Mean Variance Analysis in PracticeAssume 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 Blackboard, you will find an Excel file containing historical monthly net returns for these

assets. Assume that the risk-free rate for 1/2015 equals 0%.

QUESTIONS:

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

B Report the mean, standard deviation, and portfolio weights for both the tangency portfolio

and the minimum variance portfolio

C Compute the optimal share invested in risky assets for an investor with the utility function

U = µ − ασ 2 and values for risk aversion, α, between 10 and 40. 1 Plot the optimal

risky asset share as a function of α. 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. Add the individual assets as ’dots’

to the plot.

E Food for thought, i.e. no need to hand this part in! Suppose you form a portfolio that invests

in both the minimum variance portfolio and the tangency portfolio. When the weight on

the minimum variance portfolio equals 5, what are the weights on the individual assets

(T-bonds, corporate bonds, etc.)?