An investor is considering the purchase of zerocoupon U.S.Treasury bonds. A 30-year zerocoupon bond yielding 8% can be purchased today for $9.94. At the end of 30 years, the owner of the bond will...

An investor is considering the purchase of zerocoupon U.S.Treasury bonds. A 30-year zerocoupon bond yielding 8% can be purchased today for $9.94. At the end of 30 years, the owner of the bond will receive $100. The yield of the bond is related to its price by the following equation:

years. All of the bonds are currently yielding 8.0%. (Bond investors describe this as a flat yield curve.) The investor cannot predict the future yields of the bonds with certainty. However, the investor believes that the yield of each bond one year from now can be modeled by a normal distribution with a mean of 8% and a standard deviation of 1%.

Questions

1. Suppose that the yields of the five zero-coupon bonds are all 8.5% one year from today. What are the returns of each bond over the period?

2. Using a simulation with 1000 iterations, estimate the expected return of each bond over the year. Estimate the standard deviations of the returns.