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1、 Chapter ObjectivesThis chapter compares currency futures contracts to currency forward contracts and shows how they are priced by the marketplace.-Emphasis is placed on how currency futures contracts are similar to,and yet different from,forward contracts.The last several sections discuss implement
2、ation issues:-Delta hedges for maturity mismatches-Cross hedges for currency mismatches-Delta-cross hedges for currency and maturity mismatches第1页/共32页 Forward Market1.Forward ContractsA forward contract is an agreement between a corporation and a commercial bank to exchange a specified amount of a
3、currency at a specified exchange rate(called the forward rate)and on a specified future date.When MNCs anticipate a future need for or future receipt of a foreign currency,they can set up forward contracts to lock in the rate at which they can purchase or sell a particular foreign currency.第2页/共32页A
4、 forward hedge of the dollarUnderlying position of aFrench exporter(long$s)Sell$s forward at Ft/$(short$s and long s)Net position+$40 million+40 million-$40 million+40 million-Goodsv/$Long$ss/$Short$sThe forward contract provides a perfect hedge because the size and timing of the hedge transaction e
5、xactly offsets the size and timing of the underlying exposure.第3页/共32页 Forward Market2.Non-Deliverable Forward Contractsa.New typeA non-deliverable forward contract(NDF)does not result in an actual exchange of currencies.Instead,one party makes a net payment to the other based on a market exchange r
6、ate on the day of settlement.b.Frequently used for currency in emerging marketsc.No delivery requiredd.One party to the agreement makes a payment to the other party based on the exchange rate at the future date.第4页/共32页 NDF MarketAn NDF can effectively hedge future foreign currency payments or recei
7、pts:Expect need for 100M Chilean pesos.Negotiate an NDF to buy 100M Chilean pesos on Jul 1.Reference index(closing rate quoted by Chiles central bank)=$.0020/peso.April 1Buy 100M Chilean pesos from market.July 1Index=$.0023/peso receive$30,000 from bank due to NDF.Index=$.0018/peso pay$20,000 to ban
8、k.第5页/共32页 Forward versus Futures Contracts Comparing currency futures contracts to currency forward contracts and shows how they are priced by the marketplace.Forwards are a pure credit instrumentWhichever way the price of the spot rate of exchange moves,one party always has an incentive to default
9、(违约动机）Eg,FX,$1.475/,当汇率上升时，卖方有违约动机，当汇率下降时，买方有违约动机。The futures contract solutionA futures exchange clearinghouse takes one side of every transaction(and makes sure that its exposures cancel one another)Contracts are marked-to-market daily Require initial and maintenance margins第6页/共32页 Forwards versu
10、s futuresForwardsFuturesCounterpartyBankCME Clearinghouse（Forward contracts are created by commercial and investment banks,whereas futures contracts are usually found on futures exchanges）MaturityNegotiated3rd week of the month(US)AmountNegotiatedStandard contract sizeFeesBid-askCommissionsCollatera
11、lNegotiatedMargin accountSettlementAt maturityMost are settled early第7页/共32页Futures exchangesFinancial futures exchanges are usually associated with a commodity futures exchange2002 volumeTop 5 futures exchanges(million contracts)Eurex-Eurex(Germany&Switzerland)536.0CME-Chicago Mercantile Exchange(U
12、.S.)444.5CBOT-Chicago Board of Trade (U.K.)276.3Euronext-(Amsterdam,Brussels,Lisbon,Paris,London)221.3NYMEX-New York Mercantile Exchange(U.S.)107.4BM&F-Bolsa Mercadorias&de Futuros(Brazil)95.9Source:Futures Industry Association 第8页/共32页Forwards versus futuresFutures contracts are similar to forward
13、contractsFutures contracts are like a bundle of consecutive one-day forward contracts（期货合约是一连串可更新的1天期远期合约的组合：Each day,the previous days forward contract is replaced by a new one-day forward contract with a delivery price equal to the closing price from the previous days contract.如三个月期的远期合约，相当于90个可更新
14、的1天期的远期合约Daily settlement is the biggest difference between a forward and a futures contractFutures and forwards are nearly identical in their ability to hedge risk（在规避风险管理的功能上有相似之处）第9页/共32页 Hedging with futuresForward contracts can be tailored to match the underlying exposureForward contracts thus
15、can provide a perfect hedge of transaction exposure to currency riskExchange-traded futures contracts are standardizedThey will not provide a perfect hedge if they do not match the underlying exposure s Currency mismatch-there may not be a futures contract in the currency that you would like to hedg
16、eMaturity mismatch-there may not be a futures contract expiring on the same day as your underlying transaction exposureContract size mismatch-the underlying transaction exposure may not be an even increment of existing futures contracts 第10页/共32页 Interest rate parity revisitedSome definitionsSt,Td/f
17、=spot price at time t for expiry at time TFt,Td/f=forward price at time t for expiry at time TFutt,Td/f=futures price at time t for expiry at time TForward and futures prices are equal through interest rate parityInterest rate parity is usually expressed as a forward-looking relation from time zero
18、to time t.(Ftd/f/S0d/f)=(1+id)/(1+if)tIn the slide,IRP is expressed as a backward-looking relation from time t through the expiration date T（即根据IRP可以预测远期和期货价格）Futt,Td/f=Ft,Td/f=Std/f(1+id)/(1+if)T-t STd/f(as t T)第11页/共32页Spot and futures price convergence at expiration T Forward premium FutTd/f=STd/
19、f Fut0d/f S0d/f Futures prices converge to spot prices at expiration.第12页/共32页Maturity mismatches and basis riskIf there is a maturity mismatch,futures contracts may not provide a perfect hedgeBecause the convergence of futures prices to spot prices is nearly linear,interest rate differentials(1+id)
20、/(1+if)are often approximated by the simple difference in nominal interest rates,(id-if).The difference(id-if)is called the basisThe risk of change in the relation between futures and spot prices is called basis riskWhen there is a maturity mismatch,basis risk makes a futures hedge slightly riskier
21、than a forward hedge（当存在期限错配时，基差风险使期货套期保值相对远期套期技术而言更有风险。）第13页/共32页Maturity mismatches and Delta hedgesFutures hedge is called a delta hedge when there is a mismatch between the maturity(but not the currency)of a futures contract and the underlying exposure.When there is a maturity mismatch,a futures
22、 hedge cannot provide a perfect hedge against currency risk.第14页/共32页An example of a delta hedgeDec 16Oct 26Mar 13-S$10millionunderlying obligationFutures expiration date following the cash flowtime 0time t=227/365Sept 11Futures expiration date following the cash flowtime T=278/365第15页/共32页An exampl
23、e of a delta hedgeThere are 227days between March 13 and October 26.A hedge with the futures contract expires on September 11 only hedges against currency risk through that date.It remains exposed to changes in currency values from the end of the contract through October 26.The December futures cont
24、ract is a better choice because it can hedge currency risk through October 26 and then be sold.Suppose the spot rate is S0$/s$0.6010/s$on March 13,Annual interest rate int the United States and Singapore are i$6.24%and is$4.04%According to IRP，the forward price for exchange on October 26 is F0,t$/s$
25、=S0$/s$(1+i$)/(1+is$)t(0.6010)(1+6.24%)/(1+4.04%)227/365=$0.6089/s$It can form a perfect hedge with a long forward contract for delivery of S$10 million on October 26 in exchange for（$0.6089/s$)(S$10,000,000)=$6,089,000.As we shall see,the futures hedge using the December 16 futures contract is not
26、quite as precise.第16页/共32页An example of a delta hedge该公司利用期货合约套期3月13日买进12月到期的期货合约，并在10月26日卖出该期货合约，风险在于12月到期的期货合约运行到10月26日时的价格如何变化？12月到期的期货合约价格：Fut0,T$/s$=S0$/s$(1+i$)/(1+is$)T(0.6010)(1+6.24%)/(1+4.04%)278/365=$0.6107/s$同时，根据远期汇率预测法，10月26日的即期汇率是：ES0，t$/s$=F0,t$/s$=$0.6089/s$This expectation will hol
27、d only if interest rates,(1+i$)/(1+iS$)=1.0624/1.0404=1.02115,remains constant,This ratio is the“basis”for changes in futures prices over time 10月26日债务到期时，分三种情况讨论：情况一：基差不变：basis i$-S$=6.24%-4.04%=2.20%,因此，10月26日的即期汇率不变，即St$/S$=$0.6089/s$，在10月26日，到12月16日交割的期货合约价格就建立在之前预期的即期汇率:St$/s$=$0.6089/s$的基础上，期限
28、T-t27822751天：Futt,T$/s$=St$/s$(1+i$)/(1+is$)T-t(0.6089)(1+6.24%)/(1+4.04%)51/365=$0.6107/s$Profit on futures:Futt,T$/s$-Fut0,T$/s$=$0.6107/s$-$0.6107/s$=0Profit on underlying short position in the spot currency:-(St$/s$-ESt$/s$)=-(=$0.6089/s$-$0.6089/s$=0第17页/共32页An example of a delta hedge情况二：10月26
29、日，新加坡利率上升至：iS$=4.54%，导致新元汇率上升至：St$/S$=$0.6255/S$因此，在10月26日，到12月16日交割的期货合约价格就变为：Futt,T$/S$=St$/S$(1+i$)/(1+iS$)T-t(0.6255)(1+6.24%)/(1+4.54%)51/365=$0.6269/s$此时，公司在期货与现货的损益：Profit on futures:Futt,T$/s$-Fut0,T$/s$=$0.6269/s$-$0.6107/s$=$0.0162/s$Loss on underlying short position in the spot currency:-
30、(St$/s$-ESt$/s$)=-($0.6255/s$-$0.6089/s$=-$0.0166/s$净损益+0.01620.0166$0.0004/s$，损失总额为：$4000（总债务支出是10百万）损失增加是因为新加坡利率上升，基差改变所致。第18页/共32页An example of a delta hedge情况三：10月26日，美元利率上升至：i$=6.74%，导致新元汇率贬值至：St$/s$=$0.5774/s$因此，在10月26日，到12月16日交割的期货合约价格就变为：Futt,T$/s$=St$/s$(1+i$)/(1+is$)T-t(0.5774)(1+6.74%)/(1
31、+4.04%)51/365=$0.5795/s$此时，公司在期货与现货的损益：Profit on futures:Futt,T$/s$-Fut0,T$/s$=$0.5795/s$-$0.6107/s$=$0.0312/s$Loss on underlying short position in the spot currency:-(St$/s$-ESt$/s$)=-(=$0.5774/s$-$0.6089/s$=+$0.0315/s$净损益$0.0312/s$+$0.0315/s$+$0.000/s$，损失总额为：$3000（总债务支出是10百万）所得增加是因为新加坡利率上升，基差改变所致。
32、但总的来讲，futures contracts can provide very good hedge,because basis risk is small relative to currency risk.第19页/共32页 Contract size mismatch and the Hedge RatioThe Forward Hedge:The hedge ratio NF*of a future position is defined as NF*=Amount in forward position/Amount exposed to currency risk=-1The F
33、utures Hedge:是指保值者持有期货合约的头寸多少与需要保值的基础资产之间的比率。The hedge ratio is used to minimize the variance of the hedged position.即期汇率变化率与期货汇率变化率的关系如下：std/f=a a+b b futtd/f+etstd/f=percentage change in the spot ratefuttd/f=percentage change in the futures price std/f=(Std/f-St-1d/f)/St-1d/f and futtd/f=(Futtd/f-
34、Futt-1d/f)/Futt-1d/f This regression is designed to estimate basis risk over the maturity of a proposed hedge.The slope coefficient b=rs,fut(ss/sfut)measures the sensitivity of spot to futures prices第20页/共32页futtd/fstd/f第21页/共32页NFut*=(Amount in futures)/(Amount exposed)=-b b （通过历史数据对上式回归可以得出b b ）He
35、dge quality（对冲质量）is measured by the r-square(r2 =r rs,fut2).-r2 (or r rs,fut2)measures the percentage variation in std/f explained by variation in futtd/f.-High r2 low basis risk and a high-quality hedge.-Low r2 high basis risk and a relatively poor hedge.r-square取值在（0，1）之间Contract size mismatch and
36、 the Hedge Ratio第22页/共32页Contract size mismatch and the Hedge Ratio假设b b1.0251.025，则期货套期保值比率：NFut*=(Amount in futures)/(Amount exposed)=-b b -1.025-1.025 Amount in futures（-1.025）（Amount exposed）如上例中，该公式有100100万新元的空头，需要持有的期货多头为 Amount in futures（-1.025）（-10000000）s$10,250,000芝加哥商品期货交易所一份新元期货合约金额为125
37、,000125,000，所以，持有期货合约的规模为82 82 份期货合约:10,250,000/125,000=82:10,250,000/125,000=82第23页/共32页An example of a Hedge RatioIt is now January 8.You need to hedge a 100 million obligation due on June 3.The spot exchange rate is S0$/=$1.10/A 100,000 CME euro futures contract expires on June 16Based on st$/=a
38、a+b b futt$/+et,you estimate b b=1.020 with r2=0.95.(The relatively high r2(0.95)of this regression means that this is a relatively high quality hedge.)How many CME futures contracts should you buy to minimize the risk of your hedged position?第24页/共32页The Hedge Ratio solutionThe optimal hedge ratio
39、for this delta hedge is given byNFut*=(amount in futures)/(amount exposed)=-b(amount in futures)=(-b)(amount exposed)=(-1.020)(-100 million)=102 millionor(102 million)/(100,000/contract)=1,020 contracts第25页/共32页Currency mismatches and cross hedgesA cross hedge is used when there is a maturity match
40、but a currency mismatch即选择的期货避险合约标的商品与现货商品不同，市场上没有类似现货所发行的期货来避险时，就要找另一个现货价格有正相关，或者是同质的产品来避险。例如，一家英国公司有加元债务，可以利用美元期货的多头来规避汇率风险，因为，美元与加元是高度相关的。为加元债务避险的美元套期保值法：加元债务的现货价格变化率与美元期货价格变化率的关系如下：st/c$=a a+b b futt/$+et当二者的期限匹配时，上式可变化为：std/f1=a a+b b std/f2+etf1=currency in which the underlying exposure is den
41、ominatedf2=currency used to hedge against the underlying exposure（由前面的公式转化而来，由即期汇率变化率替代期货汇率变化率是因为期货到期时的价格与即期汇率具有趋同性。）第26页/共32页-In this case,the currency of the underlying exposure(f1)is different from the currency of the futures contract(f2).-In the delta hedge,spot rate changes(std/f)were regressed
42、 on changes in futures prices(futtd/f).-In the cross hedge,std/f2 is substituted for the independent variable futtd/f2 becausethe maturity of the futures contract is the same as that of the underlying transaction in the spot market,andfutures prices converge to spot prices at maturity.第27页/共32页An ex
43、ample of a CME cross hedgeIt is now January 18.You need to hedge a DKr（丹麦货币）100 million obligation due on June 16.Spot(cross)exchange rates are$0.75/DKr,0.75/DKr,and$1.00/.A CME futures contract expires on June 16 with a contract size of 100,000In this cross hedge,there is a maturity match but a cur
44、rency mismatch.Based on st$/DKr=a a+b b st$/+et,you estimate b b=1.040 with r2=0.89.How many CME futures contracts should you buy to minimize the risk of your hedged position?第28页/共32页The cross hedge solutionOptimal hedge ratio:NFut*=(amt in futures)/(amt exposed)=-b(amt in futures)=(-b)(amt exposed
45、)=(-1.040)(-DKr100 million)=DKr104 millionor 78 million at(DKr104m)(0.75/DKr)or 780 contracts.With an r-square of 0.89,this is a fairly high quality hedge.第29页/共32页 Delta-Cross Hedge （德尔塔交叉套期保值）总结：1.The most general case is the delta-cross hedge.A delta-cross hedge is used when there is both a curre
46、ncy and a maturity mismatch std/f1=a a+b b futtd/f2+et2.If the underlying exposure and the futures contracts are in the same currency,then f1=f2=f and the hedge is a delta hedge.3.If there is both a maturity and a currency match,then a futures hedge is nearly equivalent to a forward market hedge.std
47、/f=a a+b b std/f+et由于std/f=的相关系数为+1，所以，是完全套期保值（r2=1），套期保值比率为NFut*=-b b1 1，此时期货套期保值与远期套期保值是等值的，货币风险可以完全消除。4.A futures hedge is nearly perfect when there is a maturity and a currency match and the underlying transaction exposure is an even increment of the futures contract size.第30页/共32页A classification of futures hedges第31页/共32页感谢您的观看！第32页/共32页