Futures, Forwards, Options and Swaps:Theory and PracticeBusiness 35101-81Spring Quarter 2003April 28, 2003Dr. Galen BurghardtClass Notes -5-
Section 1BOND AND NOTE FUTURES
Bond and Note FuturesExhibit and Note Futures Basics!Specifications!Yield on a futures contract?!Deliverable set!Conversion factor!Invoice price Carr Futures1
Bond and Note FuturesExhibit and Note Futures Contract HighlightsLong-Term -Year -Year -Year BondsTreasury NotesTreasury Notes Treasury Notes(CBOT)(CBOT)(CBOT)(CBOT)Size$100,000 par value$100,000 par value$100,000 par value$200,000 par . Treasury . Treasury . Treasury . Treasury notesGradewith at least 15 yearsmaturing at least 6‰that have an originalthat have an originalremaining to maturityyears but not morematurity of not morematurity of not moreif not callable as of thethan 10 years fromthan 5 years and 3than 5 years and 3first calendar day of thethe first calendar daymonths and a remainingmonths and a remainingdelivery monthof the delivery monthmaturity of not lessmaturity of not lessthan 4 years and 3than 1 year and 9 monthsmonths as of the firstfrom the first day of thecalendar day of thecalendar month but notdelivery month. Themore than 2 years5-year Treasury Notefrom the last day ofissued after the lastthe calendar day of thecontract month will notbe eligible for deliveryinto that months hypothetical priceThe hypothetical priceThe hypothetical priceThe hypothetical priceFactorper dollar of face valueper dollar of face valueper dollar of face valueper dollar of face valueat which the bond wouldat which the note wouldat which the note wouldat which the note wouldyield 6 percent toyield 6 percent toyield 6 percent toyield 6 percent tomaturity, or to first callmaturity as of the firstmaturity as of the firstmaturity as of the firstif callable, as of the firstday of the contract monthday of the contract monthday of the contract monthday of the contract monthPrice QuotesPoints and 32ndsPoints and ‰ of 1/32Points and ‰ of 1/32Points and … of 1/32of a pointof a pointof a pointof a pointTick Size1/32 of a point1/2 of 1/32 of a point1/2 of 1/32 of a point1/4 of 1/32 of a pointand Value($)($)($)($)Long-Term -Year -Year -Year .*The minimum price fluctuation is 1/2 of 1/32 (., or + indicates 93 points and 16 and 1/2 32nds).**The minimum price fluctuation is 1/4 of 1/32 (., indicates 91 points and 16 and 1/4 32nds). Carr Futures2
Bond and Note FuturesExhibit and Note Futures Contract Highlights (continued)Treasury BondsTreasury NotesTreasury Notes Treasury Notes(CBOT)(CBOT)(CBOT)(CBOT)Daily Price3 points3 points3 points1 pointLimitTrading Hours7:20 am to 2:00 pm7:20 am to 2:00 pm7:20 am to 2:00 pm7:20 am to 2:00 .(Chicago Time)Project A:Project A:Project A:Project A:2:15 pm to 4:30 pm2:15 pm to 4:30 pm2:15 pm to 4:30 pm2:15 pm to 4:30 pm6:00 pm to 5:00 am6:00 pm to 5:00 am6:00 pm to 5:00 am6:00 pm to 5:00 am5:30 am tp 2:00 pm 5:30 am tp 2:00 pm 5:30 am tp 2:00 pm 5:30 am tp 2:00 pmDeliveryMarch, June,March, June,March, June,March, June,MonthsSeptember, DecemberSeptember, DecemberSeptember, DecemberSeptember, DecemberLast Trading7th business day7th business day7th business dayThe earlier of (1) the secondDaypreceding the lastpreceding the lastpreceding the lastbusiness day prior to thebusiness day ofbusiness day ofbusiness day ofissue day of the 2-year notethe delivery monththe delivery monththe delivery monthauctioned in the currentmonth, or (2) the lastbusiness day of thecalendar monthFirst DeliveryFirst business day ofFirst business day ofFirst business day ofFirst business day ofDaydelivery month the delivery monththe delivery monththe delivery monthLast DeliveryLast business day ofLast business day ofLast business day ofThe third business dayDay delivery monththe delivery monththe delivery monthfollowing the last trading day*The minimum price fluctuation is 1/2 of 1/32 (., or + indicates 93 points and 16 and 1/2 32nds).**The minimum price fluctuation is 1/4 of 1/32 (., indicates 91 points and 16 and 1/4 32nds). Carr Futures3
Bond and Note FuturesExhibit Treasury yield curve and CBOT futures coverage as of 3/10/%%%%%%%%%0 5 10 15 20 25 30 •Treasury futures contracts cover four key segments of the Treasury yield curve(TU=2 year, FV=5 year, TY=10-year, US=long bond).•The shaded bands above show the ranges of eligible maturities for each of thefour Volume and Open Interest(Friday, March 10, 2000) Daily Volume Open InterestContracts$ in millContracts$ in millBonds 2 60,843 26,084 5 34,992 53,49910-Year 1 69,377 16,938 5 79,237 57,9245-Year 1 03,202 10,320 4 31,448 43,1452-Year 7 ,302 730 4 6,693 4,669 Carr Futures4March-00March-05March-10March-15March-20March-25March-30
Bond and Note FuturesExhibit priceBond and note futures prices are quoted in points and 32nds of a pointfor each $100 nominal par amount. A price of 97-9 (as shown in theWall Street Journal) represents a price of 97 and 9/ of a tickThe bond futures contract is designed to represent $100,000 par valueof underlying bonds. The minimum price change (tick) is 1/32nd of apoint, or $ the bond futures price increases 1 full point (or 32/32nds), a longposition in the contract gains $1000 for each contract held. A shortposition in the contract loses $1000 for each basketSeveral Treasury issues are eligible for delivery into the futures con-tract. Carr Futures tracks about 20 more or less actively traded long-term bonds and about a dozen actively traded 6-1/2 to 10 year notes. Carr Futures5
Bond and Note FuturesExhibit Treasury Futures Pricing & Hedging ToolMar-01/late deliveryKey Dates(days*)Futures(Contract Mar-01)2Year2-year5-year10-yearBond12/29/00Market PriceClosing(-5)101-18+103-18104-27+104-201/2/01Theoretical PriceTrade(-1)101-20103-19+104-29104-181/3/01Rule-of-Thumb DV01Settlement(0) DV01 wrt1st Delivery(57)3/21/013/29/01CTD yieldLast Trade(77)(85) yieldLast Delivery(86)(90)* days from settlementOption-adjusted Duration wrtCTD -adjusted Convexity2-year5-year10-yearBOpondYield %%%%Repo distributionnormgas wrtalnormalnormalnormVealYield beta coefficientyield volatility coefficientyield date4/3/013/30/013/30/013/30/01twist # B/NCouponMaturity2:00 PMYieldMar-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndFactor32ndActualExpected$100,000DurationYield BCarry $/ Carr Futures6
Bond and Note FuturesExhibit Treasury Pricing & Hedging ToolMar-01/early deliveryKey Dates(days*)Futures(Contract Mar-01)2Year2-year5-year10-yearBond12/29/00Market PriceClosing(-5)101-18+103-18104-27+104-201/2/01Theoretical PriceTrade(-1)101-18103-20104-27+104-19+1/3/01Rule-of-Thumb DV01Settlement(0) DV01 wrt1st Delivery(57)3/21/013/29/01CTD yieldLast Trade(77)(85) yieldLast Delivery(86)(90)* days from settlementOption-adjusted Duration wrtCTD -adjusted Convexity2-year5-year10-yearBondYield %%%%Repo distributionnormalnormalnormalnormalVegas wrtYield beta coefficientyield volatility coefficientyield date3/1/013/1/013/1/013/1/01twist # B/NCouponMaturity2:00 PMYieldMar-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndCarry $/Day32-DelFactor32ndActualExpected$100,000DurationYield Carr Futures7
Bond and Note FuturesExhibit Treasury Pricing & Hedging ToolJun-01/late deliveryKey Dates(days*)Futures(Contract Jun-01)2Year2-year5-year10-yearBond12/29/00Market PriceClosing(-5)-02104-26104-181/2/01Theoretical PriceTrade(-1)101-26+104-05104-27+104-131/3/01Rule-of-Thumb DV01Settlement(0) DV01 wrt1st Delivery(149)6/20/016/28/01CTD yieldLast Trade(168)(176) yieldLast Delivery(177)(181)* days from settlementOption-adjusted Duration wrtCTD -adjusted Convexity2-year5-year10-yearBondYield %%%%Repo distributionnormalnormalnorm wrtalnormVegasalYield beta coefficientyield volatility coefficientyield date7/3/016/29/016/29/016/29/01twist # B/NCouponMaturity2:00 PMYieldJun-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndry $/Day32-DeFactor32ndActualExpected$100,000DurationYield Carr Futures8
Bond and Note FuturesExhibit Treasury Pricing & Hedging ToolJun-01/early deliveryKey Dates(days*)Futures(Contract Jun-01)2Year2-year5-year10-yearBond12/29/00Market PriceClosing(-5)101-29+104-02104-26104-181/2/01Theoretical PriceTrade(-1)101-24+104-05104-26+104-14+1/3/01Rule-of-Thumb DV01Settlement(0) DV01 wrt1st Delivery(149)6/20/016/28/01CTD yieldLast Trade(168)(176) yieldLast Delivery(177)(181)* days from settlementOption-adjusted Duration wrtCTD -adjusted Convexity2-year5-year10-yearBondYield %%%%Repo distributionVegas wrtnormalnormalnormalnormalYield beta coefficientyield volatility coefficientyield date6/1/016/1/016/1/016/1/01twist # B/NCouponMaturity2:00 PMYieldJun-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndFactor32ndActualExpected$100,000DurationYield BetaPriceRCarry $/ Carr Futures9
Bond and Note FuturesExhibit PricesPV Full market price = market price + accrued interest at settlementFutures invoice price = (conversion factor x futures price) + accrued interest at delivery!Example ( of 5/15/16)1/2/01 (settle = 1/03/01)Price=[= market of 117-21+] 49 Accrued interest= .9814[= X ] 2 181 Full market price= (last delivery day of March '01)Price= [= x ] 135Accrued interest= [= x ] 2 181 Futures invoice price= Carr Futures10
Bond and Note FuturesExhibit RP (repo) rate Invoice Price at Delivery 360 Implied RP Rate -1 x =[] []Full Purchase Price Today Days 360 Implied RP Rate for -1 x =[] [ ] 86 = (or %)•The numerator of the expression inside the brackets is the cash onewould receive at futures delivery.•The denominator is the cash one would commit to the position today.•The implied RP rate is a hypothetical rate of return on a(comparatively) riskless position.•The implied RP rate is expressed as a money market rate(notice the 360-day year) to correspond to the conventions of the financing market. Carr Futures11
Bond and Note FuturesExhibit Cheapest to Deliver (CTD)By convention, the cheapest to deliver bond (CTD) is identified as thebond with the highest implied RP rate. (A better, but infrequently usedrule, would identify the cheapest to deliver as the bond with the largestdifference between its implied RP rate and its market RP rate. This isespecially important for bonds that are “on special” in the repo market.)The cheapest to deliver bond has the lowest full purchase price relative toits futures invoice price at implied RP rate is the financing rate one would have to pay to justbreak even on the transaction. Carr Futures12
Bond and Note FuturesExhibit Carr Futures13
Bond and Note FuturesExhibit FactorsConversion factorsIssueMarch 01June of 2/15/ of 5/15/•The CBOT’s bond futures contract allows for the delivery of$100,000 face value of any . Treasury bond that has at least 15years remaining to first call as of the first delivery day of thecontract month.•To put all eligible bonds on a more or less equal footing, the CBOTuses conversion factors in calculating delivery invoice prices. Thatis, the invoice price for a bond (not including accrued interest) isthe bond’s factor times the futures price.•A bond’s conversion factor is the approximate price, in decimalform, at which the bond would (as of the first delivery day of themonth) yield 6 percent to maturity (rounded to whole quarters) orto first call if callable.•If the bond’s coupon > 6 percent, factor >1•If the bond’s coupon < 6 percent, factor < 1•Factor is unique and constant for each bond for any one contractmonth•Factors for later contract months are closer to 1 Carr Futures14
Bond and Note FuturesExhibit You Can Do with Bond and Note Futures!HedgeTreasuriesAgenciesCorporatesSwaps!TradeDirectionYield curveIntercommodityBasis Carr Futures15
Basis ConceptsSection 2BASIS CONCEPTSCarr Futures 1
Basis ConceptsExhibit Concepts!Definition!What drives the basis?Carry (coupon income, RP expense)Strategic delivery optionsOption-adjusted basis!Change in the cheapest to deliver!Fair value of a futures contract!Basis tradeConstructionP/L ComponentsCarr Futures 2
Treasury Futures Pricing & Hedging ToolMar-01/late deliveryKey Dates(days*)Futures(Contract Mar-01)2 Year2-year5-year10-yearBondClosing12/29/00(-5)Market Price101-18+103-18104-27+104-20Trade1/2/01(-1)Theoretical Price101-20103-19+104-29104-18Settlement1/3/01(0)Rule-of-Thumb Delivery3/1/01(57)Option-adjusted DV01 wrtLast Trade3/21/01(77)3/29/01(85)CTD Delivery3/30/01(86)4/3/01(90)OTR * days from settlementOption-adjusted Duration wrtCTD -year5-year10-yearBondOption-adjusted ConvexityYield %%%%Repo distributionnormalnormalnormalnormalVegas wrtYield beta volatility date4/3/013/30/013/30/013/30/01twist # B/NCouponMaturity2:00 PMYieldMar-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndFactor32ndActualExpected$100,000DurationYield BetaPriceRepoCarry $/
Treasury Pricing & Hedging ToolMar-01/early deliveryKey Dates(days*)Futures(Contract Mar-01)2 Year2-year5-year10-yearBondClosing12/29/00(-5)Market Price101-18+103-18104-27+104-20Trade1/2/01(-1)Theoretical Price101-18103-20104-27+104-19+Settlement1/3/01(0)Rule-of-Thumb Delivery3/1/01(57)Option-adjusted DV01 wrtLast Trade3/21/01(77)3/29/01(85)CTD Delivery3/30/01(86)4/3/01(90)OTR * days from settlementOption-adjusted Duration wrtCTD -year5-year10-yearBondOption-adjusted ConvexityYield %%%%Repo distributionnormalnormalnormalnormalVegas wrtYield beta volatility date3/1/013/1/013/1/013/1/01twist # B/NCouponMaturity2:00 PMYieldMar-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndFactor32ndActualExpected$100,000DurationYield BetaPriceRepoCarry $/
Treasury Pricing & Hedging ToolJun-01/late deliveryKey Dates(days*)Futures(Contract Jun-01)2 Year2-year5-year10-yearBondClosing12/29/00(-5)Market -02104-26104-18Trade1/2/01(-1)Theoretical Price101-26+104-05104-27+104-13Settlement1/3/01(0)Rule-of-Thumb Delivery6/1/01(149)Option-adjusted DV01 wrtLast Trade6/20/01(168)6/28/01(176)CTD Delivery6/29/01(177)7/3/01(181)OTR * days from settlementOption-adjusted Duration wrtCTD -year5-year10-yearBondOption-adjusted ConvexityYield %%%%Repo distributionnormalnormalnormalnormalVegas wrtYield beta volatility date7/3/016/29/016/29/016/29/01twist # B/NCouponMaturity2:00 PMYieldJun-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndFactor32ndActualExpected$100,000DurationYield BetaPriceRepoCarry $/
Treasury Pricing & Hedging ToolJun-01/early deliveryKey Dates(days*)Futures(Contract Jun-01)2 Year2-year5-year10-yearBondClosing12/29/00(-5)Market Price101-29+104-02104-26104-18Trade1/2/01(-1)Theoretical Price101-24+104-05104-26+104-14+Settlement1/3/01(0)Rule-of-Thumb Delivery6/1/01(149)Option-adjusted DV01 wrtLast Trade6/20/01(168)6/28/01(176)CTD Delivery6/29/01(177)7/3/01(181)OTR * days from settlementOption-adjusted Duration wrtCTD -year5-year10-yearBondOption-adjusted ConvexityYield %%%%Repo distributionnormalnormalnormalnormalVegas wrtYield beta volatility date6/1/20016/1/20016/1/20016/1/2001twist # B/NCouponMaturity2:00 PMYieldJun-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndFactor32ndActualExpected$100,000DurationYield BetaPriceRepoCarry $/
Basis ConceptsExhibit DefinitionBasis = Spot Price - (Conversion Factor x Futures Price)Example: 8-3/4s of 5/15/20 on 1/2/01Spot price=137-06 ()Futures price=104-20 ()Conversion factor== - ( x )= - =.2020 price points(or .2020 x 32 = measures the spread between the spot and futures pricesCarr Futures 7
Basis ConceptsExhibit Drives the Basis?PriceSpot CarrypriceForward priceFutures Strategic price xdelivery factoroptionsDelivery Basis = Spot price - (Conversion factor x Futures price)Basis = Carry + Value of strategic delivery optionsSpot price - BasisFutures price =Conversion factorSpot price - Carry - Delivery option valueFutures price =Conversion factorCarr Futures 8
Basis ConceptsExhibit Yields, Term Repo & Forward YieldsDeliverable %%%%%%% MaturitiesDeliverable Notes, March ‘01 10-Year(12/29/00 Closing, 01/02/01 Trade) Issue YieldTermCouponMaturitySpot FwdRepo (3/31/01) %% %% %% %%68/15/% %% %% %%Carr Futures 9Yield
Basis ConceptsExhibit and Forward PricingCarry = Coupon Income - RP FinancingForward price = Spot Price - CarryFutures price with a single deliverable bond = Forward price / FactorCarr Futures 10
Basis ConceptsExhibit Carry!ObjectiveOn 1/2/01, determine the price at which you would be willing tosell the 8-3/4s of 5/15/20 for delivery on 3/30/01!Market dataSpot price = 137 -06/32ndsFull price = $ RP rate = %86 days from settlement (on 1/03/01) to delivery (3/30/01)!Coupon income(Coupon/ 2) x (Days to delivery/ Days in coupon period)( / 2 ) x ( 86/ 181) = !RP financing expenseFull price x RP rate x (Days to delivery/ 360) x .06070 x ( 86 / 360) = !Net carryCoupon income - Financing - = (in price points) x 32 = (about 2/32nds)Carr Futures 11
Basis ConceptsExhibit Price = Spot Price - Carry!Market dataSpot price = 137 - 06/32ndsCarry = 1/32nd!Forward priceSpot price - Carry = 137 - 06/32nds - 2/32nds = 137-04/32nds•The forward price is the price at which you can buy the bond inthe spot market, finance the position at the RP, and just break evenon the transaction.•In this case, you can buy the bond at 137-06/32nds, sell it forwardat 107-04/32nds (for a capital loss of 2/32nds), and finance theposition at % (for a net gain in carry of 2/32nds). The capitalloss on the spot/forward trade is just offset by net Futures 12
Basis ConceptsExhibit There is More Than One Deliverable Bond!The short decides which bond to deliver and when!Which is the cheapest bond to deliver?!Shifts in the cheapest to deliver (very important)changes in yield levelschanges in yield spreads!Shifts in the best time to deliver (not very important)!What is the fair value of the futures price?Carr Futures 13
Basis ConceptsExhibit the Cheapest Bond to DeliverPrice/factorYield5%7%6%Selected Deliverable BondsCouponMaturity Price Factor Yield DV01 Modified Implied RP duration rate8 3/4s5/15/17 134-07+ 3/4s5/15/20 137-06 CTD6 1/4s8/15/23 108-03+ •The bond with the highest implied RP rate is the cheapest todeliver.•Notice that the highest implied RP rate is lower than the marketRP rate.•The 8-3/4s may not always be the cheapest bond to deliverCarr Futures 14
Basis ConceptsExhibit in the Cheapest to DeliverPrice/factorhigh-durationbond100low-durationbondYield5%7%6%Selected Deliverable BondsCouponMaturity Price Factor Yield DV01 Modified Implied RP duration rate8 3/4s5/15/17 134-07+ 3/4s5/15/20137-06 CTD6 1/4s8/15/23 108-03+ •Low-duration bonds tend to be cheapest to deliver when yields arelow.•High-duration bonds tend to be cheapest to deliver when yields arehigh.•At expiration, the cheapest to deliver bond is the bond with thelowest converted price — that is, the bond with the lowest price/conversion factor.•Before expiration, the most reliable guide to cheapness is thebond’s implied RP rate.•The implied RP is the financing rate one could pay and still breakeven buying the bond in the spot market and delivering it at thefutures invoice Futures 15
Basis ConceptsExhibit Basis-Net-Of-Carry Mar 2001Projected Basis-Net-Of-Carry For Deliverable Mar-2001 Issues (Data From Close Of 12/29/2000)#B/NYield Change (bps%):-Yr Futures on3/30/ Change (bps%):-Yr Futures on3/22/ Change (bps%):-Yr Futures on3/22/ Change (bps%): Futures on3/22/ Futures 16
Basis ConceptsExhibit Basis-Net-Of-Carry Mar 2001Projected Basis-Net-Of-Carry For Deliverable Mar-2001 Issues (Data From Close Of 12/29/2000)#B/NYield Change (bps%):-Yr Futures on3/30/ Change (bps%):-Yr Futures on3/22/ Change (bps%): Futures on3/22/ Change (bps%): Futures on3/22/ Futures 17
Basis ConceptsExhibit Scenario AnalysisCarr Futures 18
Basis ConceptsExhibit Disadvantage to Being Long FuturesPrice/-duration bond(., 6 …s of 8/23)-duration bond(., 8-3/4s of 5/17)%7%6%Selected Deliverable BondsCouponMaturity Price Factor Yield DV01 Modified Implied RP duration rate8 3/4s5/15/17 134-07+ 3/4s5/15/20 137-06 CTD6 1/4s8/15/23 108-03+ •With a modified duration of percent, the converted price ofthe 8-7/8s would increase to approximately if its yield wereto fall to 5 percent. The price of the 5-1/4s, on the other hand,with a modified duration of percent, would increase .•If yields were to rise to 7 percent, the price of the 5-7/8s would fallto just above 90. The price of the 5-1/4s would fall to approxi-mately Futures 19
Basis ConceptsExhibit point usually not 6%Price/factor6-1/4 (if yield=8-3/4)1006 1/4 (if yield >8-3/4 5/20yield of 8-3/4)5%7%6%Yield of 8-3/4 s of 5/20Selected Deliverable BondsCouponMaturity Price Factor Yield DV01 Modified Implied RP duration rate8 3/4s5/15/17 134-07+ 3/4s5/15/20 137-06 CTD6 1/4s8/15/23 108-03+ Futures 20
Basis ConceptsExhibit Price RelationshipsPriceFactor6-1/4’s of 8/23High DurationFuturesPriceBeforeExpiration8-3/4’s of 5/17Low Duration8-3/4’s of 5/20Medium DurationYield of 8 3/4’s of 5/20Carr Futures 21
Basis ConceptsExhibit of a High Duration Bond is Like a Call Option on Bond FuturesPriceFactor6 1/4's of 8/23High Duration YAYBYCYCYAYBYield US BONDForward YieldISSUE 6 1/4 Probability of Shift %%%%%%%%%%%%%%%8/15/23>>>Shift of Reference #>>>Probability |30s' Twist around |of Twist VReference %%%%% 6 1/4 Probability of Shift %%%%%%%%%%%%%%%8/15/23>>>Average overShift of Referenceshifts #>>>Probability |30s' Twist around |of Twist VReference %%%%% Futures 22
Basis ConceptsExhibit of a Low Duration Bond is Like a Put Option on BondFuturesPriceFactor8-3/4's of 5/17Low DurationFutures Price Before ExpirationYAYBYCYABYCYYieldUS BONDForward YieldISSUE 8 3/4 Probability of Shift %%%%%%%%%%%%%%%5/15/17>>>Shift of Reference #>>>Probability |30s' Twist around |of Twist VReference %%%%% 8 3/4 Probability of Shift %%%%%%%%%%%%%%%5/15/17>>>Average overShsift of Referenceshift #>>>Probability |30s' Twist around |of Twist VReference %%%%% Futures 23
Basis ConceptsExhibit of a Medium Duration Bond is Like a Straddle on Bond FuturesPriceFactor8-3/4's of 5/20Medium DurationYAYBYCYBYCYieldYAUS BONDForward YieldISSUE 8 3/4 Probability of Shift %%%%%%%%%%%%%%%5/15/20>>>Shift of Reference #>>>Probability |30s' Twist around |of Twist VReference %%%%% 8 3/4 Probability of Shift %%%%%%%%%%%%%%%5/15/20>>>Average overShift of Reference shifts#>>>Probability |30s' Twist around |of Twist VReference %%%%% Futures 24
Basis ConceptsExhibit Market Value of the Strategic Delivery Options!Basis net of carry of the 8-3/4’sBasis = at an RP rate of % = net of carry = [= - short is paying for the delivery options in theMarch ‘01 futures contract.!Market and implied RP ratesThe market RP rate is %.The implied RP rate for the 8-3/4s is %The short is giving up basis points for 86 days in exchangefor the delivery options•There are two ways of measuring the value that the market placeson the short’s strategic delivery options.•One is basis net of carry, which is approximately the amount bywhich the futures price is below the forward price.•The other is the difference between the market RP rate, whichcould be earned in the money market, and the CTD’s implied RPrate, which is the hypothetical return to cash/futures arbitrage withthe cheapest to deliver Futures 25
Basis ConceptsExhibit the Fair Value of a Futures Contract Treasury Futures Pricing & Hedging ToolMar-01/late deliveryKey Dates(days*)Futures(Contract Mar-01)2Year2-year5-year10-yearBond12/29/00Market PriceClosing(-5)101-18+103-18104-27+104-201/2/01Theoretical PriceTrade(-1)101-20103-19+104-29104-181/3/01Rule-of-Thumb DV01Settlement(0) D3/1/01Option-adjusted DV01 wrtelivery(57)3/21/013/29/01CTD yieldLast Trade(77)(85) D3/30/014/3/01OTR yieldelivery(86)(90)* days from settlementOption-adjusted Duration wrtCTD -adjusted Convexity2-year5-year10-yearBondYield %%%%Repo distributionnormalnormalnormalnormalVegas wrtYield beta coefficientyield volatility coefficientyield date4/3/013/30/013/30/013/30/01twist # B/NCouponMaturity2:00 PMYieldMar-01BasisBasisNOCDV01/ModifiedAssumedFull $TermCarryImp-RPProb. OfPrice-32ndDay32-DelFactor32ndActualExpected$100,000DurationYarry $/ield Futures 26
Basis ConceptsExhibit Futures Rich or Cheap?SpotMarketbasisTheoreticalbasisForwardMarketBNOCTheoreticalBNOCTheoretical FuturesMarket Futures•In the example above, the market futures price is higher than thefutures price. As a result, the market basis is smaller than thetheoretical basis. We conclude, then, that futures are rich.•We also see that the market value of the strategic delivery options(Market BNOC) is less than the theoretical or expected value ofthe options. Thus, the options are cheapCarr Futures 27
Basis TradingSection 3BASIS TRADINGCarr Futures 1
Basis TradingExhibit Trading!Things that affect the basis!Trade construction!P/L profiles for long and short basis positions!Types of basis trades!Examples of basis tradesCarr Futures 2
Basis TradingExhibit Trading!Basis tradingThe simultaneous trading of cash bonds and bond futures to takeadvantage of expected changes in the basis. Basis trades can bedone as spreads in the EFP (exchange of futures for physicals)market through various government bond brokers as well as in theconventional way, which involves separate cash and futurestrades.!Buying the basisBy definition, “buying the basis,” or “going long the basis” is buyingcash bonds and selling a number of futures equal to the bond’sconversion factor for every $100,000 par value of the cash example, buying $100 million of the basis of the 8-3/4s of5/15/17 (whose conversion factor is ) would mean buying$100 million face or par amount of the bond and selling1,280 [ = $100,000,000 x ( / $100,000) ] bond futures.!Selling the basisTo sell or go short the basis is just the opposite: selling or shortingthe cash bond and buying a number of futures equal to the bond’sconversion factor for every $100,000 par amount of the bond example, selling $10 million of the basis of the 7-5/8s of2/15/25 (conversion factor = ) would entail selling $10million face amount of the bond and buying 120 [= $10,000,000 x( / $100,000)] futures contracts.•Strict constructionists use the conversion factor to determine thenumber of futures contracts to buy of sell in a basis trade. Thisapproach allows one to tie changes in the P/L to changes in thebasis as it is defined. Basis positions usually have some directionalbias, which bothers traders who want to trade the cash/futuresprice spread but who do not want to take a directional position. Aduration neutral cash/futures spread trade will have a slightlydifferent P/L than a strict basis Futures 3
Basis TradingExhibit for a Long Basis Position!SettingSuppose that on August 6, 1992, September ’92 bond futures aretrading at 105-04/32nds. At the same time, the 7-1/4s of 5/16 aretrading at think that is a narrow basis at this time in thedelivery cycle and that a long basis position is likely to be profit-able. The 7-1/4s have a conversion factor of . Your openingtrade would be:Opening trade on 8/6/92 (settle 8/7/92)Buy $10 million of the 7-1/4s of 5/16 at 92 September 1992 futures at 105-04/32ndsBasis = August 20th, your views have been borne out, and you want tounwind the position. Your closing trade would be:Closing trade on 8/20/92 (settle 8/21/92)Sell $10 million of the 7-1/4s of 5/16 at 98-17/32ndsBuy 92 September 1992 futures at 106-08/32ndsBasis = Futures 4
Basis TradingExhibit for a Long Basis Position (continued)!BondsBuy $10 million of the 7-1/4s of 5/16 at $10 million of the 7-1/4s of 5/16 at 98-17/32ndsGain = x $3,125 (per 32nd) = $95, sum of these two amounts represents !Futuresthe value of the Sell 92 September bond futures at 105-04/32ndschange in the 92 September futures at 106-08/32ndsLoss = 36/32nds x 92 x $ (per 32nd) = ($103,)!Coupon interest earned (14 days)$10,000,000 x ( x (14/184) = $27, sum of these two !RP interest paid (14 days)amounts represents the value of carry.$9,929,210 x .0335 x (14/360) = ($12,)•Coupon payments are made semiannually. Coupon income iscalculated by multiplying the semiannual coupon amount by thenumber of days in the holding period divided by the actual numberof days in the particular semiannual coupon period. In this ex-ample, the actual number of days between the last coupon and thenext is 184.•RP interest is a conventional money market interest calculationassuming that one finances the entire full price — that is, priceplus accrued interest — of the Futures 5
Basis TradingExhibit P/L for a Long Basis Position!Change in the basis7-1/4s of 5/16$95, 1992 futures($103,)Net($8,)!CarryCoupon interest$27, interest($12,)Net$14,$6,•As a rough check on your trade construction, you can comparewhat you realized on the change in the price relationship betweencash bonds and futures with what you should have made. Thebasis narrowed from to for a change For a basis position of $10 million, each 32nd is worth$3,125. Thus, your profit on the change in the basis should havebeen -$8,125 [ = x $3,125]. The difference between thetheoretical gain and what you realized is due to rounding thenumber of futures. The strict definition of the basis would requireyou to sell futures, but you could only sell 92.•Notice that this long basis position made money even though thebasis fell. As it was, what the position earned in carry was morethan enough to offset the loss associated with the decrease in Futures 6
Basis TradingExhibit for a Short Basis Position!SettingIn contrast to the basis of the 7-1/4s, you believe that the basis ofthe 11-3/4s of 11/14-09 on August 6 is too wide and will narrowmore than enough over the next few days to offset any negativecarry in a short basis position. The conversion factor of the11-3/4s is .!Opening trade on 8/6/92 (settle 8/7/92)Sell $10 million of the 11-3/4s of 11/14-09 at 135 September 1992 futures at 105-04/32ndsBasis = 57/32nds!Closing trade on 8/20/92 (settle 8/21/92)Buy $10 million of the 11-3/4s at 144-11/32ndsSell 135 September 1992 futures at 106-08/32ndsBasis = Futures 7
Basis TradingExhibit for a Short Basis Position (continued)!BondsSell $10 million of the 11-3/4s at $10 million of the 11-3/4s at 144-11/32ndsLoss = x -$3,125 = ($114,)!FuturesBuy 135 September 1992 futures at 105-04/32ndsSell 135 September 1992 futures at 106-08/32ndsGain = 36/32nds x 135 x $ (per 32nd) = $151,!Coupon interest paid (14 days)$10,000,000 x ( / 2) x (14/184) = ($44,)!Reverse RP interest earned (14 days)$14,597,320 x .0325 x (14 / 360) = $18,•In this example, the reverse RP rate (at which one lends) isassumed to be 10 basis points lower than the RP rate (at whichone borrows).•If the reverse RP rate had instead been .0335 — or 10 basis pointshigher — the RP interest earned would have been $19,, or$ Futures 8
Basis TradingExhibit P/L for a Short Basis Position!Change in the basis11-3/4s of 11/14-09($114,)September 1992 futures$151, $37,!CarryCoupon interest($44,)RP interest$18,($26,)Total$10,•In this example, the short basis position made money despitenegative carry. The decrease in the basis was more than enough tooffset the cost of financing the short bond position for the life ofthe Futures 9
Basis TradingExhibit that Affect the Basis!Changes in the RP rateChanges in the slope of the yield curveChanges in yield spreadsChanges in yield levelsChanges in yield volatilityCarry and convergence•A decrease in the RP rate, or an increase in the slope of the yieldcurve, will tend to increase carry, which in tern increases the basisof any given bond.•Also, an issue’s RP rate falls if it leaves the general collateral pooland goes “on special.” Because a decrease in an issue’s RP rateincreases its net carry, it also increases that issue’s basis.•A decrease in a bond’s yield relative to yields on other deliverablebonds will increase its basis.•Pure basis positions are seldom duration neutral. The basis of alow-duration bond tends to behave like a put option, increasing invalue as bond yields rise. The basis of a high-duration bond tendsto behave like a call option, increasing in value as bond yields fall.•The value of the strategic delivery options depend on the market’sperception of yield volatility. An increase in expected yield volatilityincreases the value of the short’s strategic delivery options,thereby lowering the futures price and raising the basis of all bondsin the deliverable Futures 10
Basis TradingExhibit that Affect the Basis!Changes in the RP rateChanges in the slope of the yield curveChanges in yield spreadsChanges in yield levelsChanges in yield volatilityCarry and convergence•Extended descriptions of these trades are provided in Chapter 6 ofBurghardt, et. al., The Treasury Bond Basis, revised edition, Probus, 1994.•Selling the basis when you think the embedded delivery options are overval-ued can make money as an outright basis trade. Yield enhancement is avariant of this trade. In yield enhancement, you sell the bonds you own andreplace them with synthetic bonds that comprise cash and long positions incheap futures.•Selling the basis of a non-cheap bond differs from selling the basis of thecheapest to deliver in two ways. First, the basis net of carry for a non-cheapbond is expected to converge to a positive number rather than to , the basis of a non-cheap bond depends much more on the spreadbetween its yield and the yield of the cheapest to deliver. Basis traders oftensell the basis of the “on-the-run” bond or note. Newly issued bonds andnotes tend to trade at a premium to older issues.•Selling the on-the-run’s basis has two attractions. The first is liquidity. Thesecond is the cheapening of the bond (and corresponding decrease in itsbasis) when it is replaced at the next auction by a new Futures 11
Basis Trading•Buying cheap bases can make sense as outright basis trades or asways of buying cheap options in lieu of buying outright calls or putson futures.•If one contract month’s basis is rich or cheap relative to another’s,one can take advantage of the difference by trading the calendarspread — that is buying futures in the month for which the basis isrelatively expensive and selling futures in the month for which thebasis is relatively cheap.•Issues pass in and out of the general collateral pool in the RPmarket. As they leave the pool and go “on special,” their RP ratesfall and their bases increase. As they go off special and reenter thegeneral collateral pool, their RP rates increase, and their bases can, therefore, trade RP special Futures 12
Basis TradingExhibit a Shift in the Cheapest to DeliverMarket dataIssueDate5/31/906/1/907-1/2s of 16Price (decimal) price (decimal) %%Basis (32nds) ($/day)$$-3/4s of 14-09Price (decimal) price (decimal) %%Basis (32nds) ($/day)$$ (June 90)Price (decimal) to last delivery2524Overnight %%Term %%•Selling the basis is akin to selling the strategic delivery options. Ameasure of how much the market is paying for these options is thespread between the market RP rate and the implied RP rate on thecheapest to deliver (., the 7-1/2s on 5/31).•Between 5/31 and 6/1, the 7-1/2s are replaced by the 11-3/4s ascheapest to Futures 13
