Question

A wealthy investor holds

$700,000

worth of U.S. Treasury bonds. These bonds are currently being quoted at

105105 %

of par. The investor is concerned, however, that rates are headed up over the next six months, and he would like to do something to protect this bond portfolio. His broker advises him to set up a hedge using T-bond futures contracts. Assume these contracts are now trading at

110 -12.

a. Briefly describe how the investor would set up this hedge. Would he go long or short? How many contracts would he need?

b. It's now six months later, and rates have indeed gone up. The investor's Treasury bonds are now being quoted at

93.5 %

of par, and the T-bond futures contracts used in the hedge are now trading at

96 -20.

Show what has happened to the value of the bond portfolio and the profit (or loss) made on the futures hedge.

c. Was this a successful hedge? Explain.

a. How would the investor set up the hedge? (Select the best answer below.)

A.

The investor needs to short

7

T-bond futures contracts to hedge.This is the correct answer.

B.

The investor needs to short

70

T-bond futures contracts to hedge.

C.

The investor needs to take a long position in

7

T-bond futures contracts to hedge.Your answer is not correct.

D.

The investor needs to take a long position in

70

T-bond futures contracts to hedge.b. The profit (or loss) on the bond portfolio at the expiration date of the futures contracts is

$−80500.00.

(Round to the nearest cent. Enter a positive number for a profit and a negative number for a loss.)The profit (or loss) on the futures at the expiration date of the futures contracts is

$nothing.

(Round to the nearest cent. Enter a positive number for a profit and a negative number for a loss.)

Answer 1

(a) As the investor possesses a portfolio of Treasury Bonds, the investor is long on the bonds. This implies that the investor loses if interest rates rise and consequently bond prices fall. In order to hedge against such a bond position, the investor will sell(short) a portfolio of T-Bond Future contracts. Upon maturity, the T-Bond futures can be bought(long) back to nullify the position in the futures market.

Par Value per T-Bond = $ 100000

Number of Bonds Bought Initially = 700000/100000 = 7

Value to be Hedged = $ 700000 and T-Bond Futures Contract Size = $ 100000

Number of Futures contract required = 700000 / 100000 = 7

Hence, the correct option is (a).

(b) Current Price per Bond = 105 % of par value ($100000)

Current Value of Bond Portfolio = 1.05 x 100000 x 7 = $ 735000

T-Bond Price after 6 months = 93.5 % of par

Bond Portfolio Value = 0.935 x 100000 x 7 = $ 654500

Loss in Bond Position = 735000 - 654500 = $ 80500

Current Price of one T-Bond Futures Contract = 110-12 or 110 + (12/32) of par value = (110.375/100) x 100000 = $ 110375

Futures Portflio Value = 7 x 110375 = $ 772625

Price of T-Bond Futures Contract after 6 months = 96-20 or 96+(20/32) of par value = (96.625/100) x 100000 = $ 96625

Futues Portfolio Value = 96625 x 7 = $ 676375

Profit in Futures Portfolio = 772625 - 676375 = $ 96250

Net Gain = Profit in Futures Portflio - Loss in Bond Portflio = 96250 - 80500 = $ 15750

(c) Although the hedge is a successful one because it not only saves a loss to the investor but infact makes a neat $15750 in profit for the investor. However, the objective of any hedge is not only to prevent any loss but also to not create any gains. In that respect the hedge although successful (in saving losses) is imperfect in nature as it leads to a gain for the investor instead of the ideal "no loss no gain" scenario of a hedging action.