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International Financial Management P G Apte

CHAPTER - 8. Forwards, Swaps and Interest Parity. International Financial Management P G Apte. COVERED INTEREST ARBITRAGE A fund manager sees the following rates: USD/JPY spot: 120.00 3-month forward: 117.00 3-month Euro$ interest rate: 6% 3-month Euro ¥ : 2%

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International Financial Management P G Apte

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  1. CHAPTER - 8 Forwards, Swaps and Interest Parity International Financial Management P G Apte P.G.Apte International Financial Management

  2. COVERED INTEREST ARBITRAGE A fund manager sees the following rates: USD/JPY spot: 120.00 3-month forward: 117.00 3-month Euro$ interest rate: 6% 3-month Euro¥ : 2% $1 in a 3-month deposit becomes $1.015 at maturity $1 convert spot to ¥120, deposit, sell maturity value of deposit forward. You will have $[120(1.005)/117] = $1.0308 A riskless arbitrage profit of 1.58 cents per dollar. More than 6% p.a. without any currency risk. P.G.Apte International Financial Management

  3. 8.2 Arbitrage Without Transaction Costs Covered Interest Arbitrage: Generalisation • A German investor choosing between Eurodollar and Euro deposits does not want to incur exchange rate risk Assume no transaction costs i.e. no bid/offer spreads in forex or money markets S: the EUR/USD spot rate Fn: the EUR/USD forward rate for the n-year maturity (n= N/360 or N/365 N= No.of days to maturity) iEUR : Euro Interest rate iUSD : USD Interest rate P.G.Apte International Financial Management

  4. 8.2 Arbitrage Without Transaction Costs • Maturity value of EUR 1 in a n-year EUR deposit: EUR (1 + niEUR) • To invest in Eurodollar and eliminate all exchange risk investor must • Convert EUR into USD spot • Invest in Eurodollar deposit • Sell the USD proceeds of the deposit forward for EUR • Maturity value of 1EUR invested in this fashion is EUR[(S)(1 + niUSD)/(Fn)] What if [(S)(1 + niUSD)/(Fn)]  (1 + niEUR) ? P.G.Apte International Financial Management

  5. 8.2 Arbitrage Without Transaction Costs • Suppose (1 + niEUR) > S/Fn(1+niUSD) • A large number of arbitragers would want to liquidate dollar deposits or borrow dollars, sell USD vs. EUR in spot market, demand EUR depositsand sell EUR vs. USD forward Resulting Market forces would lead to: Increase in iUSD, increase in S, fall in iEUR, fall in Fn If (1 + niEUR) < S/Fn(1+niUSD) Market forces would lead to decrease in iUSD, decrease in S, rise in iEUR, rise in Fn. In either case, the result would be (1 + niEUR) = (S/Fn)(1+niUSD) P.G.Apte International Financial Management

  6. 8.2 Arbitrage Without Transaction Costs • Covered Interest Parity Theorem • In the absence of restrictions on capital flows and transaction costs for any pair of currencies A and B the following relation holds • (1 + niA)/(1 + niB) = S(A/B)]/[Fn(A/B)] • [Recall that S(A/B) and F(A/B) re stated as units of B per unit of A] • This is the “Covered Interest Parity (CIP) Relation” • Exploiting the departure from this relation is “Covered Interest Arbitrage” It is not a causal relation but an equilibrium condition P.G.Apte International Financial Management

  7. 8.2 Arbitrage Without Transaction Costs • If iA > iB then Fn < S A at forward discount, B at forward premium • and if iA < iB then Fn > S A at premium, B at discount The CIP relation can be written as: (1/n) [(Fn - S)/S](100) = (100)(1/n) (niB – niA)/(1 + niA)  (100)(1/n) (niB – niA) % Annualised Forward Discount/Premium  interest rate differential in % Currency with higher interest rate will be at discount. P.G.Apte International Financial Management

  8. 8.2 Arbitrage Without Transaction Costs (niB – niA) Interest Parity Line [(Fn – S)/S] (1 + niA) P.G.Apte International Financial Management

  9. 8.2 Arbitrage Without Transaction Costs • One-Way Arbitrage : Using money market to avoid dealing in spot/forward market • An example: USD/CHF spot : 1.6450, 6-month forward : 1.6580, Euro$ 6-month interest rate : 4.50% p.a., EuroCHF 6-month interest rate : 6.50% p.a. Case I: A Swiss firm need USD now. Buy spot or borrow USD, buy USD forward to repay loan Case II : A US firm needs CHF 6 months later. Buy forward or borrow USD now, convert to CHF spot, deposit, use deposit on maturity, repay USD loan P.G.Apte International Financial Management

  10. 8.2 Arbitrage Without Transaction Costs (contd.) • Generalizing the result: • Assuming one unit B is borrowed for a period of n years. To repay the loan the firm must have [1+niB] units of B when the loan matures. • To acquire it in the forward market, the firm must have Fn(B/A)[1+niB] units of A when the forward contract matures. • So the firm must now set aside an amount of A given by [Fn(B/A)(1+niB)]/(1+niA). P.G.Apte International Financial Management

  11. 8.2 Arbitrage Without Transaction Costs If the cost of the direct spot purchase is not to exceed the cost of the indirect transaction : Fn(B/A)(1+niB)/ (1+niA)  S(B/A) If this inequality does not hold, all traders who need B now will shun the spot market and there will be no spot demand for B Suppose it is satisfied as a strict inequality then Fn(B/A) (1+niB) / (1+niA) > S(B/A) Now those who need B in future will avoid forward market. Hence must have Fn(B/A) (1+niB) / (1+niA) = S(B/A) CIP P.G.Apte International Financial Management

  12. 8.3 Arbitrage With Transaction Costs • The Foreign Exchange Market • For any pair of currencies X and Y, • Spot (Y/X)bid = Sb = S(1-ts) • Spot (Y/X)ask = Sa = S(1+ts) • S is the "mid rate”. The spread 2tsS is the transaction cost. • Forward (Y/X)bid = Fb = F(1-tf) • Forward (Y/X)ask = Fa = F(1+tf) • F is the "mid-rate" and 2tfF is the transaction cost in the forward market P.G.Apte International Financial Management

  13. 8.3 Arbitrage With Transaction Costs • Eurodeposit Markets • Bid rates are rates banks will pay on deposits; Ask rates are rates they would charge on loans • The bid rate for EuroX deposits iXb = iX(1-tX) • The ask rate for EuroX loans iXa = iX(1+tX) • The bid rate for EuroY deposits iYb = iY(1-tY) • The ask rate for EuroY loans iYa = iY(1+tY) P.G.Apte International Financial Management

  14. 8.3 Arbitrage With Transaction Costs • Covered Interest Arbitrage with Transaction Costs • Consider the following rates • GBP/USD spot : 1.5625/35 Euro$ deposits : 8¼ - 8½ • Euro£ deposits : 125/8 - 13 • Consider : Borrow sterling for 1 year, convert spot to dollars, invest dollars for one year and sell the maturing dollar deposit forward. For no arbitrage profit: • 1.5625(1.0825)/Fa 1.13 or • [1.5625(1.0825)/1.13]  Fa orFa Sb(1+ixb)/(1+iya) • For arbitrage in reverse direction • Fb Sa(1+ixa)/(1+iyb) P.G.Apte International Financial Management

  15. 8.3 Arbitrage With Transaction Costs Fa Sb Fb  Sa Fa > Fb  = (1+ixb)/(1+iya)  = (1+ixa)/(1+iyb)  <  •---------------• Sb Sa •-----------------------• •---------------------• Acceptable Fb Fa Fb Fa •--------------• •-------------• Fb Fa Fb Fa Not Acceptable P.G.Apte International Financial Management

  16. 8.3 Arbitrage With Transaction Costs • One-Way Arbitrage with Transaction Costs • The following rates are available in the market : • Spot USD/CHF : 1.6010/20 3-months Forward : 1.5710/25 • CHF 3-month rates : 4 - 4¼ EuroUSD 3-month rates : 121/8 – 123/8 • Covered interest arbitrage is not profitable with these prices P.G.Apte International Financial Management

  17. 8.3 Arbitrage With Transaction Costs • Consider the case of a Swiss firm which needs $10 million 3 months from now. The firm has access to the Eurodeposit markets i.e. can borrow or lend at the Euro$ and CHF rates quoted • the firm buys dollars forward, each dollar will cost CHF1.5725 three months later • Alternatively it can borrow CHF, convert spot to dollars, place dollars in a euro$ deposit and use these to make the payment. The cost per dollar in terms of CHF outflow 3 months later is [1+0.25(0.0425)] CHF (1.6020) {------------------------} [1+0.25(0.12125)] = CHF 1.5714 , saves CHF 11000 P.G.Apte International Financial Management

  18. 8.3 Arbitrage With Transaction Costs • A firm needs currency Y now. It can obtain it in the spot market by selling X or it can get it indirectly as follows. • It borrows Y in the Eurodeposit market; • Sets aside a certain sum of X earning interest • Sells forward the maturity value of this X deposit against Y to repay the Y loan. The condition which makes direct purchase no more expensive than indirect acquisition is • Fa (Sa) [1 + iX(1-tX)] /[1 + iY(1+tY)] Fa  Sa Same argument applied to buying X will lead to FbSb P.G.Apte International Financial Management

  19. Now consider a firm which needs Y a year from now. Buy it forward or borrow X, convert to Y, deposit Y and use the deposit proceeds. For cost of direct forward purchase to be no greater than indirect acquisition via money market FaSa In the same manner, we can get the condition FbSb If some of these are violated market players will take advantage to save costs. P.G.Apte International Financial Management

  20. Arbitrage With Transaction Costs Occasionally depending upon the interest rates accessible to a firm, some of these may be violated. In particular, if rates accessible to a firm are different from Euromarket rates, firm may find one-way arbitrage profitable. Thus indirect acquisition of a currency via money market and spot market may work out to be cheaper than a forward purchase. The firm must always examine such possibilities. P.G.Apte International Financial Management

  21. Arbitrage With Transaction Costs • Covered Interest Arbitrage in Practice • Given the spot bid-ask rates as well as bid-ask rates in deposit markets, covered interest parity does not imply a unique pair of forward bid-ask rates • Political risks, Taxes and Transaction costs are also relevant factors. • If interest earned and exchange gains are taxed at different rates, the covered parity conditions must be modified. • For banks this is generally not true. They are the dominant players in the money and exchange markets. P.G.Apte International Financial Management

  22. Swaps and Deposit Markets • Banks will constantly monitor its swap rates so that they are not out of line with the forwards implied by Eurodeposit rates • A bank can "manufacture" a swap quote from Eurodeposit rates or manufacture a Eurodeposit rate from swap quotes • Suppose a customer approaches a bank for a 3 month CHF-Italian lira swap. The customer will sell CHF 1 million spot against ITL and buy CHF 1 million 3 months forward against ITL. The rates are as follows CHF/ITL Spot : 755/765 EuroCHF 3 month : 6 - 6¼ Eurolira 3 month : 15 - 15½ P.G.Apte International Financial Management

  23. 8.4 Swaps and Deposit Markets • What swap margin should the bank quote ? • Assume that the swap is done off a spot rate of CHF/ITL 760.00. The bank borrows ITL 760 million at 15½ % and delivers it to the customer. It invests the CHF 1 million received from the customer at 6% • At maturity, the bank must repay ITL 789.45m. Its CHF deposit will have grown to CHF 1.015m. The bank will break even if it charges a rate of 777.78 lire per CHF on the forward leg of the swap • This is just CIP at work. In a similar fashion, the bank can work out a breakeven deposit/loan rate in currency B by looking at deposit/loan rate in currency A and the swap margin between A and B P.G.Apte International Financial Management

  24. Interbank Forward Dealing • The buyer is really buying the swap points i.e.the interest rate differential and the spot risk is removed buy doing a spot deal in conjunction with the forward deal • The interbank forward market is really a market for duplicating the money market lending-borrowing transactions via the currency market P.G.Apte International Financial Management

  25. Interbank Forward Dealing • A movement in spot rate after a forward deal is done (accompanied by its companion spot deal), will change swap points for a given interest rate differential but may also affect the interest rate differential • The "spot risk" in forward transactions: Spot rate movements give rise to temporary short and long positions in different currencies and hence interest expenses and earnings P.G.Apte International Financial Management

  26. Option Forwards • Banks offer a contract known as option forwards in which the rate of exchange between the two currencies is fixed at the time the contract is entered into as in a standard forward but the delivery date is not a fixed date • One of the parties can, at its option, take or make delivery on any day between two fixed dates. The interval between these two dates is the option period P.G.Apte International Financial Management

  27. FORWARD-FORWARD SWAPS AND RELATED PRODUCTS Forward-Forward Swaps GBP/USD Spot : 1.4995/1.5005 3-Month swap : 92/83 9-Month swap : 290/269 3-Month Eurodollars : 5.50% 9-Month Eurodollars : 6.25% 3-Month Eurosterling : 8.00% 9-Month Eurosterling : 8.80% A trader expects USD interest rates to rise and GBP rates to soften. This would imply a reduction in the premium on the USD. P.G.Apte International Financial Management

  28. He undertakes the following two spot-forward swaps: Buy GBP 1mio spot sell 3-month forward Sell GBP 1mio spot buy 9-month forward Both swaps are done off a spot of 1.5000. Using this spot, the 3 and 9-month outright forwards are 1.4908 and 1.4731 respectively: 1.4908 = 1.5000[(1+(0.055/4))/(1+(0.08/4))] = 1.5000-0.0092 1.4731 = 1.5000[(1+0.0625*0.75)/(1+0.088*0.75)] = 1.5000-0.0269 Effectively the trader has done a forward-forward swap; sell GBP 1mio 3 months forward and buy GBP 1mio 9 months forward both against USD. The spot position is washed out. P.G.Apte International Financial Management

  29. At 3 months suppose we have: GBP/USD Spot : 1.4500 6-month Eurodollar : 7.00% 6-month Eurosterling : 8.00% 6-month GBP/USD outright : 1.45(1.035/1.04) = 1.4430 The trader buys GBP 1mio spot at 1.45 and delivers on the forward leg of the 3-month swap: P.G.Apte International Financial Management

  30. CASH FLOWS: At 3 months: STG + 1mio USD –1.45mio Spot purchase of STG STG –1mio USD +1.4908mio Delivery on the original spot-3 month swap. Net : USD 0.0408mio = USD 40800 He closes out the 9-month position by selling STG 1mio 6 months forward at the rate of 1.4430. At 9 months: STG +1mio USD –1.4731mio Delivery on the original spot-9 month swap. STG –1mio USD + 1.4430m Delivery on the 3-9 month swap. Net : USD –0.0301mio = USD -30100. TOTAL NET USD (40800-30100) + Int. on USD 40800 P.G.Apte International Financial Management

  31. STARTING RATES ONCE MORE GBP/USD Spot : 1.4995/1.5005 3-Month swap : 92/83 9-Month swap : 290/269 3-Month Eurodollars : 5.50% 9-Month Eurodollars : 6.25% 3-Month Eurosterling : 8.00% 9-Month Eurosterling : 8.80% Outrights: 3 months: 1.4903/1.4922 9 months: 1.4705/1.4736 P.G.Apte International Financial Management

  32. Forward Spread Agreement (FSA) With the data given above, the 3-9 month discount on the sterling reflects the 3-9 month forward interest rate differential. The 3-month forward 6-month rates are calculated as follows: Eurodollars: (1+0.055*0.25)(1+r$3,9*0.5) = (1+0.0625*0.75) Eurosterling: (1+0.08*0.25)(1+r£3,9) = (1+0.088*0.75) This gives : r$3,9 = 6.54% r£3,9 = 9.02% The outright forward rates for 3 and 9 months today reflect the differential (r£3,9 - r$3,9) : 1.4731 = 1.4908 [(1+ r$3,9/2)/(1+ r£3,9/2)] P.G.Apte International Financial Management

  33. The FSA seller locks in a 6-month discount of 2.48% on the sterling with reference to the 3-month rate. Suppose the notional principal is GBP 1mio. Notionally he agrees to buy sterling (i.e. sell the “foreign currency”) at 9-months at a rate 2.48% below its rate at 3 months. Three months later suppose the 6-month rates are, as above, 7% for dollars and 8% for sterling. Now the actual 6-month discount on sterling will reflect this 1% differential. The FSA buyer notionally sells sterling at a 1% discount. His gain is 1.4% on STG 1mio for 6 months or STG 7000. This is paid at 9 months or its discounted value immediately using the 6-month STG discount rate of 8% p.a. P.G.Apte International Financial Management

  34. STARTING RATES ONCE MORE GBP/USD Spot : 1.4995/1.5005 3-Month swap : 92/83 9-Month swap : 290/269 3-Month Eurodollars : 5.50% 9-Month Eurodollars : 6.25% 3-Month Eurosterling : 8.00% 9-Month Eurosterling : 8.80% Outrights: 3 months: 1.4903/1.4922 9 months: 1.4705/1.4736 P.G.Apte International Financial Management

  35. Exchange Rate Agreements (ERAs) This product was launched by Barclays bank. It is quite similar to FSA. The ERA seller agrees to receive a 3-9 USD-STG spread of 177 pips implied by the starting spot, and the 3 and 9 month USD and STG interest rates. In effect, the ERA seller expects the pound interest rate to fall and/or US interest rate to rise leading to a reduction in the premium on USD (discount on GBP). He agrees to buy GBP 9 months forward at a discount of 177 pips relative to its 3 month rate. At 3 months he will close out by selling GBP then 6 months forward at a spread to spot existing at that time. However, the bet is only on the spread. This can be looked at as follows: P.G.Apte International Financial Management

  36. EXCHANGE RATE AGREEMENT(Contd.) Today, the ERA seller agrees to do the following transactions at 3 months: Sell GBP spot, buy 6 months forward at a 6-month premium/discount implied by today’s 3 and 9 month forward rates. Buy GBP spot, and sell 6 months forward at the actual premium/discount existing at that time. Effectively, he will collect the difference between the 3-9 month spread implied by today’s rates and pay the 6 month spread that will materialize at the end of 3 months. P.G.Apte International Financial Management

  37. The notional principal is STG 1mio. If at the end of 3 months the rates are : USD/STG spot: 1.4500. 6-month interest rates are 7% and 8% for USD and STG respectively. The actual 6-month USD-STG spread is 1.4500 – 1.4500[(1.035/1.04)] = 1.4500-1.4430 = 70 pips. The ERA seller is paid USD[(0.0177-0.0070)*1mio/(1.035)] = USD 10338.16 = STG 7129.77 In general, the ERA seller is paid (CFSt,T-SFSt,T) NP: Principal A = -{NP × ------------------------} CFS: Contract Spread at t=0 [(1+rt,T×(T-t)] SFS: Actual Spread at t rt,T: Int. rate at t P.G.Apte International Financial Management

  38. Forward Exchange Agreements (FXAs) This product reproduces the payoff of the forward-forward swap without actually having to take on the two swaps on the balance sheet. Continuing the same example, the settlement amount A paid to the FXA seller (paid by FXA seller if negative) is calculated as : [(F0,t-St) + (CFSt,T-SFSt,T)] A = -{NP × ---------------------------------} + NP(F0,t-St) [(1+rt,T×(T-t)] The contract is initiated at time 0 (zero). The FXA period starts at time t and ends at time T. Both t and T are measured in years. NP, CFSt,T, SFSt,T and rt,T are as defined above. F0,t and St are forward rate at time 0 for maturity t and spot rate at time t. P.G.Apte International Financial Management

  39. Foreign Exchange Rates in India • An active forward rupee-dollar market with banks offering two-way quotes has evolved in India • The rupee-dollar spot forward margin is not entirely determined by interest rate differentials due to exchange controls on capital account transactions • With liberalisation, the correspondence between interest rate differentials and sap margins is closer than in the past. • Other forward rates computed as cross rates • For INR-USD forward quotes upto one year are available. P.G.Apte International Financial Management

  40. Foreign Exchange Rates in India • Interbank money market has just begun to develop with active interbank deposit trading and MIBOR (Mumbai Interbank Offered Rate) as the market index • Supply of and demand for forward dollars arising out of exporters and importers hedging their receivables and payables • Forward contracts in the Indian market are usually option forwards though banks do offer fixed date forwards if the customer so desires P.G.Apte International Financial Management

  41. Foreign Exchange Rates in India • Absence of a tight relationship between interest differentials and forward premia also opens up arbitrage opportunities for exporting firms related to their credit requirements • All forward transactions are for the purpose of hedging an underlying exposure such trade related payables and receivables or approved capital account transactions such as debt service • In the absence of an active money market in India and hence the interest parity linkage, it is very difficult for dealers to assess the correct forward rate which they should offer their customers P.G.Apte International Financial Management

  42. Foreign Exchange Rates in India • “Third currency forwards" are permitted i.e.a firm can buy (sell) say JPY forward against USD and leave the USD exposure open. • In recent years there has been considerable deepening of the forward markets in India against the major currencies like USD, GBP, DEM and JPY P.G.Apte International Financial Management

  43. Forward Rate Computations Example 1 On June 7 1999 a client discounted his DEM 2 million usance 90 days export bill with the export desk. The export desk reported this to the corporate dealer and asked for the conversion rate. The corporate dealer asked the USD/INR spot interbank dealer for spot quote and the USD/INR forward interbank dealer for 3 months forward swap points. The quotes given are say 42.92/93 for value spot and the forward dealer asked the corporate dealer to look at INRF= page for relevant swap points. DEM is a legacy currency and hence, must be computed in terms of EUR and converted at its fixed exchange rate of EUR / DEM 1.95583 P.G.Apte International Financial Management

  44. Forward Rate Computation Client sells DEM (or equivalent EUR) and buys USD and Client sells USD and buys INR  Thus, the computation is as follows :  USD / INR Spot Bid :: 42.92 From the Reuters page , the forward points are :  Spot over 31 Aug 99 :: 48.50 / 50.50 Spot over 29 Sep 99 :: 68.00 / 70.00 Thus for Sept.9,1999 the bid points for USD/INR are interpolated as   = [(68.00 – 48.50) / 29] * 9 days + 48.50 = 6.05 + 48.50 = 54.55 = 55 pips premium P.G.Apte International Financial Management

  45. Forward Rate Computation EUR / USD Spot Bid :: 1.0378 EUR / USD 3 month forward points bid :: 65.00 pips premium from the Reuters page directly (otherwise use interpolation) Thus, the outright DEM / INR 3 month outright forward rate for Sept. 9, 1999 is   = [ 42.92 + 0.55 ] / [ 1.95583 / ( 1.0378 + 0.0065 ) ] = 43.47 / [ 1.95583 / 1.0443 ] = 43.47 / 1.872862 = 23.2105 = 23.21 The corporate dealer would deduct his margin, say 3 paise, and arrive at the net bid rate to the client as Rs. 23.18 per DEM P.G.Apte International Financial Management

  46. Forward Rate Computation It is June 7. A client wants to buy JPY 25 million, for value three months from spot date. The import desk reports this to the corporate dealer and asks for the conversion rate. Cross Rate: Client sells INR buys USD; Sells USD buys JPY The corporate dealer gets the USD / INR rates from the Reuters INRF page. USD / INR Spot Ask :: 42.93 USD / INR 3 month forward points : ?? From the INRF page Spot over 31 Aug 99 :: 48.50 / 50.50 Spot over 29 Sep 99 :: 68.00 / 70.00 P.G.Apte International Financial Management

  47. Thus for Sept. 9, the ask points for USD/INR are interpolated as = [(70.00 – 50.50) / 29] * 9 days + 50.50 = 6.05 + 50.50 = 56.55 = 57 pips premium USD / JPY Spot Bid :: 122.30  USD / JPY 3 month forward points bid :: -154.50 pips discount from the USD/JPY page. Recall that a pip for JPY is 0.01.  Thus, the outright JPY / INR 3 month outright forward rate for Sept. 9, 1999 is   = [ 42.93 + 0.57 ] / [ 122.30 – 1.5450]= 43.50 / [ 120.7550] = 0.360234 or INR 36.0234 per 100 JPY. Add a spread of say 3 paise. Rs.36.05 per 100 JPY. P.G.Apte International Financial Management

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