An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70% in a T-bill that pays 6%.His portfolio's expected return and standard deviation are __________ and __________, respectively.

Question

Quizplus · Accepted Answer

To calculate the portfolio's expected return, we use the following formula:

Expected portfolio return = (weight of risky asset x expected return of risky asset) + (weight of T-bill x expected return of T-bill)
= (0.3 x 0.15) + (0.7 x 0.06)
= 0.087 or 8.7%

To calculate the portfolio's standard deviation, we use the following formula:

Portfolio standard deviation = sqrt[(weight of risky asset)^2 x variance of risky asset + (weight of T-bill)^2 x variance of T-bill + 2 x weight of risky asset x weight of T-bill x covariance]

Since the covariance between the risky asset and T-bill is assumed to be zero, the formula simplifies to:

Portfolio standard deviation = sqrt[(weight of risky asset)^2 x variance of risky asset + (weight of T-bill)^2 x variance of T-bill]

= sqrt[(0.3)^2 x 0.04 + (0.7)^2 x 0]
= sqrt[0.0036]
= 0.06 or 6%

An Investor Invests 30% of His Wealth in a Risky