Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 1 Chapter 10: Futures Arbitrage Strategies We use a number of tools to manage our investment portfolio for the highest return, while minimizing the risk. Some of these tools happen to be called 'derivatives.' Anonymous respondent quoted in 1996 Capital Access Survey on Derivatives © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 2 Important Concepts in Chapter 10 n Futures spread and arbitrage strategies n Cheapest-to-deliver bond n Delivery options n Use of futures in market timing, alpha capture, and asset allocation © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 3 Short-Term Interest Rate Arbitrage n 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: © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 4 Short-Term Interest Rate Arbitrage (continued) n Cash and Carry/Implied Repo Rate u Also equivalent to buying longer term and converting it to shorter term. u Example. See Table Table 10.1Table 10.1 n Eurodollar Arbitrage u Using Eurodollar futures with spot to earn an arbitrage profit. u See Table Table 10.2Table 10.2 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 5 Intermediate and Long-Term Interest Rate Arbitrage 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 2009 contract. Settlement price is 112 ($112,000) on position day. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 6 Intermediate and Long-Term Interest Rate Arbitrage (continued) u You plan to deliver the 5 1/2 of 2028 on March 8. CF = Coupon dates of February 15 and August 15. Last coupon on February 15, Days from 2/15 to 3/13 is 26. Days from 2/15 to 8/15 is 181. Accrued interest F $100,000(0.055/2)(26/181) = $ u Invoice price: F $112,000(0.9433) + $ = $106, © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 7 Intermediate and Long-Term Interest Rate Arbitrage (continued) u Next day, Notice of Intention Day, Thursday, March 9, the short invoices the long $106, The long pays for and receives the bond on Friday, March 10. u Table 10.3 shows CFs and invoice prices for other deliverable bonds on the March 2009 contract. Table 10.3 Table 10.3 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 8 Intermediate and Long-Term Interest Rate Arbitrage (continued) 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 2009 contract of 6 1/4s of May 15, u Cost of delivering bond F f 0 (T)(CF) + AI T - [(B + AI t )(1+r) (T-t) – CI t,T ] © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 9 Intermediate and Long-Term Interest Rate Arbitrage (continued) n Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) u Example: On 11/13/08, plan to deliver the 6 1/4s of 5/15/30 on the March 2009 contract on March 11. f 0 (T) = 116, CF = , AI t = 3.09, AI T = 2.00 (deliver on March 11), B = days between November 13 and March 11. Reinvestment rate = 1.0%. u Invoice price F 116(1.0296) = © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 10 Intermediate and Long-Term Interest Rate Arbitrage (continued) n Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) u There are no interim coupons paid u Forward price of deliverable bond F ( )(1.01) 118/ (1.01) 118/365 = u So the bond would cost 1.68 (= – ) more than it would return. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 11 Intermediate and Long-Term Interest Rate Arbitrage (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 6 3/4s of August 15, 2026 with CF = and price of 127 3/32, we have accrued interest of 1.65 on November 13 and 0.45 on March 11. Coupon of on February 15 is reinvested at 1.0% for 24 days and grows to 3.375(1.01) 24/365 = © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 12 Intermediate and Long-Term Interest Rate Arbitrage (continued) n Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract (continued) u Forward price is, therefore, F ( )(1.01) 118/365 – 3.38 = u Invoice price is F 116(1.0798) = u Thus, this bond would produce (= – ). So the 6 3/4 bond is better than the 6 1/4 bond. u Table 10.4 shows these calculations for all deliverable bonds. See Ctd8e.xls for these calculations. Table 10.4 Table 10.4 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 13 Intermediate and Long-Term Interest Rate Arbitrage (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 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 14 Intermediate and Long-Term Interest Rate Arbitrage (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, B 3 = spot price at 3:00 pm. CF = conversion factor © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 15 Intermediate and Long-Term Interest Rate Arbitrage (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 > 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. F At 5:00 pm, the spot price is B 5. It is profitable to purchase these bonds at 5:00 pm if B 5 < f 3 (CF). F This holds because the invoice price is locked in but the spot price of the bonds can potentially fall. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 16 Intermediate and Long-Term Interest Rate Arbitrage (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. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 17 Intermediate and Long-Term Interest Rate Arbitrage (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. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 18 Intermediate and Long-Term Interest Rate Arbitrage (continued) n Delivery Options (continued) u The End-of-the-Month Option F 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. F Similar to the wild card option because the invoice price is locked in when the futures stops trading. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 19 Intermediate and Long-Term Interest Rate Arbitrage (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. F Delivery will be made late in the month if the bond earns a coupon that exceeds the cost of financing. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 20 Intermediate and Long-Term Interest Rate Arbitrage (continued) n Implied Repo/Cost of Carry u Buy spot T-bond, sell futures. u This will produce a return (implied repo rate) of © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 21 Intermediate and Long-Term Interest Rate Arbitrage (continued) n Implied Repo/Cost of Carry (continued) u Example: On November 13, 2008, CTD bond on March contract is 6 3/4s maturing on August 15, Spot price is 127 3/32, accrued interest is 1.65, CF = and futures price is 116. From November 13 to March 11 is 118 days so T = 118/365 = There one coupon payment made with a future value of 3.38 (3.375(1.01) (24/365). Accrued interest on March 11 th, AI T = 0.45AI T = 0.45 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 22 Intermediate and Long-Term Interest Rate Arbitrage (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 this rate, then the arbitrage would be profitable. Obviously that is not the case here. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 23 Intermediate and Long-Term Interest Rate Arbitrage (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 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 24 Intermediate and Long-Term Interest Rate Arbitrage (continued) n Treasury Bond Spread/Implied Repo Rate (continued) u Implied repo rate u Example: On November 13, 2008 CTD was 6 3/4s maturing in Examine the March-June spread. March priced at f 0 (t) = 116 with CF(t) = June priced at f 0 (T) = 115 with CF(T) = AI t (March 13) = 0.45 and AI T (June 11) = No coupons in the interim so CI t,T = 0. From March 13 to June 11 is 90 days. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 25 Intermediate and Long-Term Interest Rate Arbitrage (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 Fed funds futures rate © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 26 Stock Index Arbitrage n Stock Index Arbitrage u Recall the stock index futures pricing model u Example: Let S&P 500 = , risk-free rate is 5.2%, dividend yield is 3% and time to expiration is 40 days so T = 40/365 = Futures should be at F 1305e ( )(.1096) = u Now let the actual futures price be This is too high so sell the futures and buy the index. Hold until expiration. Sell the stocks and buy back the futures. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 27 Stock Index Arbitrage (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. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 28 Stock Index Arbitrage (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 % of spot value. u Program trading. u See Table 10.5 for stock index arbitrage example. Table 10.5Table 10.5 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 29 Summary © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 30 Appendix 10: 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, © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 31 Appendix 10: Determining the CBOT Treasury Bond Conversion Factor (continued) u If MOS * = 3, u If MOS * = 6, u If MOS * = 9, © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 32 Appendix 10: Determining the CBOT Treasury Bond Conversion Factor (continued) n Example: 5 1/4s of February 15, 2029 delivered on March 2006 contract. On March 1, 2006 remaining life is 22 years, 11 months, 14 days. YRS = 22, MOS = 11. Round down so that MOS * = 9. Find CF 6 : n Then CF 9 is © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 33 (Return to text slide) © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 34 (Return to text slide) © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 35 (Return to text slide) © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 36 (Return to text slide) © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Chance/BrooksAn Introduction to Derivatives and Risk Management, 8th ed.Ch. 10: 37 (Return to text slide) © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.