Assume you are a portfolio manager for a large pension fund and in charge of allocating funds

across major asset classes. Specifically, today is $12/31/2014$ and you are assembling a portfolio

for January of $2015.$ Your investment universe consists of T$-$bonds $($Barclays U$.$S$.$ Treasury

index$),$ investment grade corporate bonds $($Barclays U$.$S$.$ Corp index$),$ domestic stocks $($S&P

$500),$ international stocks $($MSCI World index$),$ commodities $($Goldman Sachs Commodity In$-$

dex$),$ and gold. Asset allocation decisions are made based on mean variance analysis.

On Canvas, you will find an Excel file containing historical monthly net returns for these assets.

Assume that the risk$-$free rate for $1/2015$ equals $25$ basis points per month.

QUESTIONS:

A Report the mean and variance$-$covariance matrix for all assets.

B Based on the moments you estimated in A$,$ find the tangency portfolio and the minimum

variance portfolio. Report the mean, standard deviation, and portfolio weights for both

portfolios.

C In lecture $3,$ we saw that an investor with utility function U $=\backslash$mu $\backslash$alpha $\backslash$sigma $2$ will optimally allocate

a fraction w$=\backslash$mu $$rf

$2\backslash$alpha $\backslash$sigma $2$ of her investment to risky assets. Based on the optimal portfolio of

risky assets you found in B$,$ compute the risky asset share for risk aversion, $\backslash$alpha $,$ between $10$

and $40\mathrm{.}1$ Plot the optimal risky asset share as a function of $\backslash$alpha $.$ Is the function increasing

or decreasing? Explain economically why you find the slope that you do$.$

D Plot the frontier of risky assets. To do so$,$ use the minimum variance portfolio and the

tangency portfolio found above, along with the two fund separation property. Use weights

between $-25$ and $15$ on the minimum variance portfolio $($i$.$e$.-2500\%$ to $1500\%).$ Add the

individual assets as $$dots$$ to the plot.

E Suppose you form a portfolio that invests in both the minimum variance portfolio and the

tangency portfolio. If the weight on the minimum variance portfolio equals $40\%,$ what are

the weights on the individual assets $($T$-$bonds, corporate bonds, etc.$)?$

$1$Start by computing the optimal share in risky assets for a value of $\backslash$alpha $=10.$ Repeat for $\backslash$alpha $=11,\backslash$alpha $=12$ etc.

$1/1$