Consider a risk averse investor with utility function U(W) = w^.5 who is deciding how much of her initial wealth (W 0) to invest in a bond and how much to invest in a stock. The current prices of the bond and stock are B0 and S0 respectively. Although neither security pays dividends or interest, Investor A expects to receive income from selling these securities at their end-of-period prices, which are B1 for the bond and S1 for the stock. Since the bond is riskless, its end-of-period price is known with certainty to be B1= B0(1+r), where r is the riskless rate of interest. The price of the stock at t = 1 can be high or low; i.e., it will be S0(1+s) with probability .6 and it will be S0(1-s) with probability .4. Furthermore, assume that W0= $100, r = .05, and s = .3.

a) How much of the investors initial wealth should be invested in the stock, and how much in the bond?

b) What will be the investors expected wealth and standard deviation of wealth at t = 1 from this investment strategy?

c) Suppose that this investor starts out with initial wealth of $200 rather than $100. In this case, what proportion of her initial wealth should be invested in the stock, and how much in the bond?