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Consider a risk averse investor with utility function U(W) = ?W who is deciding how much of
her initial wealth (Wo) to invest in a bond and how much to invest in a stock. The current prices
of bond and stock are (Bo) and (So) respectively. Although neither security pays dividend 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-ofperiod prices is known with certainty to be B1 = Bo (1+r), where r is the riskless rate of interest.
The price of stock at t =1 can be high or low; i.e., it will be So(1+s) with probability of 0.6 and it
will be So(1-S) with probability of 0.4. Furthermore, assume that Wo= 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?
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