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Risk Management

 

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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