1. Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 11: Advanced Futures Strategies Fund managers who aren’t using futures and options are dealing with an incomplete set of resources. Paul Daley Portfolio Managers Talk Futures and Risk Management Chicago Mercantile Exchange videotape, 1995

2. Copyright © 2001 by Harcourt, Inc. All rights reserved.2 Important Concepts in Chapter 11 n Futures spread and arbitrage strategies n Short-term interest rate futures strategies n Intermediate-term interest rate futures strategies n Long-term interest rate futures strategies n Stock index futures strategies

3. Copyright © 2001 by Harcourt, Inc. All rights reserved.3 Short-Term Interest Rate Futures Strategies n Treasury Bill Cash and Carry/Implied Repo u Cash and carry transaction means to buy asset and sell futures u Repurchase agreement/repo to obtain funding u Overnight vs. term repo  Cost of carry pricing model: f 0 (T)  Cost of carry pricing model: f 0 (T) = S 0 +  u u Implied repo rate:

4. Copyright © 2001 by Harcourt, Inc. All rights reserved.4 Short-Term Interest Rate Futures Strategies (continued) n Treasury Bill Cash and Carry/Implied Repo Rate u Also equivalent to buying longer term bill and converting it to shorter term bill. u Example. See Table 11.1, p. 458. n Eurodollar Arbitrage u See Table 11.2, p. 460.

5. Copyright © 2001 by Harcourt, Inc. All rights reserved.5 Intermediate and Long-Term Interest Rate Futures Strategies u Recall the option to deliver any T-bond with at least 15 years to maturity or first call. u Adjustment to futures price using conversion factor, which is the price per $1.00 par of a 6% bond delivered on a particular expiration. u Invoice price = (Settlement price on position day)/(Conversion factor) + Accrued interest u Example: Delivery on March 2000 contract. Settlement price is 112-16 ($112,500) on position day.

6. Copyright © 2001 by Harcourt, Inc. All rights reserved.6 Intermediate and Long-Term Interest Rate Futures Strategies u You plan to deliver the 7 7/8s of 2021 on March 3. CF = 1.2207. Coupon dates of February 15 and August 15. Last coupon on February 15, 2000. Days from 2/15 to 3/3 is 17. Days from 2/15 to 8/15 is 182. Accrued interest F $100,000(.07875/2)(17/182) = $368 u Invoice price: F $112,500(1.2207) + $368 = $137,697

7. Copyright © 2001 by Harcourt, Inc. All rights reserved.7 Intermediate and Long-Term Interest Rate Futures Strategies u Next day, Notice of Intention Day, Thursday, March 2, the short invoices the long $137,.697. The long pays for and receives the bond on Friday, March 3. u Table 11.3, p. 463 shows CFs and invoice prices for other deliverable bonds on the March 2000 contract.

8. Copyright © 2001 by Harcourt, Inc. All rights reserved.8 Intermediate and Long-Term Interest Rate Futures Strategies n Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract u Recall the option to deliver any T-bond with at least 15 years to maturity or first call. u Example: Delivery on March 2000 contract of 7 7/8s of February 15, 2021. u Cost of delivering bond F f(CF) + AI T - [(B + AI t )(1+r) (T-t) - FV of coupons at T]

9. Copyright © 2001 by Harcourt, Inc. All rights reserved.9 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued) u Example: Deliver the 8 7/8s of 8/15/17 on the March 2000 contract on March 3. f = 94 1/32 = 94.03125, CF = 1.3062, AI t = 0.92, AI T = 0.41 (deliver on March 3), B = 124 21/32. 163 days between September 22 and March 3. Repo rate =.058. u Invoice price F 94.03125(1.3062) + 0.41 = 123.24

10. Copyright © 2001 by Harcourt, Inc. All rights reserved.10 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued) u Coupon of 4.4375 received on February 15 is reinvested at 5.8% for 17 days to grow to 4.4375(1.058) 17/365 = 4.45 u Forward price of deliverable bond F (124.65625 + 0.92)(1.058) 163/365 - 4.45 = 124.33 u So the bond would cost 1.09 more than it would return.

11. Copyright © 2001 by Harcourt, Inc. All rights reserved.11 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued) u All we can do, however, is compare this result with that for another bond. For the 9 1/8s of May 15, 2018 with CF = 1.3411 and price of 127 27/32, we have accrued interest of 3.22 on September 22 and 2.73 on March 3. Coupon of 4.5625 on November 15 is reinvested at 5.8% for 109 days and grows to 4.5625(1.058) 109/365 = 4.64.

12. Copyright © 2001 by Harcourt, Inc. All rights reserved.12 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued) u Forward price is, therefore, F (127.84375 + 3.22)(1.058) 163/365 - 4.64 = 129.77 u Invoice price is F 94.03125(1.3411) + 2.73 = 128.84. u Thus, this bond would cost 0.93 more than it would return. So the 9 1/8 bond is better than the 8 7/8 bond. u Table 11.4, p. 406 shows these calculations for all deliverable bonds. Software Demonstration 11.1, p. 468 shows how to use ctd2.xls to do these calculations.

13. Copyright © 2001 by Harcourt, Inc. All rights reserved.13 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued) u Why identifying the cheapest-to-deliver bond is important: F Identifying the true spot price F Calculating the correct hedge ratio

14. Copyright © 2001 by Harcourt, Inc. All rights reserved.14 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Delivery Options u The Wild Card Option F Futures market closes at 3:00 pm while spot market stays open until at least 5:00 pm. F This allows the holder of a short futures contract during the delivery month to potentially profit from a decline in the price of a deliverable bond during that two hour period in the expiration month. F Illustration: f 3 = futures price at 3:00 pm, S 3 = spot price at 3:00 pm. CF = conversion factor

15. Copyright © 2001 by Harcourt, Inc. All rights reserved.15 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Delivery Options (continued) u The Wild Card Option (continued) F Let the short own 1/CF bonds (CF must be > 1.0, so coupon must be > 8 percent). This is less than one bond per contract so additional bonds, called “the tail,” will have to be purchased in order to make delivery. F At 5:00 pm, the spot price is S 5. It is profitable to purchase these bonds at 5:00 pm if S 5 < f 3 (CF). F This holds because the invoice price is locked in but the spot price of the bonds can potentially fall.

16. Copyright © 2001 by Harcourt, Inc. All rights reserved.16 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Delivery Options (continued) u The Wild Card Option (continued) F If the spot price does not fall sufficiently, then the short simply waits until the next day. By the last eligible delivery day, the short would have to make delivery. F This is a potentially valuable option granted by the long to the short and its value would have to be reflected in a lower futures price at 3:00 pm.

17. Copyright © 2001 by Harcourt, Inc. All rights reserved.17 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Delivery Options (continued) u The Quality Option F Also called the switching option, it gives the short the right to change deliverable bonds if another becomes more attractive. This right also exists in various other futures markets. F Similar to this is the location option, which is the right to choose from among several eligible delivery locations. This can be valuable when the underlying is a storable commodity.

18. Copyright © 2001 by Harcourt, Inc. All rights reserved.18 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Delivery Options (continued) u The End-of-the-Month Option F The right to make delivery any one of the business days at the end of the month after the futures contract has stopped trading, around the third week of the month. F Similar to the wild card option because the invoice price is locked in when the futures stops trading.

19. Copyright © 2001 by Harcourt, Inc. All rights reserved.19 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Delivery Options (continued) u The Timing Option F The right to deliver on any eligible day of the delivery month. F Delivery will be made early in the month if the bond earns a coupon that is less than the cost of financing it. F Delivery will be made late in the month if the bond earns a coupon that exceeds the cost of financing it.

20. Copyright © 2001 by Harcourt, Inc. All rights reserved.20 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Implied Repo/Cost of Carry u Buy spot T-bond, sell futures. u This will produce a return (implied repo rate) of

21. Copyright © 2001 by Harcourt, Inc. All rights reserved.21 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Implied Repo/Cost of Carry (continued) u Example: On September 22, 1999, CTD bond on March contract is 8 1/8s maturing in about 21 years. Spot price is 118 21/32, accrued interest is 0.84, CF = 1.2532 and futures price is 94.03125. From September 22 to March 1 is 161 days so T = 161/365 = 0.4411. Accrued interest reflects the reinvestment of a coupon on February 15 for 15 days and the accrual of 15 days toward the next coupon. So accrued interest is F 4.0625(1.058) 15/365 + 4.0625(15/184) = 4.40.

22. Copyright © 2001 by Harcourt, Inc. All rights reserved.22 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Implied Repo/Cost of Carry (continued) u Implied repo rate is, therefore, u If the bond can be financed in the repo market for less than 5.28%, then the arbitrage would be profitable.

23. Copyright © 2001 by Harcourt, Inc. All rights reserved.23 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n A Treasury Bond Futures Spread u See Table 11.5, p. 475.

24. Copyright © 2001 by Harcourt, Inc. All rights reserved.24 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Treasury Bond Spread/Implied Repo Rate u Let time t be expiration of nearby futures and T be expiration of deferred futures. u Go long the nearby and short the deferred. u When nearby expires, take delivery and hold until expiration of deferred. This creates a forward transaction beginning at t and ending at T

25. Copyright © 2001 by Harcourt, Inc. All rights reserved.25 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Treasury Bond Spread/Implied Repo Rate (continued) u Implied repo rate u Example: On September 22, CTD was 8 1/8s maturing in about 21years. Examine the March-June spread. March priced at f 0 (t) = 94.03125 with CF(t) = 1.2532. June priced at f 0 (T) = 93.625 with CF(T) = 1.2518. AI t (March 3) = 0.38 and AI T (June 2) = 2.41. From March 3 to June 2 is 91 days.

26. Copyright © 2001 by Harcourt, Inc. All rights reserved.26 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Treasury Bond Spread/Implied Repo Rate (continued) u Implied repo rate u Compare to actual repo rate and note that this is a forward rate. u Note the turtle trade: Implied repo rate on T-bond spread to T-bill futures rate

27. Copyright © 2001 by Harcourt, Inc. All rights reserved.27 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Intermarket Spreads u NOB and MOB spreads n Bond Market Timing With Futures u Adjusting a bond portfolio’s current duration to a target duration u This is very similar to the hedging example in Chapter 10 where the target duration is zero.

28. Copyright © 2001 by Harcourt, Inc. All rights reserved.28 Intermediate and Long-Term Interest Rate Futures Strategies (continued) n Bond Market Timing With Futures (continued) u See Table 11.6, p. 480 u Predicted price change of -2.72 %. Actual change was -2.26 %. Without hedge, price change would have been -5.26 %, while predicted change without hedge would have been -5.33 %.

29. Copyright © 2001 by Harcourt, Inc. All rights reserved.29 Stock Index Futures Strategies n Stock Index Arbitrage u Recall the stock index futures pricing model u Example: Let S&P 500 = 1305.00, risk-free rate is 5.2 %, dividend yield is 3 % and time to expiration is 40 days so T = 40/365 =.1096. Futures should be at F 1305e (.052 -.03)(.1096) = 1308.15 u Now let the actual futures price be 1309.66. This is too high so sell the futures and buy the index. Hold until expiration. Sell the stocks and buy back the futures.

30. Copyright © 2001 by Harcourt, Inc. All rights reserved.30 Stock Index Futures Strategies (continued) n Stock Index Arbitrage (continued) u Now find the implied repo rate. Let f 0 (T) be the actual futures price. Then u In our example, this is u So if you could get financing at less than this rate, the arbitrage would be worth doing.

31. Copyright © 2001 by Harcourt, Inc. All rights reserved.31 Stock Index Futures Strategies (continued) n Stock Index Arbitrage (continued) u Some practical considerations F buying and selling all stocks simultaneously F buying fractional contracts F transaction costs of about.005 % of spot value. u Program trading. See Figure 11.1, p. 484. u See Table 11.7, p. 485 for stock index arbitrage example.

32. Copyright © 2001 by Harcourt, Inc. All rights reserved.32 Stock Index Futures Strategies (continued) n Speculating on Unsystematic Risk u To eliminate systematic risk in order to capture unsystematic return of a stock believed to be underpriced.  Use same hedge ratio previously obtained: N f =  Use same hedge ratio previously obtained: N f =  (S/f) u u Example: See Table 11.8, p. 488

33. Copyright © 2001 by Harcourt, Inc. All rights reserved.33 Stock Index Futures Strategies (continued) n Stock Market Timing With Futures u To change the beta on a portfolio of stocks to a target beta use the hedge ratio u See example in Table 11.9, p. 490

34. Copyright © 2001 by Harcourt, Inc. All rights reserved.34 Stock Index Futures Strategies (continued) n Arbitraging Stock Index Futures With Stock Index Options u Can construct synthetic futures with options. u Recall put-call-forward/futures parity F P e (S 0,T,X) = C e (S 0,T,X) + (X - f 0 (T))(1+r) -T F See Table 11.10, p. 492. F Example using S&P 500. On May 14, S&P 500 at 1337.80 and June futures at 1339.30. June 1340 call at 40 and put at 39. Expiration of June 18 so T = 35/365 =.0959. Risk-free rate at 4.56.

35. Copyright © 2001 by Harcourt, Inc. All rights reserved.35 Stock Index Futures Strategies (continued) n Arbitraging Stock Index Futures With Stock Index Options (continued) u So P e (S 0,T,X) = 39 u C e (S 0,T,X) + (X - f 0 (T))(1+r) -T u = 40 + (1340 - 1339.30)(1.0456) -.0959 = 40.70. u Buy put and futures for 39, sell call and bond for 40.70 and net 1.70 profit at no risk. Transaction costs would have to be considered.

36. Copyright © 2001 by Harcourt, Inc. All rights reserved.36 Summary u See Figure 11.2, p. 494 for linkages between puts, calls, and forwards/futures.

37. Copyright © 2001 by Harcourt, Inc. All rights reserved.37 Appendix 11A: Determining the CBOT Treasury Bond Conversion Factor n Determine maturity in years (YRS), months (MOS) and days as of first date of expiration month. Use first call date if callable. Ignore days. Let c be coupon rate. Round months down to 0, 3, 6, or 9. Call this MOS*. u If MOS * = 0,

38. Copyright © 2001 by Harcourt, Inc. All rights reserved.38 Appendix 11A: Determining the CBOT Treasury Bond Conversion Factor (continued) u If MOS * = 3, u If MOS * = 6, u If MOS * = 9,

39. Copyright © 2001 by Harcourt, Inc. All rights reserved.39 Appendix 11A: Determining the CBOT Treasury Bond Conversion Factor (continued) n Example: 7 7/8s of February 15, 2021 delivered on March 2000 contract. On March 1, 2000 remaining life is 20 years, 11 months, 14 days. YRS = 20, MOS = 11. Round down so that MOS * = 9. Find CF 6 : n Then CF 9 is

40. Copyright © 2001 by Harcourt, Inc. All rights reserved.40 Appendix 11A: Determining the CBOT Treasury Bond Conversion Factor (continued) n Excel spreadsheet cf1.xls described in Software Demonstration 11.2, p. 500 will calculate conversion factor.

41. Copyright © 2001 by Harcourt, Inc. All rights reserved.41 Appendix 11B: Derivation of the Hedge Ratio for Adjusting Duration With Treasury Bond Futures u The value of the position is F V = S + v f N f u Use the following results:   v f /  r =  f/  r   y s /  r =  y f /  r u All of this follows the procedure in Appendix 10A. Differentiate with respect to r, use the above results, apply the chain rule, set DUR v to DUR T and solve for N f. The approximation is

42. Copyright © 2001 by Harcourt, Inc. All rights reserved.42 Appendix 11A: Derivation of the Hedge Ratio for Adjusting Duration With Treasury Bond Futures (continued)