Let us revisit the portfolio problem in Topic $2($and in the problem above$),$ but now let us

take into account your human capital. As before, you can invest your wealth into either the

riskless asset $(1\%$ per year$)$ or in three stock market indices with the following characteristics:

Asset E$($r$)\backslash$sigma

US $8\mathrm{.}0\%19\%$

Japan $3\mathrm{.}7\%25\%$

Mexico $6\mathrm{.}0\%15\%$

Correlations

Assets US J M

US $1\mathrm{.}00\mathrm{.}50\mathrm{.}8$

J $0\mathrm{.}51\mathrm{.}00\mathrm{.}2$

M $0\mathrm{.}80\mathrm{.}21\mathrm{.}0$

Now, let us add a fifth asset, your human capital. Assume that human capital accounts

for $50\%$ of your total wealth. This is an asset that you are endowed with, but that you cannot

rebalance $($you cannot buy more human capital and you cannot sell your human capital$).$

$($i$)$ First assume that your human capital is riskless. Solve your portfolio choice problem

assuming you are a mean variance investor with $\backslash$gamma $=4.$ That is$,$ what are the optimal

weights $($of financial wealth$)$ in each stock market index and the riskless asset.

$($ii$)$ Redo part $($i$)$ assuming that your human capital is only $20\%$ of your total wealth

$($iii$)$ Now assume that human capital is risky. To keep things simple $($at first$),$ assume that

your human capital has the same return as the US stock market.

$($a$)$ If human capital is $20\%$ of your wealth, can you achieve the same Sharpe ratio as

in part $($ii$).$ If so$,$ how? If not, why not?

$($b$)$ If human capital is $50\%$ of your wealth, can you achieve the same Sharpe ratio as

in part $($i$).$ If so$,$ how? If not, why not?Let us revisit the portfolio problem in Topic $2($and in the problem above$),$ but now let us

take into account your human capital. As before, you can invest your wealth into either the

riskless asset $(1\%$ per year$)$ or in three stock market indices with the following characteristics:

Now, let us add a fifth asset, your human capital. Assume that human capital accounts

for $50\%$ of your total wealth. This is an asset that you are endowed with, but that you cannot

rebalance $($you cannot buy more human capital and you cannot sell your human capital$).$

$($i$)$ First assume that your human capital is riskless. Solve your portfolio choice problem

assuming you are a mean variance investor with $=4.$ That is$,$ what are the optimal

weights $($of financial wealth$)$ in each stock market index and the riskless asset.

$($ii$)$ Redo part $($i$)$ assuming that your human capital is only $20\%$ of your total wealth.