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Chapter 11: Advanced Futures Strategies

Chapter 11: Advanced Futures Strategies.

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Chapter 11: Advanced Futures Strategies

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  1. Chapter 11: Advanced Futures Strategies Some people think of speculative traders as gamblers; they earn too much money and provide no economic value. But to avoid crises, markets must have liquidity suppliers who react quickly, who take contrarian positions when doing so seems imprudent, who search out unoccupied habitats and populate those habitats to provide the diversity that is necessary, and who focus on risk taking and risk management. Richard M. Bookstaber Risk Management Principles and Practices, AIMR, 1999, p. 17 An Introduction to Derivatives and Risk Management, 6th ed.

  2. Important Concepts in Chapter 11 • Futures spread and arbitrage strategies • Cheapest-to-deliver bond • Delivery options • Use of futures in market timing, alpha capture, and asset allocation An Introduction to Derivatives and Risk Management, 6th ed.

  3. Short-Term Interest Rate Futures Strategies • Treasury Bill Cash and Carry/Implied Repo • Cash and carry transaction means to buy asset and sell futures • Repurchase agreement/repo to obtain funding • Overnight vs. term repo • Cost of carry pricing model: f0(t) = S0 + q • Implied repo rate: An Introduction to Derivatives and Risk Management, 6th ed.

  4. Short-Term Interest Rate Futures Strategies (continued) • Treasury Bill Cash and Carry/Implied Repo Rate • Also equivalent to buying longer term bill and converting it to shorter term bill. • Example. See Table 11.1, p. 386. • Eurodollar Arbitrage • Using Eurodollar futures with spot to earn an arbitrage profit. • See Table 11.2, p. 388. An Introduction to Derivatives and Risk Management, 6th ed.

  5. Intermediate and Long-Term Interest Rate Futures Strategies • Recall the option to deliver any T-bond with at least 15 years to maturity or first call. • Adjustment to futures price using conversion factor, which is the price per $1.00 par of a 6% bond delivered on a particular expiration. • Invoice price = (Settlement price on position day)/(Conversion factor) + Accrued interest • Example: Delivery on March 2003 contract. Settlement price is 109 28-32 ($109,875) on position day. An Introduction to Derivatives and Risk Management, 6th ed.

  6. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • You plan to deliver the 7 7/8s of 2021 on March 7. CF = 1.2029. Coupon dates of February 15 and August 15. Last coupon on February 15, 2003. Days from 2/15 to 3/7 is 20. Days from 2/15 to 8/15 is 181. Accrued interest • $100,000(.07875/2)(20/181) = $435 • Invoice price: • $109,875(1.2029) + $435 = $132,604 An Introduction to Derivatives and Risk Management, 6th ed.

  7. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Next day, Notice of Intention Day, Thursday, March 6, the short invoices the long $132,604. The long pays for and receives the bond on Friday, March 7. • Table 11.3, p. 390 shows CFs and invoice prices for other deliverable bonds on the March 2003 contract. An Introduction to Derivatives and Risk Management, 6th ed.

  8. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract • Recall the option to deliver any T-bond with at least 15 years to maturity or first call. • Example: Delivery on March 2003 contract of 8 7/8s of February 15, 2019. • Cost of delivering bond • f0(T)(CF) + AIT - [(B + AIt)(1+r)(T-t) – CIt,T] An Introduction to Derivatives and Risk Management, 6th ed.

  9. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) • Example: On 12/2/02, plan to deliver the 8 7/8s of 2/15/19 on the March 2003 contract on March 3. f0(T) = 108 3/32 = 108.09375, CF = 1.2902, AIt = 2.63, AIT = 0.49 (deliver on March 7), B = 142 30/32. 95 days between December 2 and March 7. Reinvestment rate = .015. • Invoice price • 108.09375(1.2902) + 0.49 = 139.95 An Introduction to Derivatives and Risk Management, 6th ed.

  10. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) • Coupon of 4.4375 received on February 15 is reinvested at 1.5% for 20 days to grow to 4.4375(1.015)20/365 = 4.44 • Forward price of deliverable bond • (142.9375 + 2.63)(1.015)95/365 - 4.44 = 141.69 • So the bond would cost 1.74 more than it would return. An Introduction to Derivatives and Risk Management, 6th ed.

  11. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) • All we can do, however, is compare this result with that for another bond. For the 7 1/4s of August 15, 2022 with CF = 1.1414 and price of 125 21/32, we have accrued interest of 2.15 on December 2 and 0.40 on March 7. Coupon of 3.625 on February 15 is reinvested at 1.5% for 20 days and grows to 3.625(1.015)20/365 = 3.63. An Introduction to Derivatives and Risk Management, 6th ed.

  12. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) • Forward price is, therefore, • (125.65625 + 2.15)(1.015)95/365 – 3.63 = 124.67 • Invoice price is • 108.09375(1.1414) + 0.40 = 123.78. • Thus, this bond would cost 0.89 more than it would return. So the 7 1/4 bond is better than the 8 7/8 bond. • Table 11.4, p. 393 shows these calculations for all deliverable bonds. Software Demonstration 11.1 shows how to use ctd3.xls to do these calculations. An Introduction to Derivatives and Risk Management, 6th ed.

  13. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) • Why identifying the cheapest-to-deliver bond is important: • Identifying the true spot price • Calculating the correct hedge ratio An Introduction to Derivatives and Risk Management, 6th ed.

  14. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Delivery Options • The Wild Card Option • Futures market closes at 3:00 pm while spot market stays open until at least 5:00 pm. • 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. • Illustration: f3 = futures price at 3:00 pm, B3 = spot price at 3:00 pm. CF = conversion factor An Introduction to Derivatives and Risk Management, 6th ed.

  15. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Delivery Options (continued) • The Wild Card Option (continued) • Let the short own 1/CF bonds (CF must be > 1.0, so coupon must be > 6 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. • At 5:00 pm, the spot price is B5. It is profitable to purchase these bonds at 5:00 pm if B5 < f3(CF). • This holds because the invoice price is locked in but the spot price of the bonds can potentially fall. An Introduction to Derivatives and Risk Management, 6th ed.

  16. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Delivery Options (continued) • The Wild Card Option (continued) • 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. • 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. An Introduction to Derivatives and Risk Management, 6th ed.

  17. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Delivery Options (continued) • The Quality Option • 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. • 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. An Introduction to Derivatives and Risk Management, 6th ed.

  18. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Delivery Options (continued) • The End-of-the-Month Option • The right to make delivery any of the business days at the end of the month after the futures contract has stopped trading, around the third week of the month. • Similar to the wild card option because the invoice price is locked in when the futures stops trading. An Introduction to Derivatives and Risk Management, 6th ed.

  19. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Delivery Options (continued) • The Timing Option • The right to deliver on any eligible day of the delivery month. • Delivery will be made early in the month if the bond earns a coupon that is less than the cost of financing. • Delivery will be made late in the month if the bond earns a coupon that exceeds the cost of financing. An Introduction to Derivatives and Risk Management, 6th ed.

  20. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Implied Repo/Cost of Carry • Buy spot T-bond, sell futures. • This will produce a return (implied repo rate) of An Introduction to Derivatives and Risk Management, 6th ed.

  21. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Implied Repo/Cost of Carry (continued) • Example: On December 2, 2003, CTD bond on March contract is 6 1/4s maturing in 2023. Spot price is 113 7/32, accrued interest is 1.8512, CF = 1.0290 and futures price is 108.09375. From December 2 to March 7 is 95 days so T = 95/365 = 0.2603. Coupon of 3.125 on 2/15 is received and reinvested for 20 days at 1.5% to equal • CI0,T = 3.125(1.015)20/365 = 3.13 • 181 days in current period. Next coupon accrues for 20 days so • AIT = 3.125(20/181) = 0.35 An Introduction to Derivatives and Risk Management, 6th ed.

  22. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Implied Repo/Cost of Carry (continued) • Implied repo rate is, therefore, • If the bond can be financed in the repo market for less than this rate, then the arbitrage would be profitable. Obviously that is not the case. An Introduction to Derivatives and Risk Management, 6th ed.

  23. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • A Treasury Bond Futures Spread • See Table 11.5, p. 399. An Introduction to Derivatives and Risk Management, 6th ed.

  24. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Treasury Bond Spread/Implied Repo Rate • Let time t be expiration of nearby futures and T be expiration of deferred futures. • Go long the nearby and short the deferred. • When nearby expires, take delivery and hold until expiration of deferred. This creates a forward transaction beginning at t and ending at T An Introduction to Derivatives and Risk Management, 6th ed.

  25. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Treasury Bond Spread/Implied Repo Rate (continued) • Implied repo rate • Example: On December 2, 2002 CTD was 6 1/4s maturing in 2023. Examine the March-June spread. March priced at f0(t) = 108.09375 with CF(t) = 1.0290. June priced at f0(T) = 106.84375 with CF(T) = 1.0289. AIt (March 7) = 0.35 and AIT (June 5) = 1.90. No coupons in the interim so AIt,T = 0. From March 7 to June 5 is 90 days. An Introduction to Derivatives and Risk Management, 6th ed.

  26. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Treasury Bond Spread/Implied Repo Rate (continued) • Implied repo rate • Compare to actual repo rate and note that this is a forward rate. • Note the turtle trade: Implied repo rate on T-bond spread to T-bill futures rate An Introduction to Derivatives and Risk Management, 6th ed.

  27. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Intermarket Spreads • NOB and MOB spreads • Bond Market Timing With Futures • Adjusting a bond portfolio’s current duration to a target duration • This is very similar to the hedging example in Chapter 10 where the target duration is zero. An Introduction to Derivatives and Risk Management, 6th ed.

  28. Intermediate and Long-Term Interest Rate Futures Strategies (continued) • Bond Market Timing With Futures (continued) • See Table 11.6, p. 403. • 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 %. An Introduction to Derivatives and Risk Management, 6th ed.

  29. Stock Index Futures Strategies • Stock Index Arbitrage • Recall the stock index futures pricing model • 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 • 1305e(.052 - .03)(.1096) = 1308.15 • 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. An Introduction to Derivatives and Risk Management, 6th ed.

  30. Stock Index Futures Strategies (continued) • Stock Index Arbitrage (continued) • Now find the implied repo rate. Let f0(T) be the actual futures price. Then • In our example, this is • So if you could get financing at less than this rate, the arbitrage would be worth doing. An Introduction to Derivatives and Risk Management, 6th ed.

  31. Stock Index Futures Strategies (continued) • Stock Index Arbitrage (continued) • Some practical considerations • buying and selling all stocks simultaneously • buying fractional contracts • transaction costs of about .005 % of spot value. • Program trading. • See Table 11.7, p. 408 for stock index arbitrage example. An Introduction to Derivatives and Risk Management, 6th ed.

  32. Stock Index Futures Strategies (continued) • Alpha Capture • To eliminate systematic risk in order to capture unsystematic return of a stock believed to be underpriced. • Use same hedge ratio previously obtained: Nf = b(S/f) • Example: See Table 11.8, p. 411. An Introduction to Derivatives and Risk Management, 6th ed.

  33. Stock Index Futures Strategies (continued) • Stock Market Timing With Futures • To change the beta on a portfolio of stocks to a target beta use the hedge ratio • See example in Table 11.9, p. 414. An Introduction to Derivatives and Risk Management, 6th ed.

  34. Stock Index Futures Strategies (continued) • Tactical Asset Allocation Using Stock and Bond Futures • Futures can be used to synthetically sell from one asset class and buy in another • Exposure can be shifted from one asset class to another and exposure within an asset class can also be shifted by changing the beta or duration. • See Table 11.10, pp. 415-416. An Introduction to Derivatives and Risk Management, 6th ed.

  35. Summary An Introduction to Derivatives and Risk Management, 6th ed.

  36. Appendix 11.A: Determining the CBOT Treasury Bond Conversion Factor • 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*. • If MOS* = 0, An Introduction to Derivatives and Risk Management, 6th ed.

  37. Appendix 11.A: Determining the CBOT Treasury Bond Conversion Factor (continued) • If MOS* = 3, • If MOS* = 6, • If MOS* = 9, An Introduction to Derivatives and Risk Management, 6th ed.

  38. Appendix 11.A: Determining the CBOT Treasury Bond Conversion Factor (continued) • Example: 7 7/8s of February 15, 2021 delivered on March 2003 contract. On March 1, 2003 remaining life is 17 years, 11 months, 14 days. YRS = 17, MOS = 11. Round down so that MOS* = 9. Find CF6: • Then CF9 is An Introduction to Derivatives and Risk Management, 6th ed.

  39. Appendix 11.A: Determining the CBOT Treasury Bond Conversion Factor (continued) • Excel spreadsheet cf2.xls described in Software Demonstration 11.2 will calculate conversion factor. An Introduction to Derivatives and Risk Management, 6th ed.

  40. Appendix 11.B: Derivation of the Hedge Ratio for Adjusting Duration With Treasury Bond Futures • The value of the position is • V = B + vfNf • Use the following results: • ¶vf/¶r = ¶f/¶r • ¶ys/¶r = ¶yf/¶r • This follows the procedure in Appendix 10.A. Differentiate with respect to r, use the above results, apply the chain rule, set DURv to DURT and solve for Nf. The approximation is An Introduction to Derivatives and Risk Management, 6th ed.

  41. Appendix 11.A: Derivation of the Hedge Ratio for Adjusting Duration With Treasury Bond Futures (continued) An Introduction to Derivatives and Risk Management, 6th ed.

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