Bond Return Assignment

A 30-year zero-coupon bond yields 8% today and has a face value of $100. The price of such a bond can be calculated using the bond pricing formula:

,

where P is the price of the bond, 100 is the face value of the bond, y is the yield to maturity and t is the number of years to maturity. Therefore, the current price of the bond is $9.94:

If the bond yield one year later is 8.5%, then the price of the bond is:

The return for the year is:

If, on the other hand, the bond yield one year later is 8%, the return for the year is 8%:

In fact, the yield one year from today is a normal random variable with = 0.08 and = 0.01. Use =NORM.INV(RAND(),0.08,0.01) to get a normally distributed random variable. Use a simulation with 1,000 trials to answer the following questions:

1. Produce the following output (using DADM tools)

2. Show the histogram of return for duration =20, 25, and 30.

Summary stats for _Return
Duration	20	25	30
Mean	0.100	0.110	0.123
Median	0.083	0.083	0.084
Min	-0.397	-0.483	-0.556
Max	0.946	1.273	1.654
Std Dev	0.191	0.245	0.301
95% confidence interval for the mean
Lower limit	0.088	0.095	0.105
Upper limit	0.111	0.125	0.142