Question

Suppose the December CBOT Treasury bond futures contract has a quoted price of 85'10. The 20-year Treasury bond underlying the futures contract makes 6% semiannual coupon payments and has a $1,000 par value. (Round to the nearest whole dollar.) What is the implied annual yield?

		7.21%
		7.42%
		7.67%
		7.89%
		8.20%

Use information and result from Question 7, if annual interest rates go up by 1.00 percentage point, what is the gain or loss on the futures contract? (Round to the nearest whole dollar.)

		− $ 80.00
		− $ 83.00
		− $ 85.00
		− $ 90.00
		− $ 95.00

Answer 1

a)
FV = 1000
PV = (0.85 + 0.10 / 32) * 1000 = 853.125
PMT = 1000 * 6% / 2 = 30
Nper = 20 * 2 = 40

Implied annual yield can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)*2
=RATE(40,30,-853.125,1000)*2
= 7.42%

Implied annual yield = 7.42%

b)
FV = 1000
PMT = 1000 * 6% / 2 = 30
Nper = 20 * 2 = 40
Rate = (7.42% + 1%) / 2 = 4.21%

New price of the bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(4.21%,40,-30,-1000)
= $767.25

Gain or loss on the futures contract = $767.25 - $853.125 = -$85.

Gain or loss on the futures contract = -$85