《悉尼大学固定收益证券课件Lecture 10》由会员分享，可在线阅读，更多相关《悉尼大学固定收益证券课件Lecture 10（58页珍藏版）》请在金锄头文库上搜索。
1、FACULTY OF ECONOMICS & BUSINESSInterest Rate DerivativesLecture 10 DR. ANDREW AINSWORTHFINC3019 FIXED INCOME SECURITIESLast weekSecuritisation in AustraliaCollateralised debt obligationsSub-prime crisisIntroductionForwardsFuturesU.S. Treasury futures-Delivery options-Basis-Cost of carry-Pricing-Hedg
2、ingEurodollar futuresAustralian interest rate futuresReading: Sundaresan Ch. 17Forwards versus FuturesForward contractsA buyer of a forward contract agrees to purchase one unit of the underlying asset at a specified future time the maturity or settlement or delivery dateThe price agreed to in the co
3、ntract is the forward priceThe forward price is determined when the contract is written and does not change over the life of the contractA buyer of a forward contract is long in the forward marketA seller of a forward contract is short in the forward marketThe forward price agreed to by the buyer an
4、d the seller is such that the buyer pays and receives nothing when the contract is entered intoAt maturity the short position provides the underlying asset to the long position and receives the forward price in returnForward contract cash flowsA trader buys a forward contract on coal on day 1 that w
5、ill mature on day 4The forward and spot (cash) prices of coal are given belowCash flows occur only on the settlement dateAs the cash price rises, the long forward position becomes more valuable-A loss would have eventuated if the cash price on maturity was less than 203The forward price must equal t
6、he spot price on the maturity date-Why?DateForward PriceSpot PriceCash flows1203.0200.002204.0200.503205.5204.504207.5207.5207.5 - 203 = 4.5Futures contractsA buyer of a futures contract agrees to purchase one unit of the underlying asset at a specified future time the maturity dateThe price agreed
7、to in the contract is the futures priceThe futures price is determined when the contract is writtenThe futures price agreed to by the buyer and the seller is such that the buyer pays and receives nothing when the contract is entered intoThe parties to a futures contract will need to make or receive
8、daily instalment payments toward the eventual purchase of the underlying assetThe sum of these daily payments and those made at maturity will equal the futures price when the contract was entered intoFutures contracts: Marking to marketThe daily change in the futures price determines the daily insta
9、lmentsLong position-Makes payment equal to change in daily futures price if futures price falls-Receives payment equal to change in daily futures price if futures price risesShort position-Receives payment equal to change in daily futures price if futures price falls-Makes payment equal to change in
10、 daily futures price if futures price risesThis process is called marking to market-In effect the futures contract is rewritten each day-Value of contract after daily settlement equals zeroFutures contract cash flowsThe cash flows from a futures contract will differ from a forward contractAt maturit
11、y the balance due will be the futures price agreed to at the outsetThe futures price must equal the spot price on the maturity date-Why?Why is reinvestment risk relevant for futures contracts?-May need to liquidate investments to make payments or reinvest cash flows receivedDateForward PriceSpot Pri
12、ceCash flows1203.0200.00.02204.0200.51.03205.5204.51.54207.5207.52.0Design of futures contractsFutures contracts are traded on exchanges and therefore the contracts need to be standardised-Physical delivery versus cash settlement?-Are the deliverable assets are in competitive supply?-Traders can cor
13、ner the market-U.S. Treasury futures allows the choice of which Treasury bond to deliver-Margins-Investor must deposit collateral as initial margin position in order to open a futures position -If initial margin position falls below the maintenance margin, a margin call occurs and the investor will
14、need to deposit cash to restore the initial margin-Options for the short position-Choice of physical delivery location-Choice of delivery datePayoffs under a forward/futures contractPrice at maturityProfitLossLongShortFutures PriceFutures vs. forwardsForwards differ from futures contracts in many wa
15、ys:-Futures contracts are marked to market-This causes differences in the price due to reinvestment risk and interest rate uncertainty -Forwards trade in over-the-counter (OTC) markets-Futures trade on organised exchanges -Sydney Futures Exchange (SFE), Chicago Board of Trade (CBOT)-Forwards have cr
16、edit risk because of the contract between counterparties-Futures involve clearinghouses that monitor margins and non-performance-Future contracts are standardised-Forward contracts are customisedUses of interest rates futuresHedge-Remove risk associated with a portfolio of bonds-We can undertake a d
17、uration and/or convexity hedgeSpeculate-If an increase in interest rates is expected we will sell futures contracts-There is substantial leverage because margin requirements are small-Short sales are much easier in the futures market than the spot market-Lower transaction costsArbitrage-The generati
18、on of riskless profits-Cash and carry arbitrage-Reverse cash and carry arbitrageU.S. Treasury FuturesU.S. Treasury futuresU.S. Treasury futures trade on the Chicago Board of TradeFutures traded on U.S. Treasury instruments-Bills: 13-week-Notes: 2, 3, 5 and 10-year-Bonds: 30-yearWe will focus on 30-y
19、ear T-bond futures -An important feature of these futures is that they require physical deliveryThere are many options embedded in T-bond futures that make them difficult to accurately price-These options are available to the seller during the delivery monthU.S. Treasury bond futures contract specif
20、icationsUnderlying UnitOne U.S. Treasury bond having a face value at maturity of $100,000Deliverable GradesU.S. Treasury bonds that, if callable, are not callable for at least 15 years from the first day of the delivery month or, if not callable, have a remaining term to maturity of at least 15 year
21、s from the first day of the delivery month. Invoice PriceEquals the futures settlement price times a conversion factor, plus accrued interest. The conversion factor is the price of the delivered bond ($1 par value) to yield 6 percent.Price QuotePoints ($1,000) and 1/32 of a point. For example, 134-1
22、6 represents 134 16/32. Par is on the basis of 100 pointsTick Size(minimum fluctuation)One thirty-second (1/32) of one point ($31.25)Contract MonthsMarch, June, September, and December quarterly cycleLast Trading DaySeventh business day preceding the last business day of the delivery monthLast Deliv
23、ery DayLast business day of the delivery monthWhat happens at expiry?A trader can take an offsetting position before expiry to close out their trade-If you are long futures then you take a short position prior to the expiry of the contract and you will not need to make physical deliveryOR A trader c
24、an make physical delivery to close out the futures position This will result in a loss because of the valuable delivery options that the short position in futures has-Physical delivery can occur on any day in the trading month for T-bond futuresDelivery optionsQuality option-Short futures position h
25、as choice as to which bond to deliver-Can deliver on any day of the delivery monthWildcard option-Futures trading closes at 2pm Chicago time yet delivery can occur up until 8pm-If deliverable securities were to experience a large price decline between 2pm and 8pm then the investor who is short can p
26、rofit-Each day of the delivery month has an option that lasts for six hoursEnd-of-the-month (timing) option-The futures contract stops trading seven business days before month-end but delivery can occur up until the last business day-The short investor has flexibility as to when to deliver the under
27、lying during this periodConversion factorThe quality option gives traders with the short position the choice as to which bond to deliver-They will want to deliver the cheapest bondThe CBOT uses a conversion factor to adjust the futures price either upwards if the coupon rate on the underlying bond i
28、s greater than 6% or downwards if the coupon rate is less than 6%:X is the number of months by which maturity exceeds N, so x = 0, 3, 6 or 9The conversion factor seeks to make each of the bonds available to be delivered similar, so that they are all yielding 6%A high coupon bond is expensive so the
29、trader is rewardedConversion factorTo determine the compensation paid by the investor with the long position the invoice price we use the futures price (H) multiplied by the conversion factor (CF) then add the accrued interest (AI):If the futures price = 102.25 and the conversion factor for a 5.25%
30、T-bond maturing in 28 years and 3 months = 0.8984 and accrued interest = 0.6420, what will be the invoice price?The trader with the short position can undertake this analysis with all eligible bonds to determine the cheapest to deliver (CTD)BasisThe basis is the difference between the quoted price o
31、f the deliverable T-bond less the futures price for delivery at some future date s, multiplied by the conversion factor:Long the basis: long spot and short futures-Size of futures position is the conversion factor-Long delivery options (quality, timing and wildcard options)Short the basis: short spo
32、t and long futures-Short delivery options (quality, timing and wildcard options)Note that accrued interest does not appear as it is included in both the invoice and spot pricesBasisNo arbitrage ensures that the basis in the delivery month is greater than zero for U.S. Treasury futures-If it werent t
33、hen a trader could sell futures and immediately deliver the bond to make a riskless profit-Note that this is only the case for futures where short traders have delivery options-In the case of a forward contract, the basis can be positive or negative depending on the cost of carry-Outside of the deli
34、very month, the basis can be positive or negativeValuing a U.S. Treasury futures contractHow do we value a U.S. T-bond futures contract?This isnt a trivial task because of the delivery optionsBut, we can estimate a theoretical forward price -This does not include any of the delivery options-We also
35、disregard marking to market and associated cash flowsThe process by which we can value a forward contract is through a cash and carry arbitrageThis gives rise to the forward-spot parity relationshipValuing a U.S. Treasury futures contractLet us first consider how a trader can acquire a bondIf at dat
36、e 0 a trader wants to hold at future date 1 one unit of a bond, they have two options-They can buy a forward contract at date from a seller who will deliver one unit of the bond at a price F0-Or they can borrow money to buy the bond at date 0Let us consider the fraction of a year between date 0 and
37、date 1 as tValuing a U.S. Treasury futures contractThe cash flows from these two operations are:P = spot price of bondF = forward pricer = repo rate (financing rate)c = coupon ratet = time in years to futures delivery dateDate 0Date 1Buy forward contract written on 1 unit of bond0F0Borrow money to b
38、uy 1 unit of bondP0Buy 1 unit of bond-P0Valuing a U.S. Treasury futures contractThe cost of both of these operations is equal to zero at date 0 as there are no cash flowsSo, if there are not opportunities for arbitrage then the cash flows at date 1 should also be equalIf we define cy as the current
39、yield of the bond:We arrive at the price of a forward that precludes arbitrage and is the forward-spot parity relationship:Note: It is not the price of a futures contract! Why?ExampleWhat is the theoretical forward price if the repo rate is 6% p.a., the spot price of a deliverable 10% T-bond is 97.5
40、4 and there are 6 months until delivery?The current yield is 10/97.54 = 10.25%Arbitrage opportunitiesWe can also think of the forward-spot parity relationship as a way to identify arbitrage opportunitiesCash and carry arbitrage-If the price at which you can sell a bond in the forward market (at matu
41、rity of forward contract) is greater than the cost of financing the bond, then the investor should sell forward and finance the bond-If not, then the investor should buy forward and sell the bond in a repurchase transactionNote that there are no cash flows-Selling the futures has no cash flow-Borrow
42、ing and buying the bond has no current cash flow as it is fully financedExample: cash and carry tradeA 12% coupon 20-year bond with a par value of 100 is selling at par and is deliverable against a futures contract that settles in 3 monthsThe futures price is 107The current repo rate is 8% p.a.We ca
43、n sell the futures contract at 107Borrow 100 for three months at 8% p.a.Purchase the bond for 100Example: cash and carry tradeNo initial cash outlay for this strategyAt settlement of the futures contract:-Quoted price of bond 107-Accrued interest3-Total proceeds 110From the loan:-Repay principle100-
44、Interest2-Total outlay102-Profit8Example: reverse cash and carry tradeIf the futures price had been 92 instead of 107 we could execute a different trade-We can buy the futures contract at 92-Lend 100 for three months at 8% per year-Short sell the bond for 100-At settlement of the futures contract we
45、 outlay 92 + 3 = 95-From the loan we receive 100 + 2 =102-We make a profit of 7In reality arbitrageurs would act to eliminate such profitable opportunitiesIn the previous two examples, if the futures price had been 99 there would not be arbitrage profits as inflows = outlays = 102Financing bondsFutu
46、res TradersRepo dealerPost bond as collateralReceive cashBuy bondPay cashSell futuresUnwinding the tradeFutures TradersRepo dealerTake delivery of T-bondPays cash and interest (F)Receive CF x H (invoice price)Deliver bondArbitrage opportunitiesA long position in a T-bond forward contract is equivale
47、nt to borrowing and buying the underlying bondA short position in a T-bond forward is equivalent to shorting the T-bond and investing at the risk free rateCost of carryThe difference between the repo rate and the current yield is the cost of carry-It is the cost of financing the position less the ca
48、sh yield on the underlying securityIncome earned by the long basis holder (short futures) on spot Treasury position = accrued interest (from spot settlement to futures delivery) less financing cost (from spot settlement to futures delivery)Theoretical price of a forward contract = spot price + the c
49、ost of carryThe shape of yield curve affects cost of carryCost of carryIf the repo rate is higher than the current yield then there is negative carryIf there is negative carry (r cy) the forward price will be higher than the spot price (F P)If the current yield is greater than the repo rate then the
50、re is positive carry-If there is positive carry (cy r) the forward price will be lower than the spot price (F P)If there is zero carry, the forward price will equal the spot priceRemember we have ignored interim cash flows from marking to market and delivery optionsIf the borrowing and lending rates
51、 differ the futures price will have an upper and lower boundaryThe value of futuresThe theoretical price refers to the price of a forward contract which does not provide the short investor with delivery optionsThese options will reduce the price of a futures contract relative to a forward contract-W
52、hy?Theoretical price of a futures contract = spot price + the cost of carry value of quality option value of timing option value of wildcard optionThe exact value of these options is an empirical questionBasis after carryForward price represents the price at which the bond can be sold forward to bre
53、ak evenInvoice price represents the actual revenue from delivering the bond in the futures marketThe difference between the two is the profit or loss of selling futures and borrowing and buying the bond and is the basis after carry:Forward price is the cost of carrying a deliverable bond through rep
54、o financing until deliveryThe conversion factor multiplied by the conversion factor is the revenue associated with deliveryThe difference is the profit or loss from a cash and carry position in the futures marketBasis after carryIf the basis after carry is negative then arbitrage profits can be obta
55、ined in futures-Sell futures and borrow and buy the cheapest to deliver bondBoth are usually positive, howeverBasis after carry can be separated into:-Basis less-Reinvested cash inflows plus-Financing costsWhen the carry is positive, the BAC is less than the basisThe bond with the lowest BAC is the
56、cheapest to deliverHedging using T-bond futuresIn order to hedge a position in an underlying bond using T-bond futures we need to examine the PVBP of each security:Where f = the hedge ratioWe need to take account of the cheapest to deliver bond:The number of contracts to purchase depends on the par
57、value of the futures contract and the bond to be hedgedExampleA $100m par 5.4% July 2027 T-bond has a PVBP of 486A 5.8% May 2025 T-bond is the cheapest to deliver with a conversion factor of 0.9670 and PVBP of 387Each futures contract is on $100,000 par amountWhat is the number of futures contracts
58、required to hedge this position?Eurodollar FuturesEurodollar marketEurodollars are bank deposits denominated in USD but are located outside the U.S.It is an interbank market where participating banks can borrow and lend from each other The rate at which banks offer loans top each other is the London
59、 Interbank Offer Rates (LIBOR)-It is determined by the British Bankers Association (BBA)The spot market extends out to 10 years in maturity but the depth and liquidity is concentrated at the shorter end of the marketLIBOR is seen as the benchmark rate for many markets-Swaps, commercial paper and fut
60、uresEurodollar marketHow s LIBOR determined?A panel of large banks provide the rates that they will lend to each other at-The panel includes banks such as Barclays, Credit Suisse, Deutsche, HBOS, JP Morgan, UBS, etcThe four largest and the four lowest rates are eliminated and the remaining 8 rates a
61、re averaged to get LIBORLIBOR should reflect the credit quality of the banks of the panel If there is a financial crisis that effects the bank, then we should see LIBOR increase to reflect this increased credit riskInterest on Eurodollar time deposits is calculated on an actual/360 basisEurodollar f
62、uturesEurodollar futures trade on may different exchange around the worldThey are cash settled to the 90-day LIBOR that is derived from the 90-day Eurodollar time deposit with a principal value of $1mThe contract matures at 11am London time on the second London business day immediately preceding the
63、 third Wednesday of the contract monthOne basis point change in the interest rate is equal to $25 gain/loss for each futures contract-90/360 daysThere is no delivery or timing options to complicate the pricingSettlement price of the Eurodollars futures contract will converge to LIBOR-100 x (1 LIBOR)
64、-So if LIBOR is 5% then the futures settlement price is 95Intermarket spreadsEurodollar futures contracts can be used to implement strategies designed to profit from changes in the spread with treasury securities -The TED spread uses the spread between 3-month LIBOR and 3-month T-billsIn effect the
65、strategy speculates on the difference between a risk-free rate and the rate that banks will lend to each other atThese spreads widen during a financial crisis and contract during periods of financial stability-We anticipate a flight to quality during banking crises-Japanese bank failures in 1990s, R
66、ussian default and LTCM in 1998-What about during the recent crisis?The TED spreadAustralian Interest Rate Futures ContractsAustralian interest rate futuresTraded on the Sydney Futures Exchange-Part of the Australian Securities ExchangeThere are four interest rate futures contracts-30-day interbank
67、cash futures-90-day bank bill futures-3-year bond futures-10-year bond futures10-year Treasury bond futures10 Year Treasury Bond Futures Contract UnitCommonwealth Government Treasury Bonds with a face value of A$100,000, a coupon rate of 6% per annum and a term to maturity of ten yearsContract Month
68、s: March/June/September/December up to two quarter months ahead. Minimum Price Movement: Prices are quoted in yield per cent per annum in multiples of 0.005 per cent. For quotation purposes the yield is deducted from an index of 100. The minimum fluctuation of 0.005 per cent equals approximately $40
69、 per contract, varying with the level of interest rates. Last Trading Day: The fifteenth day of the contract month (or the next succeeding business day where the fifteenth day is not a business day). Trading ceases at 12.00 noon.Settlement Day: The business day following the last permitted day of tr
70、ading. Trading Hours: 5.12pm 7.00am and 8.32am 4.30pmSettlement Method: The arithmetic mean, taken at 9.45 am, 10.30 am and 11.15 am on the last day of trading by 10 dealers, randomly selected for each time, at which they would buy and sell a series of bonds previously declared by ASX for that contr
71、act month, excluding the two highest and two lowest buying quotations and the two highest and two lowest selling quotations for each bond. All bought and sold contracts in existence as at the close of trading in the contract month shall be settled by the Clearing House at the cash settlement price.1
72、0-year Treasury bond futuresThe yield in the futures market is simply 100 futures price-If futures price is 95 then yield is 5%We can then use this yield to price the underlying bond, which is a 10-year 6% coupon CGB-There is no need to calculate accrued interest as there is always an equal number o
73、f periods to maturity because there is not physical deliveryThe value of a futures contract is given by:So if the futures yield increases the value of the contract decreases-The dollar value of a 1 basis point change in futures yield is not constant and will vary with the yieldSettlement of 10-year
74、futuresBefore the futures contract is listed the SFE announce which bonds will be part of the underlying basketThe 10-year futures are cash settled to an average of dealer quotes taken at 9.45 am, 10.30 am and 11.15 am on the last day of trading by 10 dealers for the bonds that underlie the futures
75、contractThe two highest and two lowest buying quotations and the two highest and two lowest selling quotations for each bond are excludedSettlement of 10-year futures30-day interbank cash futuresContract Unit: Average monthly Interbank Overnight Cash Rate payable on a notional sum of AUD 3,000,000 C
76、ontract Months: Monthly up to 18 months ahead Minimum Price Movement: Quoted in yield percent per annum in multiples of 0.005%, for quotation purposes yield is deducted from 100. A one basis point move of 0.01% is equal to $24.66 Last Trading Day: Trading shall cease at 4.30pm on the last business d
77、ay of the expiry month Settlement Day: The second business day after the Last Trading Day Trading Hours: 5.14pm 7.30am and 8.34am 4.30pmSettlement Price: The Cash Settlement Price is equal to 100 minus the cash settlement rate, where the cash settlement rate is the monthly average of the Interbank O
78、vernight Cash Rate for that contract month calculated by taking the sum of the daily Interbank Overnight Cash Rate, as published by the Reserve Bank of Australia, divided by the number of days for that month. On weekends and public holidays, when no Interbank Overnight Cash Rate is published the Cas
79、h Rate published on the previous business day will be used for settlement price calculation. The cash settlement price is rounded to the nearest multiple of 0.001. The Cash Settlement price shall be announced to the market by 12.00pm on the first business day following the Last Trading Day. All boug
80、ht and sold contracts in existence as at the close of trading in the contract month shall be settled by SFE Clearing at the cash settlement price. 30-day interbank cash futuresThis futures contract can be used to gauge the markets expectation of changes in the RBA cash rateThe expectation of a rate
81、change by the RBA is calculated by taking into account the number of days the RBA Target Cash Rate is known versus the number of days in the month that it is unknown-The number of days before and after the RBA Board Meeting30-day interbank cash futuresSolving for the probability of a rate change (p)
82、:X = current yield on 30 Day Interbank Cash Rate Futuresrt = current known Target Cash Rate (%)r(t + 1) = expected new Target Cash Rate (%)nb = fraction of month where cash rate known (before RBA announcement)na = fraction of month where cash rate unknown (after announcement)Rearranging, we obtain t
83、he market probability of an official rate change:30-day interbank cash futuresTrading DayDecrease to 4.25%Cash Rate at 4.50%Increase to 4.75%6 May0%90%10%7 May10%90%0%10 May2%98%0%11 May4%96%0%12 May2%98%0%13 May0%98%2%14 May0%98%2%17 May2%98%0%What you should knowForwardsFuturesU.S. Treasury futures-Basis-Cost of carry-Theoretical price-Options for the short traderEurodollar futuresAustralian futures contracts
