Investment data Distribution of annual returns on stocks and bonds Economy Probability Stocks Bonds Very strong 0.20 25% 20% Moderately strong 0.40 20% 17.5% Fair 0.25 X% Y% Moderately weak 0.10 10% 12.5% Very weak 0.05 5% 10%

A retired partner from a large brokerage firm has one million dollars available to invest in particular stocks or bonds. Each investment's annual rate of return depends on the state of the economy in the coming year. The fileP06_58.xlsxcontains the distribution of returns for these stocks and bonds as a function of the economy's state in the coming year. As this file indicates, the returns from stocks and bonds in a fair economy are listed asXandY. This investor wants to allocate her one million dollars to maximize her expected value of the portfolio one year from now.

a.IfX=Y= 15%, find the optimal investment strategy for this investor. (Hint: You could try a decision tree approach, but it would involve a massive tree. It is much easier to find an algebraic expression for the expected final value of the investment when a percentagepis put in stocks and the remaining percentage is put in bonds.)

If X = Y = 15%, the expected value of the stock investment is higher than the expected value of the bond investment.

The investor should put what% of her funds in stocks. How much into stocks.