Question

You manage a bond portfolio with a current value of $150,000,000 & a duration of 7.32. You need to hedge the interest rate risk of this portfolio for some reason. Today's date is Monday 12/10/2018, so the settlement price for a treasury bond is the 11th. You decide to use the 10 year t-note futures to hedge. The cheapest to deliver bond is the 3 percent coupon bond with maturity date of 09/30/2025 which is currently selling for a yield of 2.766% (price of 101.4766 or 1.014766 per $1 of face value).

Question: Do you long or short these contracts?

Answer 1

STEP 1)Cash market position=long S&P 500 shares worth=$ 6000000
	STEP 2)futures market value=beta*cash market value=2.4*6000000=$ 14400000
		we have to sell futures worth $ 14400000
	STEP 3)	Number of contracts=
			number of nifties=14400000/2250=6400
			since 1 contract has 100 futres so 64 contracts should short i.e sell
	STEP 4)hedging strategy is sell 64 contracts at 2250
	fair futures price=spot price*e^t(r-d)
		250*e^1(1%-2%)=250*e^-0.01
	e^0.01=1+0.01/1+(0.01)^2/2+(0.01)^3/3=1.01005
	e^-0.01=1/1.01005=7.43
	fair furures price=250*1.01005=252.51
	on 13 month
	cash market				futures market
	buy:250				sell:2250
	sell:252.51				buy:2300
	profit=2.51				loss:50
	total profit=2.51*24000=60240				total loss=50*64 contracts*100=320000
	(6000000/250=24000)
		over all loss=320000-60240=259760 $
	if drops to 1200
	cash market				futures market
	buy:250				sell:1200
	sell:252.51				buy:1205
	profit=2.51				loss:5
	total profit=2.51*24000=60240				total loss=5*6400=32000
	(6000000/250=24000)
			overall profit=60240-32000=28240
	if drops to 1207
	cash market				futures market
	buy:250				sell:2100
	sell:252.51				buy:2107
	profit=2.51				loss:7
	total profit=2.51*24000=60240				total loss=7*6400=44800
	(6000000/250=24000)
		overall profit=60240-44800=15440
	if increases to 3200
	cash market				futures market
	buy:250				sell:3200
	sell:252.51				buy:3215
	profit=2.51				loss:15
	total profit=2.51*24000=60240				total loss=15*6400=96000
	(6000000/250=24000)
		overall loss=96000-60240=35760