Problem 1. Investor A has a square root utility function (i.e._. UU'V} = M )1 whereas Investor 3 has a logarithmic utility function (ie, UUV) = In 14'] Both investors have initial wealth W}; = $100 and must decide how much how much to invest in a bond and how much to invest in a stock. The current prices of the bond and stock are BB and So respectively. Although neither security pays dividends or interest, both investors expect to receive income from selling thme securities at their end-ofperiod prices: which are 31 for the bond and 31 for the stock. Since the bond is riskless, its endofperiod price is known with certainty to be .31 = Bg{l+r], where r is the riskless rate of interest. The price of the stock at f = 1 can be high or low; i.e... it will be Sg{1+5} with probability .6 and it will be Sus) with probability .4. Furthermore, assume that Wu: $100.. r = .05., and s = .3. A. How much {in dollar and percentage terms} of Investor A's initial wealth should be invested in the stock and in the bond? . How much (in dollar and percentage terms) of Investor B's initial wealth should be invested in the stock and in the bond? C. TWho is more risk averse Investor A or Investor B? Explain why. D. Recalculate your answers for parts A and B assuming initial wealth of $200 rather than $100