attached is the original file 1. Mean-Variance OptimizationAsset E(R)=µ Var(R)=?
ID: 2748997 • Letter: A
Question
attached is the original file
1. Mean-Variance OptimizationAsset E(R)=µ Var(R)=?2Asset 1 0.06 0.0072Asset 2 0.06 0.0024Riskfree Asset 0.04Consider a mean-variance optimizing investor with the payoff function V (µ, ?) = µ?12A· ?2and level of risk aversion A = 17. ( this diagram is attached0
(a) Show that this investor would choose the riskfree asset if she could only invest in oneof the assets.
(b) Explain why this investor did not choose one of the risky assets despite their having ahigher expected return than the risk-free asset.
1. Mean-Variance Optimization Asst E Asset 0.06 Asset 2 0 (R)= | Var(R) 0.06 00024 0.0072 Riskfree Asset 0.04 -2A-2 (a) Show that this investor would choose the riskfree asset if she could only invest in one (b) Explain why this investor did not choose one of the risky assets despite their havinga Consider a mean-variance optimizing investor with the payoff function V(, ) and level of risk aversion A = 17. of the assets. higher expected return than the risk-free asset. (c) What is the variance of the riskfree asset? Why?Explanation / Answer
A. If Payoff Function is V= (µ, ) = µ1/2A· 2
AND THEN WE PUT THE VALUES OF BOTH THE ASSETS then the risk from both the assets is almost the same . Therefore the investor would choose Risk Free Asset
Asset 1 : V= (µ, ) = µ1/2A· 2
V= (0.06, 0.0072) = 0.06-1/2*17 * (0.0072 * 0.0072)
=0.05956
Asset 2 : V= (0.06,0.0024) = 0.06-1/2 *17 * (0.0024*0.0024)
=0.05955
2. The investor did not choose one of the risky assets despite their having a higher expected return than the risk-free asset because if chooses any risky asset he might loose something in return for a higher return
but if he choose risk free asset even if he earns less but he has a certainity to earn. Therefore he would choose risk free asset.
3. The Variance of Risk Free Asset would be = 0 (Zero )
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