expected return and standard deviation are __________ and __________,respectively.

Question

Quizplus · Accepted Answer

Expected return of the portfolio can be calculated as:

Portfolio Expected Return = (Weight of Risky Asset * Expected Return of Risky Asset) + (Weight of T-bill * Expected Return of T-bill)
Portfolio Expected Return = (0.40 * 0.18) + (0.60 * 0.04)
Portfolio Expected Return = 0.096

The portfolio standard deviation can be calculated as:

Portfolio Standard Deviation = sqrt[(Weight of Risky Asset)^2 * Variance of Risky Asset + (Weight of T-bill)^2 * Variance of T-bill + 2*(Weight of Risky Asset)*(Weight of T-bill)*Covariance(Risky Asset, T-bill)]

Covariance between a risky asset and a T-bill is usually zero as their returns are not related, so:

Portfolio Standard Deviation = sqrt[(0.40)^2 * 0.10 + (0.60)^2 * 0.00]
Portfolio Standard Deviation = 0.126

Therefore, the portfolio's expected return and standard deviation are 0.096 and 0.126, respectively. Option C is the correct answer.

An Investor Invests 40 Percent of His Wealth in a Risky