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 ???
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
Eric is dividing his portfolio between two assets, a risky asset that has an expected return...
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