$\text { Investment }$ $ \quad $$ \quad $$ \quad $$ \quad $$\text { A }$ $ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$\text { B }$
$\begin{array}{|l|l|l|l|l|}
\hline\
\begin{array}{l}
\text { State } \
\text { description }
\end{array} & \text { Bad state } & \text { Good state } & \text { Bad state } & \text { Good state } \
\hline \text { Probability } & 0.5 & 0.5 & 0.5 & 0.5 \
\hline \text { Payoff } & 200 & 220 & 400 & 435 \
\hline
\end{array}$
-Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?

Question

$\text { Investment }$  $  \quad $$  \quad $$  \quad $$  \quad $$\text { A }$   $  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$\text { B }$
$\begin{array}{|l|l|l|l|l|}
\hline\
\begin{array}{l}
\text { State } \
\text { description }
\end{array} & \text { Bad state } & \text { Good state } & \text { Bad state } & \text { Good state } \
\hline \text { Probability } & 0.5 & 0.5 & 0.5 & 0.5 \
\hline \text { Payoff } & 200 & 220 & 400 & 435 \
\hline
\end{array}$
-Assume the information in the table regarding the probability and payoffs of assets A and B relates to an investor who has a log utility function.What does the payoff for asset B need to be in the good state to make the investor indifferent between the two assets?

Quizplus · Accepted Answer

For investment A,the utility from the bad state is ln(200)= 5.298,and in the good state is ln(220)= 5.394.Therefore,given the probability of each state occurring is 0.5,the expected utility from the investment is therefore (0.5)(5.298)+ (0.5)(5.394)= 5.346.The investment for asset B must also be 5.346 if the investor is to be indifferent between the assets,and we know the utility of the bad state for asset B is ln(400)= 5.991.If we denote the unknown utility to be U,then 5.346 = (0.5)(5.991)+ (0.5)(U),which solving for U gives 4.701.To obtain a utility of this amount the payoff must be e^4.701 = $110.06.

Investment \text { Investment } Investment \quad \quad

$\text { Investment }$ $\quad$ $\quad$