an investor invests 40% of his wealth in a risky asset with an expected rate of
ID: 2716913 • Letter: A
Question
an investor invests 40% of his wealth in a risky asset with an expected rate of return of 0.17 and a variance of 0,08 and 60 % in T bill that pays 4.5 %, his portfolio expected return and standard deviation are: A. 0.114, 0.126 B. 0.087; 0.068 C. 0.095; 0.113 D. 0.087; 0,124 E. None of the above Question 7 of 22 (-4 Points) of 22 uesITS AIlsweltu Question: An investor invests 40 percent of his wealth in a risky asset with pays 4.5 percent. His portolio's expected return and standard deviation are an expected rate of return of 0.17 and a vaniance of 0 08 and 60 percent in a T-bill that O A 0.114,0 126 O B 0 087,0.068 O C 0 095.0 113 O D 0.087;0.124 OENone of the above c PrevExplanation / Answer
Answer
C. 0.095 and 0.113
Risky Asset
Expected rate of return = 0.17
Variance = 0.08
Weight in portfolio = 40%
T-Bill - Risk-free Asset
Rate of return = 4.5% or 0.045
Weight in portfolio = 60%
Expected return of portfolio = weight of risk-free asset * return + weight of risky asset * return
= 0.60 * 0.045 + 0.40 * 0.17
= 0.027 + 0.068
= 0.095 or 9.50%
Variance of a portfolio can be calculated using the following equation
Portfolio Variance = weight1^2*variance of asset + weight2^2*variance of asset2 + 2*weight1*weight2*Covariance (asset1, asset2)
Portfolio Variance = Weight of risky Asset ^2 * Variance + weight of risk-free asset^2 * variance of risk-free asset + 2*weight1*weight2*Covariance (risky asset, risk-free asset)
A risk-free asset has zero variance and zero standard deviation. Hence the variance of portfolio will be
Portfolio Variance = Weight of Risky Asset^2 * Variance of risky Asset
Portfolio Variance = 0.4^2 * 0.08 = 0.16 * 0.08 = 0.0128
Portfolio Standard Deviation = Square root(0.0128) = 0.113137 or 11.3% rounded off
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