Supplemental Homework

Multi-asset Portfolio Optimization

Scenario Manager

Tools->ScenariosSummary

– Scenario Summary

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).

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)

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

Compute Portfolio Return and Standard Deviation

Portfolio Expected Return: E(rp) = wTr

Excel function: SUMPRODUCT(weight,returns)Portfolio Variance: 2

p = wT w

Excel function: SUMPRODUCT(weight,MMULT(covariance,weight))

Portfolio Standard Deviation: Excel function: SQRT(Portfolio variance)

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(rp) – rF)/ p

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.