Question

It is March 10, 2020. The cheapest-to-deliver bond in a December 2020 Treasury bond futures contract is an 8% coupon bond, and delivery is expected to be made on December 31, 2020. Coupon payments on the bond are made on March 1 and September 1 each year. The rate of interest with continuous compounding is 5% per annum for all maturities. The conversion factor for the bond is 1.2191. The current quoted bond price is $137. Calculate the cash bond price, cash futures price, and quoted futures price for the contract.

Answer 1

The present value of a $3,000 bond with an 8% coupon at an 8% discount rate is $3,004.86; however, if interest rates rise to 11%, the bond's present value decreases to $2859.46.

Step-by-step explanation:

The present value of a simple two-year bond with an 8% coupon and a principal of $3,000 is as follows. At an 8% discount rate, the present value of the first year's $240 interest payment is $240 / (1 + 0.08) = $222.22. The present value of the second year's interest payment plus principal is ($240 + $3,000) / (1 + 0.08)2 = $2782.64. Therefore, the total present value of the bond at an 8% discount rate is $222.22 + $2782.64 = $3,004.86. If interest rates rise to 11%, the present value calculations change to $240 / (1 + 0.11) = $216.22 for the first year, and ($240 + $3,000) / (1 + 0.11)2 = $2643.24 for the second year. Thus, the total present value at an 11% discount rate is $216.22 + $2643.24 = $2859.46.

The cash bond price, cash futures price, and quoted futures price for the Treasury bond futures contract require calculations that account for accrued interest, the quoted bond price, the conversion factor, and interest rates. However, the question did not provide enough details to carry out these calculations precisely.