Question

A financial intermediary’s balance sheet is such that DA= 5, DL = 3. This FI has $300 million in assets and net worth (equity) of $50 million. Suppose that the FI has futures contracts available on 10-year US Treasuries. These bonds have a duration of 8.17, pay a coupon of 4%, and are priced to yield 6% and sell for $0.851 per $1. The minimum contract size is $100,000. How many contracts are required to fully hedge the interest

Answer 1

To fully hedge the interest, 500 futures contracts are required.

Step-by-step explanation:

To calculate the number of futures contracts required to fully hedge the interest, we need to determine the duration of the bonds.

Duration is a measure of the sensitivity of a bond's price to changes in interest rates. It tells us how much the price of the bond will change for a one-percentage-point change in interest rates.

In this case, the bonds have a duration of 8.17. To fully hedge the interest, we need to match the duration of the futures contracts to the duration of the bonds. Each futures contract covers $100,000 of bonds, so we divide the total value of the bonds ($50 million) by the contract size to get the number of contracts required:

Number of contracts = bond value / contract size = $50,000,000 / $100,000 = 500 contracts.