Question

Eric is dividing his portfolio between two assets, a risky asset that has an expected return of 30% and a standard deviation of 10%, and a safe asset that has an expected return of 10% and a standard deviation of 0%.

Eric's budget constraint is rx= 2σ?+10.

Eric’s utility function is ?(??,σ?)=???(??,30−2σ?). What are his optimal values of ?? and ???

Answer 1

utility function is u(rx,σx)=min{rx,30−2σx}

then Eric's optimal value of rx is where utility function is maximum, means where

rx = 30 - 2σx --- (1)

Given, Eric's budget constraint is rx= 2σ?+10

Put value of rx in (1), we get

2σ?+10 = 30 - 2σ?

2σ? + 2σ? = 30 - 10

4σ? = 20

σ? = 5

Piy this value in budget constraint, we get

rx = 2σ? + 10

= 2*5 + 10

= 20

So, rx = 20 and his optimal value of σx is 5