Forward contracts on a Treasury bond

Table

Forward	maturity	270 days
Treasury	maturity	10 years
	coupon	5% (*)
	(dirty) price	98.25
Risk-free rate		4% (**)

(*) It has just made a coupon payment; next two coupon payments will be in 182 days and in 365 days.
(**) Effective annual risk-free rate.

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[1] No-arbitrage price for the forward contract on the Treasury bond

Table

Days	coupon (per $100 face value)	Treasury	No-arbitrage forward price
0	(1) PV = 2.50/1.04^(182/365)	98.25	(2) 98.25 - 2.50/1.04^(182/365)
182	100*5%*(1/2) = 2.50
270			(3) (98.25 - 2.50/1.04^(182/365))*1.04^(270/365) = 98.62

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[2] If the Treasuary bond dirty price decreases to 98.11 over the next 60 days, the value of a short position in the 270-day forward contract on a $10 million bond is:

Table

Days	coupon (per $100 face value)	Treasury	No-arbitrage forward price
0
60	(1) PV = 2.50/1.04^(122/365)	98.11	(2) 98.11 - 2.50/1.04^(122/365)
182	100*5%*(1/2) = 2.50
270

(3) The value of the forward contract to the long:
98.11 - 2.50/1.04^(122/365) - 98.62(answer in [1])/1.04^(210/365) = -0.77693 per $100
∴-$77,693


short: +0.77693 per $100
∴+$77,693