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 u = 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 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 u = 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