An investor with risk aversion coefficient $\alpha = 5$ uses modern portfolio theory to describe his preferences over investments. Portfolio $P_1$ is given by $P_1=(\mu,\sigma)=(1.03,0)$ and portfolio $P_2$ is given by $P_2=(\mu,\sigma)=(1.046,b)$. Determine all $b$ such that this investor (weakly) prefers $P_2$ over $P_1$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$b \leq \sqrt{0.0032}$
Antwoord 2 correct
Fout
Antwoord 3 optie
$b \leq 0.16$
Antwoord 3 correct
Fout
Antwoord 4 optie
$b \leq 0.064$
Antwoord 4 correct
Fout
Antwoord 1 optie
$b\leq 0.8$
Antwoord 1 feedback
Correct:
$$\begin{align*}
U(1.03,0)&=U(1.046,b)\\
1.03 & = 1.046-2\tfrac{1}{2}b^2\\
2\tfrac{1}{2}b^2& =0.016\\
b^2 & = 0.0064\\
b & =0.08.\\
\end{align*}$$
Then it is easily seen that for $b\leq 0.08$ this investor (weakly) prefers $P_2$ over $P_1$.
Go on.
$$\begin{align*}
U(1.03,0)&=U(1.046,b)\\
1.03 & = 1.046-2\tfrac{1}{2}b^2\\
2\tfrac{1}{2}b^2& =0.016\\
b^2 & = 0.0064\\
b & =0.08.\\
\end{align*}$$
Then it is easily seen that for $b\leq 0.08$ this investor (weakly) prefers $P_2$ over $P_1$.
Go on.
Antwoord 2 feedback
Antwoord 3 feedback
Antwoord 4 feedback