You own $10 million of the 8% (semiannual), 10 year Treasury bond priced at par to...

You own $10 million of the 8% (semiannual), 10 year Treasury bond priced at par to yield 8% annually. You want to hedge your position against an increase in yields using the 8% (semiannual), 10 year Treasury bond future. There are no transaction costs. Recall the negative relation between market yields and bond prices.
1. How many Treasury bond futures do you need to hedge the position?
2. Compute and plot the profit & loss on the same diagram (long Treasury bond and Treasury bond future) varying the price of the bond as market yields range from 7.0 to 9.0% at 1/16 point intervals. YTM defines the x-axis.

Expert Solution

Since the payment frequency, yield, and maturity of both the underlying (treasury bonds) and hedge (futures contract) are matching, we can match the total value of the bond portfolio exactly with the futures contract. The portfolio is long on treasury bonds. Hence, the offsetting hedge position would be to short (sell) the futures contract worth $10 M. Each futures contract has a face value at maturity of $100,00. Since the bonds are priced at par, the no of contracts to be sold = 10,000,000/100,000= 100 contracts.

Settlement	Maturity	Period (yrs)	Yield	Coupon	Payment frequency	Price	Price formula
4/3/2019	4/3/2029	10	8.0%	8.0%	semi-annual	100.00	=PRICE(4/3/19,4/3/29,8%,8%,100,2(semi-annual),1(actual-actual))

As the yield changes, both the treasury bond portfolio and the hedged futures position will move by equal magnitude but in opposite direction, since they both are similar in all aspects. We form a P&L table for magnitude of price change for a change of 1/16 points (0.0625%) in yield.

Settlement	Maturity	Period (yrs)	Yield	Coupon	Payment frequency	Price	Change in price from par- Treasury	Change in price from par- Futures	Change in price from par- Net
4/3/2019	4/3/2029	10	7.0000%	8.0000%	semi-annual	93.20	(6.80)	6.80	0.00
4/3/2019	4/3/2029	10	7.0625%	8.0000%	semi-annual	93.63	(6.37)	6.37	0.00
4/3/2019	4/3/2029	10	7.1250%	8.0000%	semi-annual	94.05	(5.95)	5.95	0.00
4/3/2019	4/3/2029	10	7.1875%	8.0000%	semi-annual	94.48	(5.52)	5.52	0.00
4/3/2019	4/3/2029	10	7.2500%	8.0000%	semi-annual	94.90	(5.10)	5.10	0.00
4/3/2019	4/3/2029	10	7.3125%	8.0000%	semi-annual	95.33	(4.67)	4.67	0.00
4/3/2019	4/3/2029	10	7.3750%	8.0000%	semi-annual	95.75	(4.25)	4.25	0.00
4/3/2019	4/3/2029	10	7.4375%	8.0000%	semi-annual	96.18	(3.82)	3.82	0.00
4/3/2019	4/3/2029	10	7.5000%	8.0000%	semi-annual	96.60	(3.40)	3.40	0.00
4/3/2019	4/3/2029	10	7.5625%	8.0000%	semi-annual	97.03	(2.97)	2.97	0.00
4/3/2019	4/3/2029	10	7.6250%	8.0000%	semi-annual	97.45	(2.55)	2.55	0.00
4/3/2019	4/3/2029	10	7.6875%	8.0000%	semi-annual	97.88	(2.12)	2.12	0.00
4/3/2019	4/3/2029	10	7.7500%	8.0000%	semi-annual	98.30	(1.70)	1.70	0.00
4/3/2019	4/3/2029	10	7.8125%	8.0000%	semi-annual	98.73	(1.27)	1.27	0.00
4/3/2019	4/3/2029	10	7.8750%	8.0000%	semi-annual	99.15	(0.85)	0.85	0.00
4/3/2019	4/3/2029	10	7.9375%	8.0000%	semi-annual	99.58	(0.42)	0.42	0.00
4/3/2019	4/3/2029	10	8.0000%	8.0000%	semi-annual	100.00	-	-	0.00
4/3/2019	4/3/2029	10	8.0625%	8.0000%	semi-annual	100.42	0.42	(0.42)	0.00
4/3/2019	4/3/2029	10	8.1250%	8.0000%	semi-annual	100.85	0.85	(0.85)	0.00
4/3/2019	4/3/2029	10	8.1875%	8.0000%	semi-annual	101.27	1.27	(1.27)	0.00
4/3/2019	4/3/2029	10	8.2500%	8.0000%	semi-annual	101.70	1.70	(1.70)	0.00
4/3/2019	4/3/2029	10	8.3125%	8.0000%	semi-annual	102.12	2.12	(2.12)	0.00
4/3/2019	4/3/2029	10	8.3750%	8.0000%	semi-annual	102.55	2.55	(2.55)	0.00
4/3/2019	4/3/2029	10	8.4375%	8.0000%	semi-annual	102.97	2.97	(2.97)	0.00
4/3/2019	4/3/2029	10	8.5000%	8.0000%	semi-annual	103.40	3.40	(3.40)	0.00
4/3/2019	4/3/2029	10	8.5625%	8.0000%	semi-annual	103.82	3.82	(3.82)	0.00
4/3/2019	4/3/2029	10	8.6250%	8.0000%	semi-annual	104.25	4.25	(4.25)	0.00
4/3/2019	4/3/2029	10	8.6875%	8.0000%	semi-annual	104.67	4.67	(4.67)	0.00
4/3/2019	4/3/2029	10	8.7500%	8.0000%	semi-annual	105.10	5.10	(5.10)	0.00
4/3/2019	4/3/2029	10	8.8125%	8.0000%	semi-annual	105.52	5.52	(5.52)	0.00
4/3/2019	4/3/2029	10	8.8750%	8.0000%	semi-annual	105.95	5.95	(5.95)	0.00
4/3/2019	4/3/2029	10	8.9375%	8.0000%	semi-annual	106.37	6.37	(6.37)	0.00
4/3/2019	4/3/2029	10	9.0000%	8.0000%	semi-annual	106.80	6.80	(6.80)	0.00

jeff jeffy answered 1 year ago

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