Question

On August 2, a securities dealer, Ms. Marie VanZutpen, responsible for a $10 million bond portfolio is concerned that interest rates are expected to be highly volatile over the next 3 months. The fund manager decides to use Treasury bond futures to hedge the value of the bond portfolio. The current price on a December T-bond futures is 70-06. During the period August 2 to November 2, interest rates climbed rapidly causing the bond portfolio value to drop as prices of T-Bonds declined from 101-00 to 95-22. On November 2, the December T-Bond futures contract was priced at 66-22. The portfolio was sold at its market value on Nov. 2. The minimum contract size for the T-Bond futures contract is $100,000 and the minimum price change is $31.25 per tick of 1/32.

a. State what kind of hedge could MsVanZutpen take and why.

b. Compute the opportunity cost of waiting to sell the portfolio. Describe all transactions clearly.

c. Compute gain or loss in the futures market after describing the transactions.

d. Calculate the effective revenue with the hedge. Describe all transactions clearly

Answer 1

a)

As we know if the interest rates will decreases in coming 3 months than analyst will be in profit as this will incerase the price of her bonds and same if interest rate increases than bonds price will decreases. so for hedging this analyst should go short or sell the future of T-bond.

As we know that the price of T-Bond futures contracts vary inversely to the market interest rates. Therefore, higher interest rates tend to lower the price of futures and lower interest rates push the price of the futures higher.

So if bond portfolio is loosing during higher interest rates than she will be gaining through T-bond futures (Short Position).

b)

As we can see from the question that T-bond price droped from 101-00 to 95-22 (95 22/32)

So T-bond decrased by (Tick size 1/32)

101 to 100 = 32 tick decrease

100 to 99 = 32 tick decrease

99 to 98 = 32 tick decrease

98 to 97 = 32 tick decrease

97 to 96 = 32 tick decrease

96 to 95 22 / 32 = 10 tick decrease

So in total 170 tick decrease which is 170/32 = 5.3125 out of 101

Hence a $10 milion bond portfolio will reduce by 10*5.3125/101 = $0.526 milion

so opportunity cost will be $0.526 milion.

c)

Here analyst has to buy 10000000 / 100000 = 100 contracts

so per tick price will change by 31.25 * 100 = $3125

So total tick in droping the price from 70-06 to 66-22 is 6+32+32+32+10 = 112

So analyst will earn through shorting of future contract is = 112 *3125 = $350000

d)

So the loss will be limited to 526000 - 350000 = $201000

Thank You!!