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 a year assuming the 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 the risk-free case
• Min profit relative to the risk-free case
• Standard Deviation of profit, relative to the risk-free case
• Number of defaults
• Investment fraction that can be recovered in case of default