第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)

1、 Chapter 2 Derivative Securities for Currency Risk Management Currency Futures and Futures Markets第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) Chapter Overview1Financial Futures Exchanges2The Operation of Futures Markets3Futures Contracts4Forward versus Futures Market Hedges5Futures Hedges Using Cross Exchange Rates6Hed

2、ging with Currency Futures第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) 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 co

3、ntracts. The last several sections discuss implementation issues:Delta hedges for maturity mismatchesCross hedges for currency mismatchesDelta-cross hedges for currency and maturity mismatches第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) Forward Market1. Forward ContractsA forward contract is an agreement between a corpo

4、ration and a commercial bank to exchange a specified amount of a 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 whi

5、ch they can purchase or sell a particular foreign currency. 第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)A 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 forwa

6、rd contract provides a perfect hedge because the size and timing of the hedge transaction exactly offsets the size and timing of the underlying exposure. 第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) Forward Market2. Non-Deliverable Forward Contractsa. New typeA non-deliverable forward contract (NDF) does not result in a

7、n actual exchange of currencies. Instead, one party makes a net payment to the other based on a market exchange rate 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 exchan

8、ge rate at the future date. 第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)An NDF can effectively hedge future foreign currency payments or receipts: NDF MarketExpect 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.

9、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 bank. 第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) Forward versus Futures Contracts Comparing currency futures contracts to currency forward contracts and shows how they are priced

10、 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(違約動(dòng)機(jī)）Eg,FX,$1.475/,當(dāng)匯率上升時(shí)，賣方有違約動(dòng)機(jī)，當(dāng)匯率下降時(shí)，買方有違約動(dòng)機(jī)。The futures contract solutionA futures exchange clearinghouse takes one side of every tr

11、ansaction (and makes sure that its exposures cancel one another)Contracts are marked-to-market daily Require initial and maintenance margins第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) Forwards versus futuresForwardsFuturesCounterpartyBankCME Clearinghouse（Forward contracts are created by commercial and investment banks

12、, whereas futures contracts are usually found on futures exchanges）MaturityNegotiated3rd week of the month (US)AmountNegotiatedStandard contract sizeFeesBid-askCommissionsCollateralNegotiatedMargin accountSettlementAt maturityMost are settled early第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)Futures exchangesFinancial fu

13、tures 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.S.)444.5CBOT - Chicago Board of Trade (U.K.)276.3Euronext - (Amsterdam, Brussels, Lisbon, Paris,

14、 London)221.3NYMEX - New York Mercantile Exchange (U.S.)107.4BM&F - Bolsa Mercadorias & de Futuros (Brazil) 95.9Source: Futures Industry Association 第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)Forwards versus futuresFutures contracts are similar to forward contractsFutures contracts are like a bundle of consecutive one-

15、day forward contracts（期貨合約是一連串可更新的1天期遠(yuǎn)期合約的組合： 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. 如三個(gè)月期的遠(yuǎn)期合約，相當(dāng)于90個(gè)可更新的1天期的遠(yuǎn)期合約Daily settlement is the biggest difference between a

16、 forward and a futures contractFutures and forwards are nearly identical in their ability to hedge risk（在規(guī)避風(fēng)險(xiǎn)管理的功能上有相似之處）第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) Hedging with futuresForward contracts can be tailored to match the underlying exposureForward contracts thus can provide a perfect hedge of transaction exp

17、osure to currency riskExchange-traded futures contracts are standardizedThey will not provide a perfect hedge if they do not match the underlying exposures Currency mismatch - there may not be a futures contract in the currency that you would like to hedgeMaturity mismatch - there may not be a futur

18、es 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 第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) Interest rate parity revisitedSome definitionsSt,Td/f = spot price at time t for

19、 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 to time t. (Ftd/f / S

20、0d/f) = (1+id)/(1+if)tIn the slide, IRP is expressed as a backward-looking relation from time t through the expiration date T（即根據(jù)IRP可以預(yù)測(cè)遠(yuǎn)期和期貨價(jià)格）Futt,Td/f = Ft,Td/f = Std/f (1+id)/(1+if)T-t STd/f (as t T)第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)Spot and futures price convergence at expiration T Forward premium FutTd/f

21、 = STd/f Fut0d/f S0d/f Futures prices converge to spot prices at expiration.第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)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 r

22、ate differentials (1+id )/(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

23、 futures hedge slightly riskier than a forward hedge（當(dāng)存在期限錯(cuò)配時(shí)，基差風(fēng)險(xiǎn)使期貨套期保值相對(duì)遠(yuǎn)期套期技術(shù)而言更有風(fēng)險(xiǎn)。）第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)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 expo

24、sure.When there is a maturity mismatch, a futures hedge cannot provide a perfect hedge against currency risk.第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)Dec 16Oct 26Mar 13-S$10millionunderlying obligationFutures expiration date following the cash flowAn example of a delta hedgetime 0time t=227/365Sept 11Futures expirati

25、on date following the cash flowtime T=278/365第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)An example 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 va

26、lues from the end of the contract through October 26.The December futures contract 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 in the United States and Singapore are i$6.24% and i

27、s$4.04%According to IRP，the forward price for exchange on October 26 is F0,t$/s$ = 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

28、,000.As we shall see, the futures hedge using the December 16 futures contract is not quite as precise.第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)An example of a delta hedge該公司利用期貨合約套期3月13日買進(jìn)12月到期的期貨合約，并在10月26日賣出該期貨合約，風(fēng)險(xiǎn)在于12月到期的期貨合約運(yùn)行到10月26日時(shí)的價(jià)格如何變化？即期貨平倉時(shí)的價(jià)格是多少？3月13日，12月到期的期貨合約價(jià)格：Fut0,T$/s$ = S0$/s$ (1+i$)/(1+is$)T (0

29、.6010)(1+6.24%)/(1+4.04%)278/365=$0.6107/s$（以此價(jià)格買入）同時(shí)，根據(jù)遠(yuǎn)期匯率預(yù)測(cè)法，10月26日的即期匯率是： ES0，t$/s$ = F0,t$/s$ =$0.6089/s$This expectation will hold 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日債務(wù)到期時(shí)，分三種情況

30、討論：第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)情況一：基差不變：basis i$-S$=6.24%-4.04%=2.20%,因此，10月26日的即期匯率不變，即St$/S$ =$0.6089/s$，在10月26日，到12月16日交割的期貨合約價(jià)格就建立在之前預(yù)期的即期匯率: St$/s$ =$0.6089/s$的基礎(chǔ)上，期限T-t27822751天： Futt,T$/s$ = St$/s$ (1+i$)/(1+is$)T-t (0.6089)(1+6.24%)/(1+4.04%)51/365=$0.6107/s$（ 以此價(jià)格賣出）Profit on futures: Futt,T$/s$

31、 - 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第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)情況二：10月26日，新加坡利率上升至： iS$=4.54%，導(dǎo)致新元匯率上升至： St$/S$ =$0.6255/S$因此，在10月26日，到12月16日交割的期貨合約價(jià)格就變?yōu)椋?Futt,T$/S$ = St$/S$ (1+i$)/(1+iS$)T-t (0.

32、6255)(1+6.24%)/(1+4.54%)51/365=$0.6269/s$（以此價(jià)格賣出）此時(shí)，公司在期貨市場(chǎng)的收益為：Profit on futures: Futt,T$/s$ - Fut0,T$/s$ =$0.6269/s$0.6107/s$=$0.0162/s$新元升值帶來的債務(wù)成本增加，即現(xiàn)貨市場(chǎng)公司損失為：Loss on underlying short position in the spot currency: -(St$/s$ - ESt$/s$ )=-($0.6255/s$- $0.6089/s$=-$0.0166/s$凈損失+0.01620.0166$0.0004/

33、s$，損失總額為：$4000（總債務(wù)支出是10百萬）損失增加是因?yàn)樾录悠吕噬仙?，基差改變所致。第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)情況三：10月26日，美元利率上升至： i$=6.74%，導(dǎo)致新元匯率貶值至： St$/s$ =$0.5774/s$因此，在10月26日，到12月16日交割的期貨合約價(jià)格就變?yōu)椋?Futt,T$/s$ = St$/s$ (1+i$)/(1+is$)T-t (0.5774)(1+6.74%)/(1+4.04%)51/365=$0.5795/s$（以此價(jià)格賣出）此時(shí)，公司在期貨市場(chǎng)的損失為：Profit on futures: Futt,T$/s$ - Fu

34、t0,T$/s$ =$0.5795/s$-$0.6107/s$ =$0.0312/s$由于新元貶值，公司債務(wù)成本節(jié)約，即公司收益為：Loss on underlying short position in the spot currency: -(St$/s$ - ESt$/s$ )=-($0.5774/s$- $0.6089/s$=+$0.0315/s$凈收益 $0.0312/s$ +$0.0315/s$ +$0.0003/s$，收益總額為：$3000所得增加是因?yàn)樾录悠吕噬仙?，基差改變所致。但總的來講，futures contracts can provide very good hed

35、ge, because basis risk is small relative to currency risk. 第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng) 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 Futures Hedge: 是指保值者持有期貨合約的頭寸規(guī)模與需

36、要保值的基礎(chǔ)資產(chǎn)之間的比率。 The hedge ratio is used to minimize the variance of the hedged position.即期匯率變化率與期貨匯率變化率的關(guān)系如下：std/f = a + 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-Futt-1d/f)/Futt-1d/f Thi

37、s 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第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)futtd/fstd/f第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)NFut*=(Amount in futures)/(Amount exposed) =-b （通過歷史數(shù)據(jù)對(duì)上式回歸可

38、以得出b ）Hedge quality （對(duì)沖質(zhì)量）is measured by the r-square (r2 = rs,fut2). r2 (or 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）之間Contract size mism

39、atch and the Hedge Ratio第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)Contract size mismatch and the Hedge Ratio假設(shè)b1.025，則期貨套期保值比率： NFut*=(Amount in futures)/(Amount exposed) =-b -1.025 Amount in futures （-1.025）（ Amount exposed）如上例中，該公式有1000萬新元的空頭，需要持有的期貨多頭為 Amount in futures （-1.025）（ -10000000） s$10,250,000芝加哥商品期貨交易所一份

40、新元期貨合約金額為125,000，所以，持有期貨合約的規(guī)模為82 份期貨合約:10,250,000/125,000=82第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)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

41、+ b futt$/ + et , you estimate 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?第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)The Hedge Ratio solutionThe

42、 optimal hedge ratio 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第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)Currency mismatches and cross hedgesA cr

43、oss hedge is used when there is a maturity match but a currency mismatch即選擇的期貨避險(xiǎn)合約標(biāo)的商品與現(xiàn)貨商品不同，市場(chǎng)上沒有類似現(xiàn)貨所發(fā)行的期貨來避險(xiǎn)時(shí)，就要找另一個(gè)現(xiàn)貨價(jià)格有正相關(guān)，或者是同質(zhì)的產(chǎn)品來避險(xiǎn)。例如，一家英國公司有加元債務(wù)，可以利用美元期貨的多頭來規(guī)避匯率風(fēng)險(xiǎn)，因?yàn)?，美元與加元是高度相關(guān)的。為加元債務(wù)避險(xiǎn)的美元套期保值法：加元債務(wù)的現(xiàn)貨價(jià)格變化率與美元期貨價(jià)格變化率的關(guān)系如下： st/c$ = a + b futt/$+ et當(dāng)二者的期限匹配時(shí)，上式可變化為：std/f1 = a + b std/f2 +

44、etf1 = currency in which the underlying exposure is denominatedf2 = currency used to hedge against the underlying exposure （由前面的公式轉(zhuǎn)化而來，由即期匯率變化率替代期貨匯率變化率是因?yàn)槠谪浀狡跁r(shí)的價(jià)格與即期匯率具有趨同性。）第講用于匯率風(fēng)險(xiǎn)管理衍生產(chǎn)品貨幣期貨和期貨市場(chǎng)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 on changes in futures prices (futtd/f). In the cross hedge, std/f2 is substituted for the indepe