This problem set, is designed to help you understand the basic of Mean-Variance Analysis.You will be asked to apply aspects of Mean-Variance Portfolio Theory to some basic problems.You will also be asked to experiment with a pre-packaged Portfolio Optimization spreadsheet to develop a feel for Mean-Variance Analysis.

Part 1: Problems

1.Suppose you have two asset classes to invest in.The first is large-cap stocks, which has an expected return of 15% (per year) and volatility of 15%.The second is a government bond index, which has an expected return of 5% and volatility of 10%.The correlation between the two is 0.50.

Calculate (manually) the return and volatility of a portfolio that is 75% invested in large-cap stocks and 25% invested in government bonds.

On a spreadsheet, plot out expected return and risk trade-off as you range the weight from 0% to 100%.Be sure to plot expected return on the vertical axis and risk on the horizontal axis.

See how the plots change as you change the correlation to 0.00 and to -0.50.

2.Suppose that the risk-free rate is 5% and the expected return on a stock fund is 13%.An investor with $1 million to invest wants to achieve a 17% rate of return combining the risk-free asset and the stock fund.

How much would the investor need to deposit (or borrow) in the risk-free asset?

What if the investor wants to achieve a 6% rate of return?

Part 2: Portfolio Optimization Software

GSM Capital, a large investment bank, is attempting to market its new asset allocation product that provides its clients with personalized advice. The slick Excel-based product, dubbed "UCD GSM Portfolio Optimizer" provides asset allocation mixes over the equity markets of the G-5 countries and one risk-free asset. Investors can use the product in two ways. They can either input their risk aversion, or they can specify a target expected return for the portfolio.

The portfolio optimizer can be found on the class website ('GSM_PortOpt.xls').The firm's current Capital Market Assumptions for asset classes have already been entered for you.A Technical Appendix (below) provides more detail on its function.

To make sure the product is indeed robust and yields sensible results the Vice-President in charge of this project has tasked you to test the product.You are asked to see if the recommended portfolio produced by the software makes sense.He has the following questions:

Questions

a)Measure what the benefit of global diversification is for someone who is 100% invested in the U.S.What is the increase in the expected return that can be achieved for the same level of risk?(Hint: use 'Goal Seek' or 'Solver').

b)What is the highest expected return you can obtain if you accept 20% volatility of risk?What is your allocation in the risk-free asset?

c)Can this optimizer recommend a portfolio that provides the highest expected return with a risk of 20% volatility, but without borrowing cash?

d)At the expected return you use in (a), a very small amount of wealth is allocated to French equities.Incroyable mais vrai."Is there something wrong with the inputs?" asks the V.P.Try varying various inputs to get the allocation to French equities up to 10% of the equity portion of the portfolio.Try varying

a.the expected return on French equities

b.its volatility of French equities

c.the French-US equity correlation.

In each case, describe your experience.How does the allocation to French equities change when you change these input variables?What is the intuition behind these effects?

e)Among the capital market assumptions in part d), which parameter is your results most sensitive to if we want to increase allocations to French equities?That is, if you vary a parameter by 0.01 (or 1.00%), which parameter makes the largest difference?