Hedging with T-bond Futures Example: Suppose a mortgage banker has agreed on March 1st to supply $1 million in funds to clients wishing to purchase homes. The terms of the agreement are for 12% mortgages over 20 years. So, 12% is the “market rate” as of March 1st, when this agreement is made. Furthermore, the broker has agreed to supply these funds on May 1st, (2 months later).

Hedging with T-bond Futures Many mortgage bankers (including this one) make these agreements before they have the $1 million dollars in hand. So, they must shop around to find a buyer for the 12% mortgages that will be established on May 1st. The buyer purchases the mortgages and provides funds to be passed on to the home buyers. The mortgage banker will play middle man.

Hedging with T-bond Futures It takes time to shop around for a buyer. Many insurance companies look for such opportunities to invest part of their excess cash. Suppose on April 15th, the mortgage banker finds a willing insurance company to buy the mortgages.

Example continued: Mar 1 Apr 15 May 1 Between Mar 1st (when the prevailing interest rates were 12%) and April 15th, when the insurance company entered the picture, interest rates could have changed! If interest rates went up, the insurance firm might only give the mortgage broker, say, $940,000 for the $1 million in mortgages. This would leave the banker to have to come up with the additional $60,000. If interest rates went down, however, the insurance firm might be willing to pay a premium for the $1 million in mortgages, say, $1,050,000. This would be an unexpected increase in revenue to the banker, as he only needed $1 million.

Questions: How could the Mortgage Broker hedge against this Interest Rate Risk using Treasury Bond Futures (a.k.a. Interest Rate Futures)? Should the broker take a long or short position? How many contracts to cover exposure? When should these contracts be entered into and when should they be closed out (reverse the position)?

Example continued: How could the Mortgage Broker hedge against this Interest Rate Risk? Use Treasury Bond Futures (a.k.a. Interest Rate Futures). Current situation: If interest rates go up, banker gets hurt If interest rates go down, banker profits. To hedge, we want an instrument that has the opposite reactions to interest rate changes!

When is money made with a Long position When is money made with a Long position? 1 Long Treasury Bond Futures Contract Treasury Bond Futures have a $100,000 contract size Day Futures Price (in 32nds) Futures Price (in decimals) Daily Gain (Loss) Cumulative Gain (Loss) Margin Account Balance Maintenance Call? (at $3,923.44) Initial 104-20 104.625 5231.25 Nov 17 104-28 104.875 250 5481.25 No … Nov 27 105-14 105.438 563 813 7981.75 Our hedge goal: Profits when rates rise; Losses when rates fall. With a LONG position above, we see that when interest rates fall (and therefore the bond prices rise), it leads to a gain. This will compound our gains when rates rise and compound our losses when rates rise. So, a long position won’t work for hedging purposes.

When is money made with a Short position When is money made with a Short position? 1 Short Treasury Bond Futures Contract Treasury Bond Futures have a $100,000 contract size Day Futures Price (in 32nds) Futures Price (in decimals) Daily Gain (Loss) Cumulative Gain (Loss) Margin Account Balance Maintenance Call? (at $3,923.44) Initial 104-20 104.625 5231.25 Nov 17 104-28 104.875 -250 4981.25 No … Nov 27 105-14 105.438 -563 -813 4418.25 Our hedge goal: Profits when rates rise; Losses when rates fall. With a SHORT position above, we see that when interest rates fall (and therefore the bond prices rise), it leads to a loss. This is the pattern that we want for our hedging purposes.

How many contracts to short? We have a $1 million in mortgages to hedge. Contract size for Treasury bonds are $100,000 each. So, short 10 contracts ($1 million / $100,000). Note: this example assumes that the mortgages and the T-bond futures contracts react similarly to changes in interest rates. In fact, this is a bit more complicated. But we haven’t covered Duration yet!

When to open and close contracts Date/Event Mortgage Markets Futures Markets March 1 Banker agrees to loan $1 million at 12% for 20 years. The loans are to be funded on May 1st. No cash exchanges hands here. Banker simultaneously shorts (sells) 10 Treasury-bond futures contracts with a delivery date past May 1st. April 15 Loans are sold to Insurance Company. Banker will receive these sale proceeds on May 1 based on Apr 15th interest rates. Mortgage banker will conduct reversing trades (buy 10 contracts), thereby locking in the gain/loss associated with them. If Interest rates rise between March 1 and April 15… Loans are sold to Insurance Company for a price below $1 million. Banker LOSES. Each short Futures contract is closed out at a GAIN because the increase in interest rates have driven down futures prices for bonds. If Interest rates fall between March 1 and April 15… Loans are sold to Insurance Company for a price above $1 million. Banker GAINS. Each short Futures contract is closed out at a LOSS because the decrease in interest rates have pushed up futures prices for bonds.