. Consider a risk averse investor with utility function U (W ) = W^0.5 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 W 0= $100, r = .05, and s = .3.

A. How much of the investor's initial wealth should be invested in the stock, and how much

in the bond?

B. What will be the investor's 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?