Exercise 2 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong: What is the utility function?

See Modern portfolio theory.

Antwoord 3 feedback

Wrong: Use the utility functions.

See Modern portfolio theory.

Antwoord 4 feedback

Wrong: What is the utility function?

See Modern portfolio theory.