Carter has a current wealth of $ 100,000. He is trying to decide how much of his wealth to invest in Treasury bills (a risk-free asset) and a portfolio of bonds. The T-Bill pays a sure return of 2.5% (R_f = .025) and the portfolio has an expected return (R_m) based on the following probability distribution of payoffs:

Probability Payoff (Monetary Flows of Bonds)

.25 $ 800

.50 $ 650

.25 $ 200

Assume that Jack purchased the portfolio of bonds for a price of $ 5,000.

1. Calculate the expected return (R_m) and standard deviation (_m ) on the portfolio of bonds. Note that both the return and standard deviation must be taken as a percentage of the price of the bond.
2. Given your results in part A, calculate the slope of the budget constraint. Provide an intuitive meaning of this slope term.
3. If the expected return on the portfolio of bonds and T-Bills (R_p) is 18 % (0.18), what is the risk (_p) associated with the portfolio?

What would happen if the risk on the bond portfolio (_m) increased? How would this impact a risk-averse individuals optimal risk-return choice? Demonstrate this with the appropriate diagram and carefully explain your results.