第2讲用于汇率风险管理的衍生产品：货币期货与期货市场

Chapter 2Derivative Securities for Currency Risk ManagementCurrency Futures and Futures MarketsChapter Overviewn 1 Financial Futures Exchangesn 2 The Operation of Futures Marketsn 3 Futures Contractsn 4 Forward versus Futures Market Hedgesn 5 Futures Hedges Using Cross Exchange Ratesn 6 Hedging with Currency FuturesChapter Objectivesn 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 n The last several sections discuss implementation issues:- Delta hedges for maturity mismatches- Cross hedges for currency mismatches- Delta-cross hedges for currency and maturity mismatchesForward Market1. Forward ContractsA 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 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 exactly offsets the size and timing of the underlying exposure. Forward Market2. Non-Deliverable Forward Contractsa. New typen 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 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. n 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.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. Forward versus Futures Contractsn Comparing currency futures contracts to currency forward contracts and shows how they are priced by the marketplace. n Forwards are a pure credit instrumentqWhichever 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。n The futures contract solutionqA futures exchange clearinghouse takes one side of every transaction (and makes sure that its exposures cancel one another)qContracts are marked-to-market daily qRequire initial and maintenance marginsForwards versus futuresForwards FuturesCounterparty Bank CME Clearinghouse（ Forward contracts are created by commercial and investment banks, whereas futures contracts are usually found on futures exchanges）Maturity Negotiated 3rd week of the month (US)Amount Negotiated Standard contract sizeFees Bid-ask CommissionsCollateral Negotiated Margin accountSettlement At maturity Most are settled earlyFutures exchangesn Financial 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.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 Forwards versus futuresn Futures contracts are similar to forward contractsq 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q Daily settlement is the biggest difference between a forward and a futures contractn 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 futuresn Forward contracts can be tailored to match the underlying exposureForward contracts thus can provide a perfect hedge of transaction exposure to currency riskn Exchange-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 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 Interest rate parity revisitedn Some definitionsSt,Td/f = 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 Tn Forward and futures prices are equal through interest rate parityn Interest rate parity is usually expressed as a forward-looking relation from time zero to time t.(Ftd/f / S0d/f) = (1+id)/(1+if)tn 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）Futt,Td/f = Ft,Td/f = Std/f (1+id)/(1+if)T-t STd/f (as t T)Spot and futures price convergence at expirationT Forward premium FutTd/f = STd/f Fut0d/f S0d/f Futures prices converge to spot prices at expiration.Maturity mismatches and basis riskn If there is a maturity mismatch, futures contracts may not provide a perfect hedgen Because the convergence of futures prices to spot prices is nearly linear, interest rate differentials (1+id )/(1+if ) are often approximated by the simple difference in nominal interest rates, (id-if). n The difference (id-if) is called the basisq The risk of change in the relation between futures and spot prices is called basis riskq 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 hedgesn 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.n When there is a maturity mismatch, a futures hedge cannot provide a perfect hedge against currency risk.Dec 16Oct 26Mar 13-S$10millionunderlying obligationFutures expiration date following the cash flowAn example of a delta hedgetime 0 time t=227/365Sept 11Futures expiration date following the cash flowtime T=278/365An example of a delta hedgen There are 227days between March 13 and October 26.n A hedge with the futures contract expires on September 11 only hedges against currency risk through that date. It remains exposed to changes in currency values from the end of the contract through October 26.n The December futures contract is a better choice because it can hedge currency risk through October 26 and then be sold.n Suppose the spot rate is S0$/s$ $0.6010/s$ on March 13, Annual interest rate in the United States and Singapore are i$ 6.24% and is$ 4.04%n 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=$0.6089/s$n 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)=$6,089,000.As we shall see, the futures hedge using the December 16 futures contract is not quite as precise.An example of a delta hedgen 该公司利用期货合约套期 3 月 13日 买进 12月到期的期货合约，并在 10月 26日卖出该期货合约，风险在于 12月到期的期货合约运行到10月 26日时的价格如何变化？即期货平仓时的价格是多少？n 3月 13日， 12月到期的期货合约价格：Fut0,T$/s$ = S0$/s$ (1+i$)/(1+is$)T (0.6010)(1+6.24%)/(1+4.04%) 278/365=$0.6107/s$（以此价格买入）n 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 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 T-t 278 227 51天：Futt,T$/s$ = St$/s$ (1+i$)/(1+is$)T-t (0.6089)(1+6.24%)/(1+4.04%) 51/365=$0.6107/s$（ 以此价格卖出）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情况二： 10月 26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=$0.6269/s$（以此价格卖出）此时，公司在期货市场的收益为：Profit on futures: Futt,T$/s$ - Fut0,T$/s$ =$0.6269/s$ $0.6107/s$=$0.0162/s$新元升值带来的债务成本增加，即现货市场公司损失为：Loss on underlying short position in the spot currency:-(St$/s$ - ESt$/s$ )=-($0.6255/s$- $0.6089/s$=-$0.0166/s$净损失 +0.0162 0.0166 $0.0004/s$，损失总额为： $4000（总债务支出是 10百万）损失增加是因为新加坡利率上升，基差改变所致。情况三： 10月 26日，美元利率上升至： i$=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+4.04%) 51/365=$0.5795/s$（以此价格卖出）此时，公司在期货市场的损失为：Profit on futures: Futt,T$/s$ - Fut0,T$/s$ =$0.5795/s$-$0.6107/s$= $0.0312/s$由于新元贬值，公司债务成本节约，即公司收益为：Loss on underlying short position in the spot currency:-(St$/s$ - ESt$/s$ )=-($0.5774/s$- $0.6089/s$=+$0.0315/s$净收益 $0.0312/s$ +$0.0315/s$ +$0.0003/s$，收益总额为： $3000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 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: 是指保值者持有期货合约的头寸规模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 + 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 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 pricesn futtd/fstd/fNFut*=(Amount in futures)/(Amount exposed) =-b （通过历史数据对上式回归可以得出 b ）n Hedge quality （对冲质量） 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）之间Contract size mismatch and the Hedge RatioContract size mismatch and the Hedge Ratio假设 b 1.025，则期货套期保值比率：NFut*=(Amount in futures)/(Amount exposed) =-b -1.025 Amount in futures （ -1.025）（ Amount exposed）如上例中，该公式有 1000万新元的空头，需要持有的期货多头为Amount in futures （ -1.025） （ -10000000） s$10,250,000芝加哥商品期货交易所一份新元期货合约金额为 125,000，所以，持有期货合约的规模为82 份期货合约 :10,250,000/125,000=82An example of a Hedge Ration It is now January 8. You need to hedge a 100 million obligation due on June 3. q The spot exchange rate is S0$/ = $1.10/q A 100,000 CME euro futures contract expires on June 16q Based on st$/ = a + 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. )q How many CME futures contracts should you