# Solutions to Case the Harvard Management Company (2001)

You will design an excel spreadsheet that allows you to answer the following questions: i) Given figures in Exhibits 4 and 11 what is the expected return and volatility of the policy portfolio? ii) Find an efficient portfolio having the same expected return as the policy portfolio but lower volatility. iii) Find an efficient portfolio having the same volatility as the policy portfolio but higher expected return. iv) Repeat question ii using the constraints in Exhibit 13. v) Repeat question iii using the constraints in Exhibit 13. vi) Consider the following seven asset classes: Domestic Equity, Foreign Equity, Emerging Markets, Private Equity, Commodities, Inflation-Indexed Bonds, and Cash. Using HMC’s input assumptions (see Exhibit 11, and also using the constraints shown on Page 22, Exhibit 12), what would be the allocation across these seven security classes if HMC was looking for optimal portfolios that would have expected real returns of 4, 5, 6, 7, and 8%. For each of these cases, also show the resulting standard deviation of the portfolio, and the Sharpe (efficiency) ratio (see footnote a in Exhibit 12). vii) Redo part (vi) but now constrain the minimum and maximum weights on the seven different asset classes using the constraints shown in Exhibit 13. It may not be possible to achieve some of the expected real returns you were getting earlier. If that is the case, use five expected real return levels that you can attain. viii) Compare the investment opportunities implied by part (vi) to those in part (vii). ix) Explain the pros of the mean variance paradigm.

x) Explain the cons.

I will describe how to perform portfolio optimization in class. Excel is equipped with an optimizer (Solver) that requires you to specify what you are trying to maximize or minimize, the variables (weights) that may be adjusted in order to maximize portfolio efficiency, and the constraints imposed on...

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