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-of-period 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.
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Write My Essay For Me- How much of the investor’s initial wealth should be invested in the stock, and how much in the bond?
- What will be the investor’s expected wealth and standard deviation of wealth at t = 1 from this investment strategy?
- 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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