Lecture $9-$ Myopic asset allocation

You have a market with $4$ assets, having a mean of ${\left[\begin{array}{cccc}0\mathrm{.}12& 0\mathrm{.}15& 0\mathrm{.}05& 0\mathrm{.}20\end{array}\right]}^{\text{'}}$ and

covariance matrix $\left[\begin{array}{cccc}0\mathrm{.}0400& 0\mathrm{.}0350& 0\mathrm{.}0000& 0\mathrm{.}0300\\ 0\mathrm{.}0350& 0\mathrm{.}0625& 0\mathrm{.}0000& 0\mathrm{.}0450\\ 0\mathrm{.}0000& 0\mathrm{.}0000& 0\mathrm{.}0000& 0\mathrm{.}0000\\ 0\mathrm{.}0300& 0\mathrm{.}0450& 0\mathrm{.}0000& 0\mathrm{.}0900\end{array}\right].$

If your risk aversion is $3$ what is your optimal portfolio?

Under which conditions is the portfolio choice of long$-$term investors who can re$-$

balance their portfolios myopic?

Lecture $10-$ Strategic asset allocation with labor in$-$

come

You are a civil servant who has a very secure government job paying $.$l$\mathrm{.}36,000$ p$.$a$.$

You are $27$ years old and are sure to retire at $70$ with a pension paying $40\%$ of

you income for another $20$ years. Currently your only asset is cash to the value of

$L^{\text{'}}100,000$ which you inherited from a relative. You consider your optimal investment

of this amount into the stock market and cash holding. If you expect the stock

market to rise by $8\%$ p$.$a$.$ with a volatility of $25\%$ p$.$a$.$ and the risk free rate is $6\%$

p$.$a$.,$ how much would you invest into the stock market? How would this allocation

have changed $20$ years later, assuming you have not accumulated more financial

wealth. How can you explain the difference?

Assume an absolute risk aversion of $3.$

Why do you hedge against the risk in your labor income using the stock market?