An investor is considering the decision to buy N=1000 bonds of the 1-, 2-, 3-, 4-, and 5-year zero-coupon bonds mentioned above for an year assuming probability of default p = 0.01, 0.02, 0.025, 0.026, and 0.027 for each bond respectively. The risk-free interest rate is 2 percent, and the recovery rate is 60%. a) What would be the fair coupon for each bond, for hypothetical investors who do not care about risk and instead consider only the expected value of their investments? b) Characterize each portfolio (1-, 2-, 3-, 4-, and 5-year zero-coupon bonds) separately along the following parameters in Excel and provide a brief description of the findings: Average payout Highest payoff Lowest payoff Max profit relative to risk-free case Min profit relative to risk-free case Standard Deviation of profit, relative to risk-free case Number of defaults Investment fraction that can be recovered in case of default c) Characterize the whole portfolio (#5000) along the parameters listed under b) in Excel and provide a brief description of the findings. d) How often do the individual portfolios as well as the whole portfolio return less than the risk-free rate? Define this variable as % of time loss in a table in Excel and comment on the findings. e) Consider the case when an investor can hold up to one thousand of each type of bonds for an year. What combination(s) of holding the five types of bonds would lead to the highest and lowest return? Comment on the findings. (Note: Where applicable, consider a market coupon of 10% as a spread to lenders over the fair coupon