Hedging and Duration Management with Fixed Income Futures

1. Hedging and Duration Management with Fixed Income Futures Taipei Interest Rate Futures Conference November 20, 2003 Nick Ronalds, CFA Senior Vice President ABN AMRO Incorporated

2. “The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk.” Peter Bernstein, Against the Gods.

3. Comments by Tony Latter, Deputy Chief Executive, Hong Kong Monetary Authority • Derivatives have brought substantial benefits to the commercial community, in facilitating hedging and hence business planning more generally, and have enabled the financial institutions to offer a progressively wider range of services and greater efficiency in the intermediation process, as well as to exploit market imperfections and other trading opportunities for their own gain. November 5, 2001, Hong Kong See http://www.info.gov.hk/hkma/eng/speeches/speechs/tony/20011106.htm for complete text of his comments.

4. “The hardest thing to convey to a controller is that if you’re doing nothing, you’re speculating.”Christine Snouffer, Treasury Risk Manager, Fellowes Corp.

5. Advantages of Futures • Low transactions costs • Transaction costs can be as little as 5% of cash market for comparable exposure. • price transparency • Positions can be offset • System financial integrity • Off-balance sheet items. • “Level playing field” for all participants

6. ABN AMRO Futures • Global Capabilities - Local presence and Expertise • Full product range including: Interest rates, equity indices, energy, metals, grains, softs as well as O-T-C metals and energy products. • Membership on all major futures exchanges around the world

7. ABN AMRO Futures • 450 Futures professionals in nine offices (Paris, London, New York, Chicago, Singapore, Sydney, Hong Kong, Tokyo and Seoul) • Expect to clear and/or executed 350 Million contracts in 2003. • Backed by the resources of ABN AMRO Bank. (Group capital of 31.1 euros)

8. Key Areas of Futures Expertise • Open Outcry Execution in Fixed Income Derivatives including: Eurodollar, Treasury Bond & Note futures. • Open outcry and electronic execution of all major U.S. and non-U.S. equity index and fixed income futures. • Client-focused access to global futures markets, including our 24-hour desk, access to our local specialists around the world, and electronic execution where available. • Options Strategies • Electronic Delivery of Client Trade and Clearing Data

9. ABN AMRO Futures - Highlights • A range of electronic Order Entry Solutions suited to client needs. • Global Capabilities - Local presence and expertise • Number one in Execution Volume for CME Eurodollar Futures & Options • No. 2 overall in CME execution volume in 2002, including interest rates and equity futures. • Top Five in Execution Volume in CBOT Treasury Futures& options

10. World Futures Volume

11. World Options on Futures

12. Total World Futures + Options on Futures

13. Global Futures & Options by Subgroup

14. Part 1A Conceptual Introduction

15. A Conceptual Introduction To Treasury Futures: • They are highly liquid contracts with low transactions costs. • Treasuries are traded on the Chicago Board of Trade (CBOT). There are March, June, September and December contracts. • They are priced off of a basket of cash Treasury notes or bonds (CBOT). • The Treasuries in the basket can be delivered at expiration of the futures contract , assuring a strong correlation to the Treasury market.

16. Other Bond Futures • Other sovereign debt futures such as the German Bund contract, for the most part are structured similarly to the U.S. Treasury Futures contracts.

17. Treasury Futures Are Used To: • Hedge fixed income securities - Sovereign debt, Treasuries, Corporates, MBS, Agencies, etc. • Create synthetic money market vehicles that can be traded as part of an arbitrage strategy in conjunction with other real or synthetic money market instruments. • Achieve portfolio allocation strategies that unbundled the decision of market exposure from relative value decisions. • Extend or shorten duration. • Speculate on the direction of interest rates. • Remember: doing nothing = speculation

18. The Users of Treasury Futures: • Broker/dealers who hedge their fixed income inventories or opt to express interest rate views with futures. • Portfolio managers who may opt to hedge, manage duration, or make preemptive allocation decisions based upon the pattern of funds coming in or leaving the fund. These managers may work for a mutual fund, pension fund, insurance company, bank, or the treasurers department of a corporation. • CTAs and hedge funds who may hedge or speculate on the direction of interest rates.

19. Treasury Note and Bond Futures Cover 4 Points on the US Yield Curve. Contract Details Include the Following:

20. Cash and Futures Markets Price Notations : The fractional part of the price is denoted in 32nds i.e. 107-25 = 107 25/32 = 107.78125 in Decimal and 107-25 ¹ 107.25 decimal. Cash market price progression : 107-25, 107-25+, 107-26 … T-Bond futures price progression : 102-25, 102-26, 102-27 … 10-Year / 5-Year T-Note futures price progression : 104-25, 104-255, 104-26… 2-Year T-Note price progression :103-2500, 103-2525, 103-2550 ...

21. Review of Duration • Duration tells you by what percentage a bond or bond portfolio will change in price with a 100 bp change in yield.

22. Treasuries 2-yr Note - 3 5-yr Note - 5 10-yr Note - 9 Bond - 28 The Number of Different Treasuries that May be Delivered into the December 2003 Contracts?

25. Part 2Conversion Factors, etc.

26. Conversion Factors • Conversion factors adjust the price of a deliverable bond or note, with different coupon, maturity and yield characteristics, to the equivalent price of an 6.00 % coupon. • To calculate invoice price of treasury issue, to be delivered into the futures contract. • Securities with coupons > 6.00 % will have conversion factors > 1.0000 to reflect a premium. • Securities with coupons < 6.00 % will have conversion factors < 1.0000 to reflect a discount

27. Ex: Nov 6, 2003. Five Year Note issues deliverable against the Dec-03 Five Year Futures Contract (Last Delivery Date Dec 31, 2003) These would be the prices if yields were 6%

28. Conversion Factors • In effect, as you can see, what conversion factors are doing is establishing the relative values of the various deliverable issues.

29. Conversion Factors Conversion Factors (CF) are used to determine futures invoice price : FIP = (FP x CF) + AI where: FIP = Futures Invoice Price FP = Futures Price CF = Conversion Factor AI = Accrued Interest

30. Conversion factors • There’s one little problem with the conversion factors. • They don’t do a perfect job of establishing relative prices of the deliverable bonds! • As a result, some bonds are slightly “cheaper” than others, and one will be the “cheapest to deliver,” or CTD.

31. Pricing--“Cost of Carry Model” The price of a futures should be: Futures = S(1 + rf + c - y)t Costs of storage & insurance, as a % of spot = 0 Price of CTD Repo rate The “coupon” In this case, the repo or financing cost is higher than the coupon, so futures are above spot.

32. Price Basis { CTD Futures x Conversion Factor Convergence at expiration Delivery Month Basis and Convergence

33. Part 6Constructing a Basic Hedge

34. Hedge objective • What is the objective of a hedge? • To establish a position with a hedge instrument such that changes in the value of the hedge instrument exactly offset changes in the value of the instrument being hedged.

35. Dollar Value of a Basis Point (BPV or DV01) • With Treasury futures, we equate the the values of the instrument being hedged and the hedge instrument using the value of a basis point.

36. Dollar Value of a Basis Point (BPV or DV01) • Definition : It is the dollar change in the price of cash instrument due to a basis point (0.01) change in the yield. • Since it represents the sensitivity to a given change in yield, it is useful, among other things, when constructing precise hedges.

37. Using “BPV” to Hedge a Fixed Income Position With Treasury Futures Number of contracts required = BPV cash issue BPV futures Where: BPV futures = BPV cheapest-to-deliver CTD conversion factor

38. Using “BPV” to Hedge a Fixed Income Position • On Nov 6, a trader wants to hedge a $10 M long position in a 30yr bond treasury, the 5 3/8 of 02/15/31. The treasury issue has a BPV of $146.10 per $100,000, i.e. • The BPV of the portfolio is $14,610 per $10 Million. • The trader wants to hedge this position using the Dec-03 bond futures contract. • On Nov 6, the CTD issue for the Dec-03 bond futures contract was the 6 7/8 of 08/15/25. This issue had a conversion factor of 1.1049 and a BPV of $145.10 per $100,000.

39. BPV of Futures • Remember, the invoice price of a treasury delivered into a futures contract is • Price x Conversion Factor +AI • Since we multiply the futures price by the conversion factor to get the invoice price, which should be very close to the market value of the bond…

40. BPV of Futures • To get the basis point value of the futures, we need to divide the BPV of the bond by the conversion Factor: • BPV (Futures) = Price (CTD)/CF

41. Using “BPV” to Hedge a Fixed Income Position BPV of Future = BPV CTD / Conversion Factor of CTD = $145.10 / 1.1049 = $131.32 per $ 100,000. Hedge Ratio = BPV of portfolio / BPV of future = $14,610 / $131.32 = 111 The trader should sell 124 of the Dec-03 bond futures contracts.

42. Hedging with Financial Futures : • Choose the futures contract that most closely describes the nature of the underlying risk in order to minimize yield-curve risk. • Choose the futures expiration month that most closely matches the time period to be addressed while keeping in mind that the “nearby” contract is the most liquid. • The right hedge ratio will equalize the “BPV”s of the hedged issue and the futures position, but some immunization risk (yield-curve risk) may still remain.

43. Important Question! • Suppose you have hedged a bond portfolio with a 5.50 % yield. • Now you hedge that portfolio, removing market risk • What will the yield on your portfolio now be?

44. Using Futures to Adjust Duration

45. Duration Management

46. Adjusting Duration of a Bond Portfolio Containing Futures Target Bond Bond Portfolio - Portfolio Hedge = BPV BPV Ratio Futures BPV

47. Duration Management Closing Date : Nov 6, 2003 Settlement Date : Nov 10, 2003 Coupon Maturity # of Quoted Market Price Total Modified Equivalent MM/DD/YY Contracts Price (P+AI) Market Price Duration Duration (32nds) (Decimal) # * (P+AI) 3.375 04/30/04 400 101-03 1.011494 40,459,760 0.481 0.19 3.500 11/15/06 315 102.21+ 32,865,935 2.816 0.89 1.043363 6.500 02/15/10 125 115-02 1.165285 14,566,063 5.170 0.65 4.875 02/15/12 154 104-16+ 1.056151 16,264,725 6.730 1.04 Weighted Cash Position 994 104,156,482 2.78

48. Managing Duration • Your portfolio duration is 2.78 • Suppose you want a portfolio with the return and volatility characteristics provided by a duration of 5.0?

49. Basis Point ValuesDuration x Portf Value x .0001 • Portfolio BVP: • 2.78 x .0001 x $104,156,482 = $27,799.56 • Target BVP: • 5.00 x .0001 x $104,156,482 = $52,078.24 • Dec-03 Five Year Treasury Futures BPV: • BPV of CTD: $39.50 per $100,000 • Conversion Factor of CTD: .8908 • BPV of futures: $39.50/.8908 = $44.34

50. Adjusting Duration of a Bond Portfolio Containing Futures $52,078.24 - $27,799.56 Hedge = Ratio $44.34 = 547.56, or buy 548 contracts.