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

  2. INTER-BANK FORWARD DEALING • September 18, 2009 • BANK A : "Bank A calling. Three-month yen-dollar please.” • BANK B : "Thirty two; twenty five." • BANK A : "Fifteen dollars yours at thirty two". • BANK B : "OK. Let's use a spot of 99.60 which is for • value September 20; I buy 15 million USD at 99.28 for • value December 20, 2009”. • Bank B will square up by doing a swap in which it buys USD spot and sells 3 months forward. This creates a spot position which may offset an existing spot position or must be offset by money market transactions unless it finds a counterparty which wishes to buy USD 3 months forward.

  3. Forward Rate Computation • Transaction Date : December 13, 2009 • Spot Date : December 15, 2009 • EUR Exporter : 90 days maturity • EUR exporter wants to cover 3 months forward : Forward maturity on March 15, 2010 • Sell EUR Buy USD • Sell USD Buy INR • (EUR/INR)bid = (EUR/USD)bid (USD/INR)bid

  4. The EUR/USD Page


  6. From the INRF page: USD/INR spot: 47.4425/75 Spot-February: 34.50/35.50 Spot-March: 51.00/52.00 We need rate for March 15. The required premium is [(51.00-34.50)/31](15) + 34.50 = 42.48 paise rounded to 43 paise The outright for March 15 is 47.4425+0.43 = 47.8725 From the EURF page EUR/USD spot: 1.0180/83 3-months: 68.90/69.30 3-month outright: 1.0180+0.006890=1.0249 3-month (EUR/INR)bid = (47.8725)(1.0249) = 49.06 Deduct a margin say 4 paise and give customer a rate of 49.02

  7. 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 : 41.93 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

  8. 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 :: 120.30 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   = [ 41.93 + 0.57 ] / [ 120.30 – 1.5450]= 42.50 / [ 118.7550] = 0.357880 or INR 35.788 per 100 JPY rounded off to INR 35.79 per 100 JPY. Add a spread of say 3 paise. Quote: Rs.35.82 per 100 JPY.

  9. OPTION FORWARDS • Delivery date to be chosen by the contract buyer within a specified interval. • A 3 month forward with delivery option over 3rd month • A 6 month forward with delivery option over last three months. • Banks extract maximum premium or give least discount • GBP/USD spot : 1.6565/70 2 Mth. 15/10 3 Mth 22/17 • Customer wants to buy USD, 3 months forward, option over 3rd month. USD at premium at 2 months, greater premium at 3 months. Bank will charge 3 months premium. The bank will give USD(1.6565-0.0022) or USD1.6543 per GBP.

  10. OPTION FORWARDS • If customer wanted to sell USD, bank would give only 2 months premium. • USD/CHF Spot : 1.1570/75 3 Months : 15/20 • (1) Customer wants to buy USD 3 months forward option period from spot to 3 months. Rates? • (2) Customer wants to buy CHF. Rates? • In the Indian market, length of option period cannot exceed one month.

  11. FOREX AND MONEY MARKETS • Annualised %Premium/Discount, T-year forward • = [(Forward-Spot)/(Spot)] × (1/T) × 100 • Use mid rates for quick calculations. • Annualised forward margin = Interest rate differential • True for fully convertible currencies with no capital controls. • Currency with higher interest rate will be at discount. • 3-month Euro LIBOR : 5% p.a. 3-month USD LIBOR : 3% • USD will be at a 3-month forward premium of 2% p.a. This implies that the 3-month forward EUR/USD rate will be 0.5% lower than the spot rate.

  12. 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 Relation” • Exploiting the departure from this relation is “Covered Interest Arbitrage”

  13. 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.

  14. Arbitrage Without Transaction Costs (niB – niA) Interest Parity Line [(Fn – S)/S] (1 + niA)

  15. Arbitrage Without Transaction Costs • One-Way Arbitrage : Using money market to avoid dealing in spot/forward market : An example • USD/CHF spot : 1.2450 • 6-month forward : 1.2680 • USD 6-month interest rate : 4.50% p.a. • CHF 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

  16. Arbitrage Without Transaction Costs • 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).

  17. 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

  18. 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

  19. Arbitrage With Transaction Costs • Global Money Markets : “Eurocurrency” markets or in general “offshore” markets • Bid rates are rates banks will pay on deposits; ask rates are rates they would charge on loans • The bid rate for currency X deposits iXb = iX(1-tX) • The ask rate for currency X loans iXa = iX(1+tX) • The bid rate for currency Y deposits iYb = iY(1-tY) • The ask rate for currency Y loans iYa = iY(1+tY)

  20. 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 or Fa  Sb(1+ixb)/(1+iya) • For arbitrage in reverse direction • Fb Sa(1+ixa)/(1+iyb)

  21. Arbitrage With Transaction Costs Fa Sb Fb  Sa Fa > Fb  = (1+ixb)/(1+iya)  = (1+ixa)/(1+iyb) •---------------• Sb Sa •-----------------------• •---------------------• Fb Fa Fb Fa Acceptable •--------------• •-------------• Fb Fa Fb Fa Not Acceptable

  22. 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 USD 3-month rates : 12⅛ – 12⅜ • Covered interest arbitrage possibilities are absent and no risk-less profit to be had by way of interest arbitrage

  23. 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 deposit-loan markets i.e. can borrow or lend at the USD and CHF rates quoted above • the firm buys dollars forward, each dollar will cost CHF1.5725 three months later

  24. Arbitrage With Transaction Costs • Alternative, 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 A saving of CHF 0.0011 per USD or CHF 11000 for the USD 10 million. Such savings are often possible especially when interest rates accessible to a company differ from euro market rates.

  25. 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.

  26. Arbitrage With Transaction Costs 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 Now compare the cost of direct spot purchase of X against Y and indirect acquisition The condition which makes direct purchase no more expensive than indirect acquisition is : • Fb Sb

  27. 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 All these conditions impose further constraints on forward rates.

  28. 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.

  29. 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.

  30. Taxes and CIP Consider a German investor. Each EUR invested for a year at home brings, post tax, EUR[1+(1-I)iG], where I is the tax rate on ordinary income and iG is the EUR interest rate. A covered investment in dollars yields, pre-tax, [S(EUR/$)/F(EUR/$)][1+iUS] = [(S-F)/F](1+iUS) + (1+iUS) The first term on the RHS is the exchange gain and the second term is principal plus interest. Post tax, the return is 1+(1-I)iUS + (1-C)[(S-F)/F](1+iUS)   Here C is the capital gains tax rate. The investor would be indifferent if the two returns are equal i.e. if 1+(1-I)iG= 1+(1-I)iUS + (1-C)[(S-F)/F](1+iUS) Or iG-iUS = [(1-C)/(1-I)][(S-F)/F](1+iUS) With no taxes or C and I equal, the equilibrium condition would be  iG-iUS = [(S-F)/F](1+iUS), the CIP relation.   If C < I, then (1-C) > (1-I) and [(1-C)/(1-I)] > 1. Hence the equilibrium condition must satisfy : iG-iUS > [(S-F)/F](1+iUS)

  31. 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

  32. Swaps and Deposit Markets • Suppose a customer approaches a bank for a 3 month CHF-MEP swap. The customer will sell CHF 1 million spot against MEP and buy CHF 1 million 3 months forward against MEP. At the time, the forward markets in MEP are very thin and volatile. There is however a market in Euro-MEP deposits. The rates are as follows CHF/MEP Spot : 8.9725/30 EuroCHF 3 month : 6 - 6¼ EuroMEP 3 month : 10 - 10½

  33. Swaps and Deposit Markets • What swap margin should the bank quote • Assume that the swap is done off a spot rate of CHF/MEP 8.9725. The bank borrows MEP 8.9725 million at 10½ % and delivers it to the customer. It invests the CHF 1 million received from the customer at 6% • At maturity, the bank must repay MEP 9.2080m. Its CHF deposit will have grown to CHF 1.015m. The bank will break even if it charges a rate of MEP 9.0719 per CHF on the forward leg of the swap

  34. THE VALUE OF A FORWARD CONTRACT A forward contract is costless to enter into (there may be a small flat fee to meet some administrative expenses) i.e. for the buyer of a forward contract, there is no cash outflow involved at the initiation of the contract. Obviously, the value of the contract must be zero at that time. Now consider the value of the contract on the day of maturity, T. If the delivery price specified is K and the spot price of the currency on that day is ST, the long side of the contract i.e. the party who had agreed to take delivery of the underlying asset at a price K makes a gain of (ST - K) which can of course be negative. What about the value of the contract on an intermediate date between initiation and maturity? t0 tT S(t0) St F(t0,T) Ft,T

  35. Suppose today is time “t”. Consider a forward contract initiated at time t0 to buy one unit of currency B at time T at a price of F(t0, T) units of currency A. This was the market forward rate at time t0 for contracts expiring at time T. Its value today is V(t,t0,T) = (Ft,T – K)/[ [1+iA(T-t)] Here Ft,T is the market forward rate at time t – today- for a contract expiring at time T and iA is the risk-free interest rate in currency A. Cancellation of a Forward Contract before Maturity Date On August 15, an exporter sells GBP 250,000 two months forward at a rate of Rs.88.50. The delivery date is October 15. On September 15, the exporter requests the bank to cancel the contract. The bank will effectively sell GBP 50,000 to the customer one month forward at the forward selling rate. The bank will cover itself by buying one month forward.

  36. Suppose the rates on September 15 are : Interbank spot GBP/INR: 87.40/87.45 1-month forward : 15/30 Exchange margin : 0.15% One month forward selling rate : 87.75(1.0015) = 87.88 Amount to be paid to the customer : Rs.[(88.50-87.88)(250000)] = Rs.155000. This payment would be due on October 15. Discounted value of this amount can be paid on September 15 using an appropriate rate of discount such as the PLR. A flat fee for cancellation would be charged. Often corporate customers want early settlement or postponement of settlement dates of outstanding forward contracts. This involves cancellation of the outstanding contract and booking a new forward contract.

  37. GETTING AROUND CONTROLS NON-DELIVERABLE FORWARDS (NDF) What is an NDF? An NDF is conceptually similar to an outright forward foreign exchange transaction. A (notional) principal amount, forward exchange rate and forward date are all agreed at the deal’s inception. The difference is that there will be no physical transfer of the principal amount in an NDF transaction. The deal is agreed on the basis that net settlement will be made in US dollars - or another fully convertible currency - to reflect any differential between the agreed forward rate and the actual exchange rate on the agreed forward date. It is a cash-settled outright forward.

  38. The NDF market offers an alternative hedging tool for foreign investors with local currency exposure or a speculative instrument for them to take positions offshore in the local currency. The use of Asian NDF markets by nonresidents in part reflects restrictions on their access to domestic forward markets. However, in some cases, such as Korea, onshore players are also important counterparties in the NDF market of the home currency. The NDF markets for some Asian currencies have existed at least since the mid-1990s. Tightening of controls after the Asian crisis may have boosted their growth in some cases.

  39. Access to onshore forward markets by non-residents Chinese Renminbi : No offshore entities participate in onshore markets Indian Rupee : Allowed but subject to underlying transactions requirement Indonesian Rupiah: Allowed but restricted and limited Korean Won : Allowed but subject to underlying transactions requirement Philippine Peso : Allowed but restricted and limited New Taiwan Dollar : Only onshore entities have access to onshore market Sources: HSBC (2003); National data.

  40. According to the latest information available from Deutshe Bank estimates, the average daily turnover in NDF market for Korean Won, the most liquid NDF market, has increased from USD 700-1000 mn in 2003-04 to USD 3000 mn in 2008-09. The Chinese Yuan now has an average daily turnover of USD 1000 mn, followed by Indian Rupee at USD 800 mn in 2008-09. The growing market for NDFs in emerging-market currencies is an example of financial innovation to meet the needs of market participants. These markets provide private companies and investors a method of hedging their exchange rate exposures in situations where local governments impose constraints on nonresident access to on-shore markets

  41. These markets have evolved for the Indian Rupee, as for other emerging market currencies, following foreign exchange convertibility restrictions. It is serving as an avenue for foreign entities to hedge their currency exposure to the Indian markets. This market also derives liquidity from non-residents wishing to speculate in the Indian Rupee without exposure to the currency and from arbitrageurs who try to exploit the differentials in the prices in the onshore and offshore markets. The Indian Rupee NDF market is most active in Singapore, Hong Kong (hŏng kŏng), and Dubai. At present, there are no controls on the offshore participation in INR NDF markets. However, the onshore financial institutions in India are not allowed to freely transact in the NDF markets. What is permitted is that domestic banking entities have specific open position and gap limits for their foreign exchange exposures and through these limits domestic entities can transact in the NDF markets.

  42. How is an NDF settled? A fixing methodology is agreed when an NDF deal is contracted. It specifies how a fixing rate is to be determined on the fixing date, which is normally two working days before settlement, to reflect spot value. Generally, the fixing spot rate is based on a reference page on Reuters or Bloomberg with a fallback of calling four leading dealers in the relevant market for a quote. Settlement is made in the major currency: paid to, or by, the customer, and reflects the differential between the agreed forward rate and the fixing spot rare. Why use a non-deliverable forward? The non-deliverable forward market allows offshore parties to hedge exchange rate exposures on many Asian and African currencies, without any physical transfer of these currencies and without having to deal in the local market. Therefore, local counterparty risk and the cost of holding accounts in local currencies can be avoided. Further, US dollar-settled NDFs between two offshore counterparties are not generally subject to local monetary controls.

  43. How does an NDF work? • An investor has invested US$2 million in stock on the Taiwanese stock market for one year. He expects the stock market to rise, but is worried about potential Taiwan dollar (T$) depreciation. He wishes to hedge his foreign exchange exposure using an NDF. • A non-deliverable forward rate of T$ 35.80 per US dollar is agreed between the bank and the customer. • The principal amount is US$2 million. • There are three possible outcomes in one year's time: the T$ has reached the forward rate, depreciated further or appreciated relative to the forward rare. Examples of the three scenarios ate shown below.

  44. NDF EXAMPLE Outcome A Outcome B Outcome C US Dollar/Taiwan Dollar Depreciated No Change Appreciated Fixing spot rate 36.10 35.80 35.50 Equivalent amount ($) 1983379.50 2000000.00 2016901.41 Settlement ($) Bank pays customer $16620.50 No net payment Customer pays bank $16901.41

  45. Currency-linked Deposits Deposits in a major currency with the return linked to the exchange rate of an NDF currency are offered by banks. The yield reflects the implied local interest rates derived from the NDF market, which may be significantly higher than the major currency interest rates. The NDF currency-linked deposit is particularly suitable for asset managers who need to hold a physical asset, but, at the same time, wish to gain access and exposure to higher yielding markers. These deposits not only have many of the same advantages as NDFs, but they also often allow depositors to assume a lower credit risk or to earn more interest than depositing onshore. NDF currency-linked deposits cannot normally be withdrawn or terminated prior to the fixed maturity date. Should a currency-linked depositor wish to make an early withdrawal, the bank will use its best endeavors to accommodate it, although the terms which allow early withdrawal will depend on market considerations.

  46. How does an NDF Currency-linked Deposit Work? • An investor wishes to receive a Philippine peso interest rate on US$2 million for six months and assumes the peso currency exposure on both the principal and interest element of his deposit. He uses a peso-linked deposit. • Assume peso coupon is 17.50% pa (six-month US$ Libor is 5.50%). • The current spot rate for dollar/peso is 43.50. • Interest yield at the end of the six months = US$2 million x 17.50% x 180/360 = US$175,000.00. • Principal plus interest at maturity if unlinked would be US$2,175,000.00. • Linked redemption amount = US$2,175,000 x 43.50/Fixing spot rate. • Examples of the three possible outcomes in six months' time are shown in the table below.

  47. NDF CURRENCY LINKED DEPOSIT - EXAMPLE Outcome A Outcome B Outcome C US Dollar/Peso at fixing 47.50 43.50 39.50 Redemption amount ($) 1991842.11 2175000 2395253.16 Return ($) -8157.89 175000 395253.16 Annualized Return -0.81% 17.50% 39.53%