Class Note for FINOPMGT 413 at UMass(2)
Class Note for FINOPMGT 413 at UMass(2)
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Date Created: 02/06/15
Week 3 The Foreign Exchange Markets Spot quotes bidask Spreads triangular arbitrage Forward rates FINOPMGT 413 Spot and Forward Markets Foreign exchange trading occurs in two separate but connected markets Spot and the Forward market Spot market Buying and selling of fX with settlement in 2 business days from today Forward market Settlement occurs at some future date That is you may enter into a forward contract to buy 10 million Yen 90 days from today FINOPMGT 413 FX Rate Quotes We can View FX rates as quotes in director indirect terms Direct a direct fX quote is in units of domestic currency per unit of foreign currency DCF C For exam le a Auote of the USDBritish Pound is direct for the US ifit is quoted as 19631USBP Indirect an indirect fX quote is in units of foreign currency per unit of domestic currency FCDC Example 10686 YenUSS is an indirect quote for the US but direct quote for the Yen We will interpret every quote as being direct DCFC Therefore we will always think of whichever country is in the denominator as being the foreign country Please always remember this convention FINOPMGT 413 AppreciationDepreciation A currency is said to appreciate depreciate against a foreign currency if you can buy more less foreign currency per unit of domestic currency Examples The WSJ reported the following on Wednesday Yesterday afternoon in New York the euro was at 14635 om 14827 late Monday The Euro buys less dollars on ruesaay as opposed to Monday therefore the Euro depreciated and the appreciated If the Yen rate changed from 10686 Yen to 10674 Y has the Yen appreciated or depreciated Answer Depreciated When the currency is quoted in direct terms then an increase decrease in the quote is an appreciation depreciation of the foreign currency When its quoted in indirect terms then an increase in the rate is an appreciation of the domestic currency FINOPMGT 413 Cross Rates The cross rate is the exchange rate for converting one foreign currency to another For example the rate for YenBP would be a called a cross rate If we know the exchange rate for USYen and USBP we can easily calculate the cross rate Example Friday Sept 14 2007 USBP20068 YenUS 11530 USEuro13878 What is the YenBP cross rate Answer 23138 YenBF What is the EuroBP cross rate Answer 14460 EuroBP Qt Given the rates of the previous week diu L115 1 en appreciate or depreciate against the BP FINOPMGT 413 Arbitraging Cross Rates 12 Suppose a bank quotes you the following rates USBP 18193 YenUS 11027 and 199 YenBP The implied YenBP cross rate from the BP Yen quotes is 20061 YenBP If the implied Cross rate uoes IlUL equal the quoted cross rate there there exists an arbitrage opportunity in this case the arbitrage opportunity has a speci c name triangular arbitrage How would you actually implement such an arbitrage Buy low sell high In other words you buy the currency Where it is cheaper and sell Where it is more expensive FINOPMGT 413 Arbitraginu Cross Rates 12 The Yen is cheaper at 20061 YBP and more expensive at 199 YenBP So you buy Yen 20061 sell BP and sell Yen 199 buy BP How do you implement the arbitrage trade You simultaneously make the following trades Buy Yen for US 11027 Sell Yen for BP 199 Sell BP for US 18193 US 1 gt 11027 Yen 11027Yen Yen 11027 gt 11027199 05541 BP199 YenBP BP 05541gt 10081 US 18193BP You make gains of 8100 for every 1 million in capital FINOPMGT 413 Summarizing Steps in Triangular Arbitrage Assume that the three currencies are the USS and two other foreign currencies and that you want to make your arbitrage in US 31gt 1 Identify the weaker nonUS currency between implied cross rate and quoted cross rate Yen is weaker at imA lied cross rate of 20061 YenBP as comA ared with actual quote of 199 YenBP 2 Buy the weak currency low Buy Yen 11027 YUS 1 gt 11027 Yen 3 Sell the currency you bought in 2 high at the crossrate to buy the other currency cheap Sell Yen 199 YenBP 11027 Yen gt05541BP 4 Sell the currency high to buy the US cheap Sell BP 18193 USBP 05541 BP gt 10081 FINOPMGT 413 BidAsk Spreads As the dealer who trades foreign currency with J ou has to make money there is a bidask spread associated with the quote ie the price for buying the foreign currency is different from the price fOl selling ulC currency Bid the price at which the dealer is willing to buy the foreign currency Ask or Offer the price at which the dealer is willing to sell the foreign currency FINOPMGT 413 Examples of BidAsk Spreads BPUS 1822018229 BP The quote of 18220 is the bid or the price at which the dealer will buy the BP foreign currency and 18229 is the ask price Qt On a 1000000 roundtrip transaction with the BF What is the cost that you incur because of the bidask spread on BP Ans 494 FINOPMGT 413 BidAsk Rates and indirect Quotes Suppose the rate is quoted in indirect terms What is the bid ask Example YenUSD 10766 10772 We have to be careful of how the currency is quoted to gure out the bid and ask using the principle that the dealer will buy foreign currency low and sell FC high Thus the dealer will buy bid Yen at 10772 and sell offer at 107 66 and the dealer will buy USD at 107 66 and sell at 10772 If the currency is quoted in direct indirect then the lower higher number is the bid A word of warning Its easy to get confused unless you always use one convention FINOPMGT 413 BidAsk and Cross Rates 12 Suppose a US bank quotes 1701936 BP and 0985067 Euro What would be the cross rate for EuroBP in Frankfurt In Frankfurt the dealer will buy BP at the lower rate and sell BP at a higher rate in terms of the Euro So the cross rate will re ect this Bid the dealer buys BP at 17 019 lower price bid and sells Euro at 09867 hivher 1 rice ask l701909867l7250 EuroBP FINOPMGT 413 BidAsk and Cross Rates 22 Similarly to get the offer rate the dealer will sell BP at the higher rate in terms of Euro So Dealer sells BP for USD at offer or ask rate of US17036BP and buys Euro at bid rate of 09850 So the offer rate for EuroBP is l7036O9850l7295 bum1511 Therefore the cross rate is 1725017295 EuroBF FINOPMGT 413 Triangular Arbitrage with BidAsk Spreads 12 1 1701936 BP 2 0985067Eur0 3 1720017300 EuroBP The implied cross rate is 1724895 EuroBP Does this constitute a triangular arbitrage FINOPMGT 413 Triangular Arbitrage with BidAsk Spreads 22 For there to be a triangular arbitrage J ou have to be able to buy low and sell high Dealer 1 implied cross rate 1724895 Dealer 2 1720017300 Can you buy the BP low and sell it high No Because one dealer sells you BP 17290 while the second buys 17200 You cannot reverse the transaction also because the second dealer will sell you at 173 00 and the rst dealer buys at 17248 In each cas J Vu lose money Qt Can you give examples of a quote that would allow for arbitrage Provide two examples one where the BP is priced too low and one where it is priced too high FINOPMGT 413 Forward Rate Basics 12 What is ad orwara rate agreement The forward exchange contract is an agreement to exchange currencies in the future at a xed exchange rate How does one determine the forward exchange rate Answer by the basic pricing principle that the forward exchange rate should be such that it does not allow for arbitrage FINOPMGT 413 B381po According to he WSJ on 262008 the spot for the Japanese Yen was at 10686 the 3 month forward was at 10624 the 6month forward at 10576 Thus the Yen traded at a premium was stronger in the futures market Does the futures prices indicate that the market expects the Yen to appreciate over the next year FINOPMGT 413 What determines the Forward Rate Expectations 10 n0t determine tne Iorward excnange rate It does not matter that people think or feel that the currency is going to depreciate or appreciate What determines the forward exchange rate The forward exchange rate only depends on the relative interest rates FINOPMGT 413 The Forward Exchange Rate The forward exchange rate only depends on the relative interest rates Here are the Eurocurrency interest rates as of 262008 from the C a June Eurodollar 243 June Euroyen 067 We shall see that the Yen forward is at a premium to the s ot Yen is stron er because the interest rates in Yen are lower that the interest rates in US FINOPMGT 413 An example to motivate the pricing of the forward future Suppose as an importer of Japanese goods you need to make a payment in Yen exactly one year from today However you don t want to take any exchange rate risk how can you eliminate exchange risk W ave V options 1 Enter into a forward contract today this will guarantee you an exchange rate of F where F is the forward exchange rate 2 Buy Yen today at the spot rate S and hold the Yen until you need it in the future FINOPMGT 413 Determining the forward rate Which option will you prefer Answer you should be indifferent between the two because if they are priced such that you prefer one over the other ou can make an arbitra e rofit Consider the rst option when you enter into a forward contract today at F Y If you start off with 1 today then this will guarantee you 11 rUS F YenU SD This assumes that you invest your 1 in an US bank and earn the US interest rate FINOPMGT 413 The Forward Rate when Exchange Rat are Vluoted in Direct Terms It is important to note the units is it DCFC or FCDC Suppose the rate is quoted in direct terms Yen Then the 1year forward price would be F Sl rUSl rJP Yen In general for n days when we use the Eurocurrency 1ntereSI rates F S1 rUS n360 1 rJP n360 We will use the notation that represents the interest rate in the foreign currency so that we can also write F S1 rn360 1 1 quot n360 FINOPMGT 413 CME Eurocurency Quotes Note The C 4 quotes the interest rate contracts as lOOr Where r is the interest rate If the December Eurodollar rate is 243 the futures contract will be quoted at 100 243 9757 Thus to get the interest rate from the futures contract price subtract the futures price from 100 If the futures price is 95285 then uic interest laLC 1s 100952854715 FINOPMGT 413 Pricing the Currency Future The spot on 262008 is 10657 YenUS The June Euroyen contract is at 9933 and the June Eurodollar contract is at 9757 From the price of the futures contract the interest rates are US interest rate 100 97570243 Yen interest rate 100 99330 067 What would be the price of the June 08 Yen futures contract The contract expires on the second business day before the third Wed of the month Thus the expiration date is June 16 Therefore there are 131 calendar days left to expiration The June Futures price is computed as F 10657100067 X1313601 00243 X131360 10589 Yen FINOPMGT 413 An approximation for the forward premium Suppose n360 1year Then with some algebraic manipulation we can write the forward premium as where F S are quoted in direct terms F SS r rl r For low levels of interest rates we can approximate this as FSS r r That is the oneyear forward premium is approximately equal to the difference in interest rates If the forward is Auotes for n da s we can annualize it 360nFSS r r Thus if the Japanese interest rates are 2 lower than US interest rates then the 1year Yen forward will be approximately at a premium of 2 over the spot FINOPMGT 413 Forward PremiumDiscount If F gtS then we say that the foreivn currencd is tradinv at a premium F lt S then we say that the foreign currency is trading at a discount Note that F gtS F lt5 also implies that rgtr rltr FINOPMGT 413 Forward Contracts and Arbitrage in the MOIIUy Markets If the forward contract is not correctly 1 riced then J ou may be able to make arbitrage pro ts from this this is called covered interest arbitrage FINOPMGT 413 Covered Interest Arbitrage You have the following data 90 day interest rates 1 BP r 420430 lendingborrowing rates 2 Dollar r 17 01 85 lendingborrowing rates Exchange Rates Spot S 1520015300 BP 90 day forward F 1515015200 BP Is there an arbitrage FINOPMGT 413 The Mechanics of the Arbitrage 1 Borrow 1US at 185 for three months so you need to repay 1 0018590360 1004625 after three months 2 Buy BP at offer price to get ll53 06536 BP 3 Lend BP for three months at lending rate of 420 so at end of three months you have 065361 0042903600660458 BP 4 Sell BP 0660458 in the forward market at bid of 1515BP to get 1000593 Net gain 100059310045 lt 0 So there is no arbitrage Now construct an exam lgptghdelmonstrate an arbitrage Summarizing the conditions for absence of arbitrage To ensure that there is no arbitrage in either direction it must be that 1 FbidSask1 rl n3601rb n360 lt 1 2 SbidFask1rl n3601 rb n360 lt 1 Note tha 1 represents the lending interest rate and b represents the borrowing interest rate FINOPMGT 413 L reat1ng a synthet1c Interest rate By borrowinglending in a currency and then hedging your exposure with a forward contract can effectively allow you to get different effective interest rates The synthetic net cost of lending or borrowing can be quickly calculated precisely in the following manner We can rewrite the relation between F S r and r as follows 1 FSSl r 1 r 0r 1 swap points Sl r l r So r synthetic l FSSlrl Note that you again have to be careful of bidask borrowinglending rates FINOPMGT 413 Forward Quotation in terms of Swap Spreads Often the forward market luotation is 1 rovided in terms of a swap spread FS A swap is an exchange in this case it is an exchange of the spot for the forward or Vice versa Example Spot Yen 0007540Yen 6 Month Swap Rate 000020 premium Forward 0007 5400000200007 740 The foreign currency Yen is quoted at a premium FINOPMGT 413 Swap Rate with BidASK bpreads Suppose the spot for the BP is quoted at 15235 15340BP with the one month swap spread at 0004100039 and the three month swap spread at 0011400119 How do we get the bidask spread for the forward We use the rule that the bidask spreads should increase in the forward market So we subtract the swap spread if the bid is higher than the offer and add if the bid is lower than the offer Thus one month forward 1519415301 and the three month forwar i 44915459 FINOPMGT 413 Using Futures How many contracts 14 Suppose you need to make a payment of 100000000 Yen in a few days Today you decide to hedge against exchange rate risk by buying futures contract on the C 4 Qt how many contracts will you buy You look up the product specifications on the C a and nd that each futures contact is equal to 122500000 Yn So you need to buy 100 1258 contracts FINOPMGT 413 Using Futures Marking to market 24 The futures contact is market to market on a daily basis Thus if have to book any gains or loss at settlement on a daily basis Suppose the futures price ncreases by 36 from the previous day Recall that the Yen contract is quoted in 1 1000000 so that the change in the price is equal to 0000036 How much do you gain per contract For each 1 0000001 change in the contract the value of the contract changes by 12500000X00000011250 Thus for a change of 3 6 the value of the contract chan es b 450 In this case as the value of the futures increases the Yen appreciates you make 450 per contract FINOPMGT 413 Using Futures The hedge 34 The Yen futures on Monday Tue and Wed settles at 8110 8146 8155 You own 8 contracts On Tuesday you make 450 X 8 3600 On Wed you make 1125u A o 900 Suppose the futures matures also on Wed so you take delivery of the 12500000 X 8 100000000 Yen at the rate of 0008155Yen You pay 815500 for the Yen What is the net rate you get Your total net cash ow is 125000003600 900811000 As expected the net rate you get for your 100 million Yen is 0008110Y because you hedged on Monday at that price FINOPMGT 413 Using Futures Other Issues 44 It is yer likel that ou ma not be able to match either the maturity or the amount with a futures contract You have to be careful you don t end up increasing risk instead of reducing risk Because futures are marked to market you have to be careful that you have the liquidity to make your margin calls in case the market moves against you Thus if you don t have the cash to may your payments you may be forced to close out your position prematurely To see the effect of liquidity assume that to hedge your Yen liabilities you have to hold a long 100 million Yen futures position for 1 year Suppose now the Yen depreciates by 50 Examine how your cash ow changes FINOPMGT 413
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