Question

A wealthy investor holds ​$600,000 worth of U.S. Treasury bonds. These bonds are currently being quoted at 107​% 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 111​-00

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 94.5​% of​par, and the​ T-bond futures contracts used in the hedge are now trading at 97​-24.Show what has happened to the value of the bond portfolio and the profit​ (or loss) made on the futures hedge.

Profit (or loss) in the bond portfolio at the expiration date of the futures contracts is $______.

Profit (or loss) on the futures at the expiration date of the futures contracts is $________.

The net profit (or loss) of the combined hedge portfolio is $_______.

c. Was this a successful​ hedge? Explain.

Answer 1

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Answer:

(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 = 600000/100000 = 6

Value to be Hedged = $ 600000 and T-Bond Futures Contract Size = $ 100000

Number of Futures contract required = 600000 / 100000 = 6

(b) Current Price per Bond = 107 % of par value ($100000)

Current Value of Bond Portfolio = 1.07 x 100000 x 6 = $ 642000

T-Bond Price after 6 months = 94.5 % of par

Bond Portfolio Value = 0.945 x 100000 x 6 = $ 567000

Loss in Bond Position = 642000 - 567600 = $ 74400

Current Price of one T-Bond Futures Contract = 111-10 or 111 + (00/32) of par value = (111/100) x 100000 = $ 111000

Futures Portflio Value = 6 x 111000 = $ 666000

Price of T-Bond Futures Contract after 6 months = 97-24 or 97+(24/32) of par value = (97.75/100) x 100000 = $ 97750

Futues Portfolio Value = 97750 x 6 = $ 586500

Profit in Futures Portfolio = 666000 -586500 = $ 79500

Net Gain = Profit in Futures Portflio - Loss in Bond Portflio =79500 -74400 = $ 5100

(c) Although the hedge is a successful one because it not only saves a loss to the investor but infact makes a neat $5100 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.