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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Chapter 2,Derivative Securities for Currency Risk Management,Currency Futures and Futures Markets,Chapter Overview,1,Financial Futures Exchanges,2,The Operation of Futures Markets,3,Futures Contracts,4,Forward versus Futures Market Hedges,5,Futures Hedges Using Cross Exchange Rates,6,Hedging with Currency Futures,Chapter Objectives,This 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 implementation issues:,Delta hedges for maturity mismatches,Cross hedges for currency mismatches,Delta-cross hedges for currency and maturity mismatches,Forward Market,1. Forward Contracts,A forward contract,is an agreement between,a corporation 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 which they can purchase or sell a particular foreign currency.,A forward hedge of the dollar,Underlying position of a,French exporter (long $s),Sell $s forward at F,t,/$,(short $s and long,s),Net position,+,$,40 million,+,40 million,-,$,40 million,+,40 million,-Goods,v,/$,Long $s,s,/$,Short $s,The forward contract provides,a perfect hedge because,the,size and timing,of the,hedge transaction exactly,offsets the size and timing,of the underlying exposure.,Forward Market,2. Non-Deliverable Forward Contracts,a. New type,A,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 rate on the day of settlement.,b. Frequently used for currency in emerging markets,c. No delivery required,d. One party to the agreement makes a payment to the other party based on the exchange rate at the future date.,An NDF can effectively hedge future foreign currency payments or receipts:,NDF Market,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 1,Buy 100M Chilean pesos from market.,July 1,Index = $.0023/peso,receive $30,000 from bank due to NDF.,Index = $.0018/peso,pay $20,000 to bank.,Forward versus Futures C,ontracts,Comparing,currency futures contracts,to,currency forward contracts,and shows how they are priced by the marketplace.,Forwards are a pure credit instrument,Whichever way the price of the spot rate of exchange moves, one party always has an,incentive to default(,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 solution,A 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,Forwards versus futures,Forwards,Futures,Counterparty,BankCME,Clearinghouse,（Forward contracts are created by commercial and investment banks, whereas futures contracts are usually found on futures exchanges）,Maturity,Negotiated3rd week of the month (US),Amount,NegotiatedStandard contract size,Fees,Bid-askCommissions,Collateral,NegotiatedMargin account,Settlement,At maturityMost are settled early,Futures exchanges,Financial futures exchanges are usually associated with a commodity futures exchange,2002 volume,Top 5 futures exchanges,(million contracts),Eurex,- Eurex (Germany & Switzerland),536.0,CME,-,Chicago Mercantile Exchange,(U.S.),444.5,CBOT,-,Chicago Board of Trade,(U.K.),276.3,Euronext,- (Amsterdam, Brussels, Lisbon, Paris, London),221.3,NYMEX,- New York Mercantile Exchange (U.S.),107.4,BM&F,- Bolsa Mercadorias & de Futuros (Brazil),95.9,Source: Futures Industry Association,Forwards versus futures,Futures contracts are similar to forward contracts,Futures 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个可更新的1天期的远期合约,Daily settlement,is the biggest difference between a forward and a futures contract,Futures 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）,Hedging with futures,Forward contracts can,be tailored,to,match,the,underlying exposure,Forward contracts thus can provide a perfect hedge of transaction exposure to currency risk,Exchange-traded futures contracts are standardized,They 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 hedge,Maturity mismatch,- there may not be a futures contract expiring on the same day as your underlying transaction exposure,Contract size mismatch,- the underlying transaction exposure may not be an even increment of existing futures contracts,Interest rate parity revisited,Some definitions,S,t,T,d/f,= spot price at time t for expiry at time T,F,t,T,d/f,= forward price at time t for expiry at time T,Fut,t,T,d/f,= futures price at time t for expiry at time T,Forward and futures prices are equal through interest rate parity,Interest rate parity is usually expressed as a,forward-looking relation,from time zero to time t.,(F,t,d/f,/ S,0,d/f,) = (1+i,d,)/(1+i,f,),t,In 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）,Fut,t,T,d/f,= F,t,T,d/f,= S,t,d/f,(1+i,d,)/(1+i,f,),T,-,t, S,T,d/f,(as t T),Spot and futures price convergence at expiration,T,Forward,premium,Fut,T,d/f,= S,T,d/f,Fut,0,d/f,S,0,d/f,Futures prices converge to spot prices at expiration.,Maturity mismatches and basis risk,If there is a,maturity mismatch,futures contracts may not provide a perfect hedge,Because the convergence of futures prices to spot prices is nearly linear, interest rate differentials (1+i,d,)/(1+i,f,) are often approximated by the simple difference in nominal interest rates, (i,d,-i,f,).,The difference (i,d,-i,f,) is called the,basis,The risk of change in the relation between futures and spot prices is called,basis risk,When there is a maturity mismatch, basis risk makes a futures hedge slightly riskier 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。）,Maturity mismatches and,Delta hedges,Futures 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 hedge cannot provide a perfect hedge against currency risk.,Dec 16,Oct 26,Mar 13,-S$10million,underlying obligation,Futures expiration date following the cash flow,An example of a delta hedge,time 0,time t=227/365,Sept 11,Futures expiration date following the cash flow,time T=278/365,An example of a delta hedge,There are 227days between March 13 and October 26.,A hedge with the futures contract expires on September 11 only hedges against currency risk through that date. It remains exposed to changes in currency values from the end of the contract through October 26.,The December futures contract is a better choice because it can hedge currency risk through October 26 and then be sold.,Suppose the spot rate is,S,0,$/s$,$0.6010/s$ on March 13, Annual interest rate int the United States and Singapore are i,$,6.24% and i,s$,4.04%,According to IRP，the forward price for exchange on October 26 is,F,0,t,$/s$,= S,0,$/s$,(1+i,$,)/(1+i,s$,),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)=$6,089,000.,As we shall see, the futures hedge using the December 16 futures contract is not quite as precise.,An example of a delta hedge,该公司利用期货合约套期3月13日,买进12月到期的期货合约，并在10月26日卖出该期货合约，风险在于12月到期的期货合约运行到10月26日时的价格如何变化？,12月到期的期货合约价格：,Fut,0,T,$/s$,= S,0,$/s$,(1+i,$,)/(1+i,s$,),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：,E,S,0，t,$/s$,=,F,0,t,$/s$,=,$0.6089/s$,This expectation will hold only if interest rates,(1+i,$,)/(1+i,S$,)=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,S,t,$/S$,=,$0.6089/s$，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:,S,t,$/s$,=,$0.6089/s$,的基础上，期限T-t27822751天：,Fut,t,T,$/s$,= S,t,$/s$,(1+i,$,)/(1+i,s$,),T-t, (,0.6089)(1+6.24%)/(1+4.04%),51/365,=$0.6107/s$,Profit on futures:,Fut,t,T,$/s$,- Fut,0,T,$/s$,=,=$0.6107/s$-$0.6107/s$=0,Profit on underlying short position in the spot currency:,-(,S,t,$/s$,-,E,S,t,$/s$,),=-(,=,$0.6089/s$- $0.6089/s$=0,An example of a delta hedge,情况二：10月26日，新加坡利率上升至：,i,S$,=4.54%，导致,新元汇率上升至：,S,t,$/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：,Fut,t,T,$/S$,= S,t,$/S$,(1+i,$,)/(1+i,S$,),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:,Fut,t,T,$/s$,- Fut,0,T,$/s$,=$0.6269/s$-$0.6107/s$=$0.0162/s$,Loss on underlying short position in the spot currency:,-(,S,t,$/s$,-,E,S,t,$/s$,),=-($0.6255/s$- $0.6089/s$=-$0.0166/s$,净损益+0.01620.0166$0.0004/s$，损失总额为：$4000（总债务支出是10百万）,损失增加是因为新加坡利率上升，基差改变所致。,An example of a delta hedge,情况三：10月26日，美元利率上升至：,i,$,=6.74%，导致,新元汇率贬值至：,S,t,$/s$,=,$0.5774/s$,因此，在10月26日，到12月16日交割的期货合约价格就变为：,Fut,t,T,$/s$,= S,t,$/s$,(1+i,$,)/(1+i,s$,),T-t, (,0.5774)(1+6.74%)/(1+4.04%),51/365,=$0.5795/s$,此时，公司在期货与现货的损益：,Profit on futures:,Fut,t,T,$/s$,- Fut,0,T,$/s$,=$0.5795/s$-$0.6107/s$,=$0.0312/s$,Loss on underlying short position in the spot currency:,-(,S,t,$/s$,-,E,S,t,$/s$,),=-(,=,$0.5774/s$- $0.6089/s$=+$0.0315/s$,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。,但总的来讲，futures contracts can provide very good hedge, because basis risk is small relative to currency risk.,Contract size mismatch,and,the Hedge Ratio,The Forward Hedge: The hedge ratio N,F,*,of a future position is defined as,N,F,*,=Amount in forward position/Amount exposed to currency risk=-1,The Futures 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：,s,t,d/f,=,a,+,b,fut,t,d/f,+ e,t,s,t,d/f,=percentage change in the spot rate,fut,t,d/f,=percentage change in the futures price,s,t,d/f,= (S,t,d/f,-S,t-1,d/f,)/S,t-1,d/f,and fut,t,d/f,= (Fut,t,d/f,-Fut,t-1,d/f,)/Fut,t-1,d/f,This regression is designed to estimate basis risk over the maturity of a proposed hedge.,The slope coefficient,b,=,r,s,fut,(,s,s,/,s,fut,) measures the sensitivity of spot to futures prices,fut,t,d/f,s,t,d/f,N,Fut,*=(Amount in futures)/(Amount exposed) =,-,b,（通过历史数据对上式回归可以得出,b,）,Hedge quality （对冲质量）is measured by the r-square (r,2,=,r,s,fut,2,).,r,2,(or,r,s,fut,2,) measures the percentage variation in s,t,d/f,explained by variation in,fut,t,d/f,.,High r,2,low basis risk and a high-quality hedge.,Low r,2, high,basis risk and a relatively poor hedge.,r-square,取值在（,0,，,1,）之间,Contract size mismatch,and,the Hedge Ratio,Contract size mismatch,and,the Hedge Ratio,假设,b1.025，则期货套期保值比率：,N,Fut,*=(Amount in futures)/(Amount exposed) =,-,b,-1.025,Amount in futures （-1.025）（ Amount exposed）,如上例中，该公式有100万新元的空头，需要持有的期货多头为,Amount in futures （-1.025）,（ -10000000）,s$10,250,000,芝加哥商品期货交易所一份新元期货合约金额为125,000，所以，持有期货合约的规模为82 份期货合约:10,250,000/125,000=82,An example of,a Hedge Ratio,It is now,January 8,.,You need to hedge a,100 million,obligation due on,June 3,.,The spot exchange rate is,S,0,$/,= $1.10/,A,100,000,CME euro futures contract expires on,June 16,Based on s,t,$/,=,a,+,b,fut,t,$/,+ e,t, you estimate,b,= 1.020,with,r,2,= 0.95.(,The relatively high r,2,(0.95) of this regression means that this is a relatively high quality hedge.,),How many CME futures contracts should you buy to minimize the risk of your hedged position?,The,Hedge Ratio,solution,The optimal hedge ratio for this delta hedge is given by,N,Fut,*,=(,amount in futures,)/(amount exposed),= -,b,(,amount in futures,) = (-,b,)(amount exposed),= (-1.020)(-100 million) =,102 million,or (102 million) / (100,000/contract),=,1,020 contracts,Currency mismatches and cross hedges,A,cross hedge,is used when there is a maturity match but a,currency mismatch,即选择的期货避险合约标的商品与现货商品不同，市场上没有类似现货所发行的期货来避险时，就要找另一个现货价格有正相关，或者是同质的产品来避险。,例如，一家英国公司有加元债务，可以利用美元期货的多头来规避汇率风险，因为，美元与加元是高度相关的。为加元债务避险的美元套期保值法：加元债务的现货价格变化率与美元期货价格变化率的关系如下：,s,t,/,c$,=,a,+,b,fut,t,/,$,+,e,t,当二者的期限匹配时，上式可变化为：,s,t,d/,f1,=,a,+,b,s,t,d/,f2,+,e,t,f,1,= currency in which the underlying exposure is denominated,f,2,= 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。）,In this case, the currency of the underlying exposure (f,1,) is different from the currency of the futures contract (f,2,).,In the delta hedge, spot rate changes (s,t,d/f,) were regressed on changes in futures prices (,fut,t,d/f,).,In the cross hedge, s,t,d/f2,is substituted for the independent variable fut,t,d/f2,because,the maturity of the futures contract is the same as that of the underlying transaction in the spot market, and,futures prices converge to spot prices at maturity.,An example of a CME,cross hedge,It 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,$1.00/,.,A CME futures contract expires on,June 16,with a contract size of,100,000,In this cross hedge, there is a maturity match but a currency mismatch.,Based on,s,t,$/DKr,=,a,+,b,s,t,$/,+ e,t, you estimate,b,= 1.040,with,r,2,=,0.89,.,How many CME futures contracts,should you buy to minimize the risk of your hedged position?,The cross hedge solution,Optimal hedge ratio:,N,Fut,*,= (,amt in futures,)/(amt exposed) = -,b,(,amt in futures,) = (-,b,)(amt exposed),= (-1.040)(-DKr100 million) =,DKr104 million,or,78 million,at (DKr104m) (0.75/DKr),or,780 contracts,.,With an r-square of 0.89, this is a fairly high quality hedge.,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 currency and a maturity mismatch,s,t,d/,f1,=,a,+,b,fut,t,d/,f2,+,e,t,2.If the underlying exposure and the futures contracts are in the same currency, then f,1,= f,2,= 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.,s,t,d/,f,=,a,+,b,s,t,d/,f,+,e,t,由于,s,t,d/,f,=的相关系数为+1，所以，是完全套期保值（r,2,=1），套期保值比率为,N,Fut,*=,-,b1，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.,A classification of futures hedges,
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