You have a bond that pays a $3 coupon in 1 year and a $3 coupon in two years and a $3 coupon in three years. It matures in three years with principal repayment of $100 (paid at the same time as the final coupon). Suppose 1-year, 2-year, and 3-year zero coupon bond prices are 0.99, 0.97, and 0.92, respectively. Which is closest to the fair market price of the bond that you have?

You would like would like to swap the uneven payments (note that the payments are $3 in year 1, $3 in year 2, and $103 in year 3) associated with the bond described above for payments of equal amounts in 1 year, in 2 years, and in 3 years. Assuming you can find a swap counterparty who offers you a fair deal (and that interest rates are unchanged from those described above, what is closest to the swap rate amounts will you receive in each year as a result of the swap?

The price of a 1-year zero coupon bond is 0.97. The price of a 2-year zero coupon bond is 0.93. The price of a 3-year zero coupon bond is 0.85. The price of a 4-year zero coupon bond is 0.78. You are a borrower who anticipates needing to borrow $100,000 for one year at the end of year 3 and would like to guarantee the rate on your upcoming loan (i.e., after 3 years you will need a $100,000 loan which will last for one year). Which is closest to the interest rate you will be able to guarantee if there are no transactions costs and you get a fair deal in the interest rate forward market?

 

  

2. a) (7 points) The discount factors for different maturities (t) are as follows: t (years) 0.5 1.5 2 Z(0,t) 0.9480 0.9260 0.8840 0.8530 Calculate the duration and the convexity of a portfolio which consists of all of the following securities: 2 units of 1-year fixed-rate coupon bonds with a coupon rate of 6%, which pay coupons semi-annually, and which have a face value of $100 each; 6 units of 2-year zero-coupon bonds, with a face value of $100 each; 1 unit of a 1.5-year floating-rate bond paying the 6-month semi-annually- compounded spot rate (and no spread) semi-annually, with a face value of $100, which has just been issued. b) (3 points) If the continuously-compounded spot yield curve shifts downwards by 3%-points parallelly, by how many dollars will the value of the portfolio in question a) change approximately? Use the second-order Taylor-approximation (i.e., duration and convexity).