FINANCE 4244: DEBT AND MONEY MARKETS



FIXED INCOME SECURITIES

LECTURE OUTLINE: FUTURES TWO

PROFESSOR DAVID T. BROWN

WARRINGTON COLLEGE OF BUSINESS

UNIVERSITY OF FLORIDA

The objective of this class is to teach you hedge interest rate risk using financial futures. We look at long hedges, short hedges and cross-hedges.

I. Long Hedge.

A long hedge occurs when an investor takes a long position in a futures contract to hedge the risk of an anticipated lending position. In simple terms, a long hedge is used to eliminate the risk associated with buying a bond in the future.

Long Hedge Example.

Today is January 1 and a pension fund manager will receive $1,000,000 in March to invest for the fund until June. The manager wants to lock in a rate today to invest the funds received in the future.

1. The expected 90-day rate in March is 7.45% so the March 90-day T-Bill futures contract futures sell for $98.22 = 100/(1.0745)1/4.

2. The manager buys a $1,000,000 in face value of 90 day T-Bill futures contracts today (1.02 contracts).

3. Assume the 90-day rate in March turns out to be 7.00%. The futures contracts expire worth $98.32.

4. The profits from the futures contracts are

[98.32 - 98.22](10,000)(1.02) = $1,020.

5. The manager invests $1,001,020 in March at 7.00%. This gives the investor (1,001,020)(1.07)1/4 or $1,018,096.

6. If the manager had invested $1,000,000 at 7.45%, the manager would have $1,018,126 which is what you get with the hedged position when rates are 7%.

II. Short Hedge.

A short hedge occurs when an investor takes a short position in a futures contract to hedge the risk of an anticipated borrowing position. In simple terms, a short hedge is used to eliminate the risk associated with issuing a bond in the future.

Short Hedge Example.

A firm with the ability to borrow at the risk-free rate wants to issue a one-year zero coupon bond in one year. To hedge the firm shorts (today) a one-year zero coupon bond futures that expires in one year.

7. Suppose that r1 = r2 = 10%. The market expects the one year rate in one year to be 10% and the price of a one year zero coupon bond futures contract that expires in one year is F = 100/(1.10) = $90.91.

8. The following table shows the possible outcomes in one year from the short hedge. Bt+1 represents the proceeds from the bond issue and F - Pt+1 is the futures contract profit or loss.

Interest rate next year Bt+1 F- Pt+1

r = 9% 91.74 -.83

r = 10% 90.91 0.00

r = 11% 90.09 +.82

9. In each case, the funds available for investment, the bond issue proceeds and the gain or loss from the futures contract equal $90.91. In this sense, the firm has locked in a borrowing rate of 10%.

III. Cross Hedging.

The above long and short hedge examples work perfectly because there exists a futures contract that to make or take delivery of bond identical to the bond issued or invested in. However, in practice, perfect hedges are rare.

Cross Hedge Example. Suppose the firm in the previous example that plans to issue a one year bond in one year can only short hedge by shorting a 180-day T-Bill futures that expires in one year. Again assume that r1 = r2 = 10% and the market expects the 180 day rate in one year to be 10%: F = 100/(1.10)½ = $95.34.

10. Assume that all term structure shifts are parallel so that 180 day and one year rate in one year are the same.

Rates next year Issue Proceeds Futures Proceeds Borrowing Costs

9% 91.74 -.44 9.53%

10% 90.91 0.00 10.00%

11% 90.09 +.42 10.48%

This hedge eliminates some risk however, the hedge does not work perfectly. What could you do to eliminate

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