1. Supplemental Homework Multi-asset Portfolio Optimization

2. Scenario Manager  Tools->Scenarios  Summary –Scenario Summary

3. Homework Instructions  Download the data file (index data.xls) from the course website.  Compute the historic monthly returns for each index: –Monthly return (assume continuous compounding): returnt = ln(Pt / Pt-1).

4. Compute Historic Sample Statistics  Compute the arithmetic average returns, population standard deviations, sample size, the variance-covariance matrix and the correlation matrix for T-Bond, S&P 500 Index, S&P 600 Index, Japan Index, and German Index. –Excel functions: AVERAGE(), STDEVP(), COUNT(). –For the correlation matrix, use Excel’s Data Analysis Command (located under Tools)

5. More on the Covariance Matrix  For the covariance matrix, you may use any of the following approaches. –Excel command: Tools (Add-in), Data Analysis, Covariance. Complete the upper half of the covariance matrix. –Following the directions in Benninga 8.3 and compute the covariance matrix using the excess returns approach. –Create the user-defined function, VarCovar, in Benninga 8.4

6. Compute Portfolio Return and Standard Deviation  Portfolio Expected Return: E(r p ) = w T r  Excel function: SUMPRODUCT(weight,returns)  Portfolio Variance:  2 p = w T  w  Excel function: SUMPRODUCT(weight,MMULT(covariance,we ight))  Portfolio Standard Deviation: Excel function: SQRT(Portfolio variance)

7. Reward-to-Risk (Sharpe) Ratio  Assume that the risk-free rate is 0.25% per month (3% per year).  Reward-to-standard deviation ratio = (E(r p ) – r F )/  p

8. Finding the Optimal Risky Portfolios  Assign equal weights to the initial portfolio.  Use Solver in Excel to find the optimal portfolio under each of the following cases.  Save the weights for each case as a scenario.  There is always at least one constraint: sum of weight must equal to 1.  Generate a scenario summary report containing the portfolio return and standard deviation and reward-to-standard deviation ratio for all cases.