Chapter 13

1. Chapter 13 Interest Rate Futures: Applications and Pricing

2. Applications and Pricing • Hedging debt positions • Speculative positions • Managing asset and liability positions • Formation of synthetic fixed-rate and floating-rate debt and investment positions • Pricing of futures contracts using the carrying-cost model • Use of foreign currency futures contracts to hedge international investment and debt position against exchange-rate risk

3. Hedging • Naïve Hedge • Cross Hedge

4. Naïve Hedging Model • The simplest model to hedge a debt position is to use a naive hedging model. • For debt positions, a naive hedge can be formed by hedging each dollar of the face value of the spot position with one market‑value dollar in the futures contract. • A naive hedge also can be formed by hedging each dollar of the market value of the spot position with one market‑value dollar of the futures.

5. Long Hedge - Future 91-Day T-Bill Investment • Consider the case of a treasurer of a corporation who is expecting a $5 million cash inflow in June that she is planning to invest in T‑bills for 91 days. • If the treasurer wants to lock in the yield on the T‑bill investment, she could do so by going long in June T‑bill futures contracts.

6. Long Hedge - Future 91-Day T-Bill Investment • Example: If the June T‑bill contract were trading at the index price of 95, the treasurer could lock in a yield (YTMf) of 5.1748% on a 91‑day investment made at the futures' expiration date in June:

7. Long Hedge - Future 91-Day T-Bill Investment • To obtain the 5.1748% yield, the treasurer would need to form a hedge in which she bought nf = 5.063291 June T‑bill futures contracts (assume perfect divisibility): nf = Investment in June = $5,000,000 = 5.063291 Long Contracts f0 $987,500

8. Long Hedge - Future 91-Day T-Bill Investment • At the June expiration date, the treasurer would close the futures position at the price on the spot 91‑day T‑bills. • If the cash flow, CF, from closing is positive, the treasurer would invest the excess cash in T‑bills. • If it is negative, the treasurer would cover the shortfall with some of the anticipated cash inflow earmarked for purchasing T-bills.

9. Long Hedge - Future 91-Day T-Bill Investment • Hedge Relation:

10. Long Hedge - Future 91-Day T-Bill Investment • Suppose at the June expiration, the spot 91-day T-bill rate is at 4.5%. • The manager would find T-bill prices higher at $989,086 but would realize a profit of $8,030.38 from closing the futures position. • Combining the profit with the $5M CF, the manager would be able to buy 5.063291 T-bills and earn a rate off the $5M investment of 5.1748%.

11. Long Hedge - Future 91-Day T-Bill Investment

12. Long Hedge - Future 91-Day T-Bill Investment • Suppose at the June expiration, the spot 91-day T-bill rate is at 5.5%. • The manager would find T-bill prices lower at $986,740 but would realize a loss of $3,848 from closing the futures position. • With the inflow of $5 million, the treasurer would need to use $3,848 to settle the futures position, leaving her only $4,996,152 to invest in T‑bills. • However, with the price of the T‑bill lower in this case, the treasurer would again be able to buy 5.063291 T‑bills, and therefore realize a 5.1748% rate of return from the $5 million investment.

13. Long Hedge - Future 91-Day T-Bill Investment

14. Long Hedge - Future 91-Day T-Bill Investment • Note, the hedge rate of 5.1748% occurs for any rate scenario.

15. Long Hedge - Future 182-Day T-Bill Investment Case: • Money market manager is expecting a $5M CF in June that she plans to invest in a 182-day T-bill. • Since the T-bill underlying a futures contract has a maturity of 91 days, the manager would need to go long in both a June T-bill futures and a September T-bill futures (note there is approximately 91 days between the contract) in order to lock in a return on a 182-day T-bill investment.

16. Long Hedge - Future 182-Day T-Bill Investment • If June T-bill futures were trading at IMM of 91 and September futures were trading at IMM of 91.4, then the manager could lock in a 9.3% rate on an investment in 182-day T-bills by going long in 5.115 June T-bill futures and 5.11 September contracts.

17. Long Hedge - Future 182-Day T-Bill Investment

18. Long Hedge - Future 182-Day T-Bill Investment • Suppose in June, the spot 91-day T-bill rate is at 8% and the spot 182-day T-bill rate is at 8.25%. • At these rates, the price on the 91-day spot T-bill would be $980,995, the price on the 182-day spot would be $961,245, and if the carrying-cost model holds, the price on the September futures would be $979,865. • At these prices, the manager would be able to earn a profit of $24,852 from closing both futures contract (which offsets the higher T-bill futures prices) and would be able to buy 5.227 182-day T-bills, yielding a rate of 9.3% from a $5M investment.

19. Long Hedge - Future 182-Day T-Bill Investment

20. Long Hedge - Future 182-Day T-Bill Investment • Suppose in June, the spot 91-day T-bill rate is at 10% and the spot 182- day T-bill rate is at 10.25%. • At these rates, the price on the 91-day spot T-bill would be $976,518, the price on the 182-day spot would be $952,508, and if the carrying-cost model holds, the price on the September futures would be $975,413. • At these prices, the manager would incur a loss of $20,798 from closing both futures contracts. However, with lower T-bill futures prices, the manager would still be able to buy 5.227 182-day T-bills, yielding a rate of 9.3% from a $5M investment.

21. Long Hedge - Future 182-Day T-Bill Investment

22. Short Hedge: Managing the Maturity Gap • In June, a bank makes a $1M loan for 180 days that it plans to finance by selling a 90-day CD now at the LIBOR of 8.258% and a 90-day CD ninety days later (in September) at the LIBOR prevailing at that time. • To minimize its exposure to market risk, the bank goes short in 1.03951 September Eurodollar futures at 92.4 (IMM). • By doing this, the bank is able to lock in a rate on its CD financing for 180 days of 8.17%.

23. Managing the Maturity Gap • Bank sells $1M of CD now (June) at 8.258%. At the September • maturity, the bank would owe $1,019,758. • To hedge this liability, the bank would go short in 1.03951 Eurodollar • futures at $981,000.

24. Managing the Maturity Gap • In September, the bank will sell a new 90-day CD at the prevailing LIBOR to finance its $1.019758M debt on the maturing CD plus (minus) any debt (profit) from closing its short September Eurodollar futures position. • If the LIBOR rate is higher, the bank will have to pay greater interest on the new CD, but it will realize a profit on its futures that, in turn, will lower the amount of funds it needs to finance. • On the other hand, if the LIBOR is lower, then the bank will have lower interest payment on its new CD, but it will also incur a loss on its futures position and therefore have more funds that need to be financed.

25. Managing the Maturity Gap • As shown in the exhibit on the next slide, at a September LIBOR’s of 7.5% or 8.7%, the bank’s total debt at the end of the 180-day period will be $1,039,509, which equates to a rate of 8.17%. • Note: This is true for any rate.

26. Managing the Maturity Gap

27. Cross Hedge: Price-Sensitivity Model • Cross Hedging is hedging a position with a futures contract in which the asset underlying the futures is different than the asset to be hedged. • Example: • Future CP sale hedged with T-bill futures • AA Bond portfolio hedged with T-bond futures

28. Cross Hedge: Price-Sensitivity Model • One model used for cross hedging is the price‑sensitivity model developed by Kolb and Chiang (1981) and Toers and Jacobs (1986)). • This model has been shown to be relatively effective in reducing the variability of debt positions. • The model determines the number of futures contracts that will make the value of a portfolio consisting of a fixed‑income security and an interest rate futures contract invariant to small changes in interest rates.

29. Cross Hedge: Price-Sensitivity Model

30. Cross Hedging Example: Hedging a Future CP Issue with T-bill Futures • A company plans to sell a 182-day CP issue with a $10M principal in June to finance its anticipated accounts receivable. • The company would like to lock in the current CP rate of 6%, ensuring it of funds from the CP sale of $9.713635M. • Using the price-sensitivity model, the company locks in a rate by going short in 20 June T-bill futures contracts at IMM index = 95.

31. Cross-Hedging Example: Hedging a Future CP Issue with T-Bill Futures

32. Cross Hedging Example: Hedging a Future CP Issue with T-bill Futures • If CP sold at a discount yield that was 25 BP greater than the discount yield on T-bills, then the company would be able to lock in a rate on its CP of 5.48% when it sold its CP and closed its futures position (assuming the time of the CP sale and T-bill futures expiration are the same).

33. Cross Hedging Example: Hedging a Future CP Issue with T-bill Futures

34. Cross Hedging Example: Hedging a Future AAA Bond Sale Issue with T-bill Futures • Bond portfolio manager plans to sell AA bond portfolio in June. Currently, the fund has the following features: • Current Value = $1.02M, • YTM = 11.75% • Duration = 7.66 years • Weighted Average Maturity = 15 years.

35. Cross Hedging Example: Hedging a Future AAA Bond Sale Issue with T-bill Futures • Suppose the manager is considering hedging the portfolio against interest rate changes by going short in June T‑bond futures contracts currently trading at f0 = 72 16/32 with the T-bond most likely to be delivered on the contract having the following features: • YTM = 9%, • Maturity = 18 years • Duration of 7 years • Using the Price‑Sensitivity Model, the portfolio manager could hedge the bond portfolio by selling 14 futures contracts.

36. Cross Hedging Example: Hedging a Future AAA Bond Sale Issue with T-Bond Futures

37. Cross Hedging Example: Hedging a Future AAA Bond Sale Issue with T-bill Futures • If the manager hedges the bond portfolio with 14 June T‑bond short contracts, she will be able to offset changes in the bond portfolio's value resulting from interest rate changes.

38. Cross Hedging Example: Hedging a Future AAA Bond Sale Issue with T-bill Futures • Example, suppose interest rates increased from January to mid‑May causing the price of the bond portfolio to decrease from 102 to 95 and the futures price on the June T‑bond contract to decrease from 72 16/32 to 68 22/32. • In this case, the fixed‑income portfolio would lose $70,000 in value (decrease in value from $1,020,000 to $950,000). • This loss, though, would be partially offset by a profit of $53,375 on the T‑bond futures position: Futures Profit = 14[$72,500 ‑ $68,687.50] = $53,375. • Thus, by using T‑bond futures the manager is able to reduce some of the potential losses in her portfolio value that would result if interest rates increase.

39. Speculating with Interest Rate Futures • While interest rate futures are extensively used for hedging, they are also frequently used to speculate on expected interest rate changes. • A long futures position is taken when interest rates are expected to fall. • A short position is taken when rates are expected to rise.

40. Speculating with Interest Rate Futures • Speculating on interest rate changes by taking such outright or naked futures positions represents an alternative to buying or short selling a bond on the spot market. • Because of the risk inherent in such outright futures positions, though, some speculators form spreads instead of taking a naked position. • A futures spread is formed by taking long and short positions on different futures contracts simultaneously.

41. Speculating with Interest Rate Futures Outright Positions: • Long: Expect rates to decrease • ST Rates: use T-bills or Eurodollar futures • LT Rates: use T-bonds or T-note futures • Short: Expect rates to increase • ST Rates: use T-bills or Eurodollars futures • LT Rates: use T-bonds or T-note futures

42. Speculating with Interest Rate Futures Spread: • Intracommodity Spread: long and short in futures on the same underlying asset but with different expirations. • Intercommodity Spread: Long and short in futures with different underlying assets but the same expiration.

43. Intracommodity Spread • More distant futures contracts (T2) are more price-sensitive to changes in the spot price than near-term futures contracts (T1):

44. Intracommodity Spread • A speculator who expected the interest rate on long-term bonds to decrease in the future could form an intracommodity spread by going • long in a longer-term T-bond futures contract and • short in a shorter-term one. • This type of spread will be profitable if the expectation of long-term rates decreasing occurs.

45. Intracommodity Spread • That is, the increase in the T-bond price resulting from a decrease in long-term rates, will cause the price on the longer-term T-bond futures to increase more than the shorter-term one. As a result, a speculator’s gains from his long position in the longer-term futures will exceed his losses from his short position. • If rates rise, though, losses will occur on the long position; these losses will be offset partially by profits realized from the short position on the longer-term contract

46. Intracommodity Spread • If a bond speculator believed rates would increase but did not want to assume the risk inherent in an outright short position, he could form a spread with • a short position in a longer term contract and • a long position in the shorter term one.

47. Intracommodity Spread • Note that in forming a spread, the speculator does not have to keep the ratio of long- to-short positions one-to-one, but instead could use any ratio (2-to-1, 3-to-2, etc.) to give him his desired return-risk combination.

48. Intercommodity Spread:Rate-Anticipation Swap • Consider the case of a spreader who is forecasting a general decline in interest rates across all maturities (i.e., a downward parallel shift in the yield curve). • Since bonds with greater maturities are more price sensitive to interest rate changes than those with shorter maturities, a speculator could set up a rate-anticipation swap by going long in the longer-term bond with the position partially hedged by going short in the shorter-term one.

49. Intercommodity Spread:Rate-Anticipation Swap • Instead of using spot securities, the specualtor alternatively could form an intercommodity spread by going long in a T-bond futures contract that is partially hedge by a short position in a T-note (or T-bill) futures contract. • On the other hand, if an investor were forecasting an increase in rates across all maturities, instead of forming a rate-anticipation swap with spot positions, she could go short in the T-bond futures contract and long in the T-note. • Forming spreads with T-note and T-bond futures is one of the more popular intercommodity spread strategies; it is referred to as the NOB strategy (Notes over Bonds).

50. Intercommodity Spread:Quality Swap • Another type of intercommodity spreads involves contracts on bonds with different default risk characteristics; it is an alternative to a quality swap. • For example, a spread formed with futures contracts on a T-bond and a Municipal Bond Index (MBI) or contracts on T-bills and Eurodollar deposits. • Like quality swaps, profits from these spreads are based on the ability to forecast a narrowing or a widening of the spread between the yields on the underlying bonds.