4. Pricing and Valuation of Various Derivatives. 4.1 Forward Contracts:

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1 4. Pricing and Valuation of Various Derivatives This chapter discusses the structure, pricing and valuation of various derivative instruments. It is divided into six parts. The first part discusses forward contracts. The second part covers swap pricing and application of interest rate swap and currency swap. The third part covers futures contract including forward rate agreement, interest rate futures, etc. The fourth part covers various options contracts with pricing and their application. The fifth part covers packaged forward contracts. Lastly, Futures Options contracts are discussed. 4.1 Forward Contracts: Forward contract can be defined as an agreement to buy or sell an asset on a specified day for a specified exercise price. The underlying asset can be commodity, currency etc. One of the parties to the contract assumes a long position and therefore he agrees to buy the underlying asset on a certain specified future date for a certain specified price. The other party assumes a short position and therefore agrees to sell the same asset on the same date and for the same price. The forward contracts are normally traded outside the exchange (OTC). Forward contracts are privately negotiated and are not standardized. Further, the two parties must bear each other's credit risk. Since the contracts are not exchange traded, there is no marking to market requirement, which allows a buyer to avoid almost all capital outflows initially (though some counter-parties might set collateral requirements). Thus because of the lack of standardization in these contracts, there is very little scope for a secondary market in forwards Salient Features of Forward: NCFM derivatives module has enumerated the following salient features of forward contracts: They are bilateral contracts and hence exposed to counter - party risk. Each contract is custom designed, and hence is unique in terms of contract size, expiration date and the asset type and quality. The contract price is generally not available in public domain. The contract has to be settled by delivery of the asset on expiration date. In case, the party wishes to reverse the contract, it has to compulsorily go to the same counter party, which being in a dominant situation can command the price it wants Currency forwards: Forward contracts in which the underlying asset is currency exchange rate, is called currency forward. It is mainly used by those who have foreign currency inwards or outwards at a future date i.e. importers, exporters and bankers/dealers. An important segment of the forex derivatives market in India is the Rupee forward contracts market. This has been growing rapidly with increasing participation from corporates, exporters, importers, banks and FIIs. Till February 1992, forward contracts were permitted only against trade related exposures and these contracts could not be cancelled except where the underlying transactions failed to materialize. In March 51

2 1992, in order to provide operational freedom to corporate entities, unrestricted booking and cancellation of forward contracts for all genuine exposures, whether trade related or not, were permitted. Although due to the Asian crisis, freedom to rebook cancelled contracts was suspended, which has been since relaxed for the exporters but the restriction still remains for the importers. Some of the RBI guidelines regarding forward contract are furnished below: 1. Residents: Genuine underlying exposures out of trade/business o Exposures due to foreign currency loans and bonds approved by RBI o Balances in EEFC accounts 2. Foreign Institutional Investors: o They should have exposures in India 3. Non-resident Indians/ Overseas Corporates: o Dividends from holdings in a Indian company o Deposits in FCNR and NRE accounts o Investments under portfolio scheme in accordance with FERA or FEMA The forward contracts are also allowed to be booked for foreign currencies (other than Dollar) and Rupee subject to similar conditions as mentioned above. The banks are also allowed to enter into forward contracts to manage their assets - liability portfolio. The cancellation and rebooking of the forward contracts is permitted only for genuine exposures out of trade/business up to one year for both exporters and importers, whereas in case of exposures of more than one year, only the exporters are permitted to cancel and rebook the contracts. Also another restriction on booking the forward contracts is that the maturity of the hedge should not exceed the maturity of the underlying transaction. Cross currency forwards are also used to hedge the foreign currency exposures, especially by some of the big Indian Corporates. The regulations for the cross currency forwards are quite similar to those of Rupee forwards, though with minor differences. For example, a corporate having underlying exposure in Yen, may book forward contract between Dollar and Sterling. Here even though its exposure is in Yen, it is also exposed to the movements in Dollar vis a vis other currencies. The regulations for rebooking and cancellation of these contracts are also relatively relaxed. The activity in this segment is likely to increase with increasing convertibility of the capital account Pricing of forward contracts: For arriving at forward price, the cost of carry method can be applied. If the investor does not book a forward contract, the alternative for him is to buy at the spot market and hold the underlying asset. In such a contingency he would incur the spot price plus the cost of carry. The cost of carry refers to the difference between the costs and the benefits that accrue while holding an asset. Suppose a groundnut oil producer needs kg of nuts for processing in two months. To lock in the price of the groundnut today, he can buy it and carry it for two months. One cost of this strategy is the opportunity cost of funds. To come up with the purchase price, he must either borrow money or reduce his earning assets by that amount. Beyond interest cost, however, carry costs vary depending upon the nature of the asset. For a 52

3 physical asset such as groundnut, he incurs storage costs (e.g., rent and insurance). At the same time, by storing groundnut, he avoids the costs of possibly running out of his regular inventory before two months are up and having to pay extra for emergency deliveries. This benefit is called convenience yield. Convenience yield is a reward for those who keep the advance stock of underlying asset and therefore avoid speculative price in case of emergency purchase. Thus, the cost of carry for a physical asset equals interest cost plus storage costs less convenience yield, that is, Carry costs = Cost of funds + storage cost - convenience yield. For a financial asset, such as a stock or a bond (interest bearing security), storage costs are negligible. Moreover, income (yield) accrues in the form of quarterly cash dividends or semiannual coupon payments. Thus the cost of carry for a financial asset can be modified from the previous formula as follows: Carry costs = Cost of funds income accrued. Carry costs and benefits are modeled either as continuous rates or as discrete flows. Some costs/benefits such as the cost of funds (i.e., the risk-free interest rate(r)) are best modeled continuously. The dividend yield on a broadly based stock portfolio and the interest income on a foreign currency deposit also fall into this category. Other costs/benefits like non-annual cash dividends on individual common stocks, semi-annual coupons on bonds, and warehouse rent payments for holding an inventory of grain are best modeled as discrete cash flows. In the interest of conciseness, only continuous costs are considered here. Dividend income from holding a broadly based stock index portfolio or interest income from holding a foreign currency (i.e. (i)) is typically considered as a constant, continuous rate. The income, as it accrues, is re-invested in more units of the asset. In this way, buying e (-it ) units of a stock index portfolio today grows to exactly one unit at time T, and produces a net terminal value of _S T - S e ((r - i) T). For a stock index portfolio investment, the cost of carry rate equals the difference between the risk-free rate of interest r and the dividend yield rate i; and equals the difference between the domestic interest rate r and the foreign interest rate i for a foreign currency investment. The total cost of carry paid at time T is Carry costs = S [e ((r - i) T) 1 ]. (1) The value of a forward contract is linked to the cost of carry of the underlying asset. Since a forward contract requires its buyer to accept delivery of the underlying asset at time T, buying a forward contract today is a perfect substitute for buying the asset today and carrying it until time T. The present value of the payment obligation under the forward contract strategy is f e (-rt), and the present value of the latter strategy is S e (-it). Since both strategies provide exactly one unit of the asset at time T, (i.e., _S T ), their costs must be identical, f e (-rt) = S e (-it). (2a) 53

4 If the relation (2a) does not hold, costless arbitrage profits would be possible by selling the overpriced instrument and simultaneously buying the under-priced one. The relation (2a) is the present value version of the cost of carry relation. A more familiar version is the future value form, f = S e [(r - i) T]. (2b) When the prices of the forward and the asset are such that Equation (2a) and/or Equation (2b) hold exactly, the forward market is said to be at full carry. Unless costless arbitrage is somehow impeded, the forward market will always be at full carry. The difference between the forward price and the asset price is frequently referred to as the basis Non Deliverable Forward Contracts: An NDF is a short-term committed forward cash settlement currency derivative instrument. It is essentially an outright (forward) FX contract whereby on the contracted settlement date, profit or loss is adjusted between the two counterparties based on the difference between the contracted NDF rate and the prevailing spot FX rates on an agreed notional amount. Non-Deliverable Forward (NDF) has become a popular instrument available to corporate treasurers who wish to hedge their exposure to foreign currencies which are not internationally traded and which do not possess a forward market for non-domestic players like Indian Rupee (INR), Philippine Peso (INR), Taiwan Dollars (TWD), Korean Won (KRW), Indonesian rupiah (IDR) and Chinese Renminbi (CNY). NDFs are also distinct from deliverable forwards in that NDFs trade outside the direct jurisdiction of the authorities of the corresponding currencies The NDF markets for some Asian currencies have existed at least since the mid 1990 s. NDFs are commonly quoted for time periods of one month up to one year, and are normally quoted and settled in U.S. dollars. Thus they have become a popular instrument for corporations seeking to hedge exposure to foreign currencies that are not internationally traded.(singhania K., 2004) The NDF market is typically an offshore market, free from regulatory control of the currency s home monetary authority. New York, Singapore, and London are major centers with the first two specializing in Latin American and Asian currencies respectively and the third across both sets. Hong Kong is an important trading centre for Asian currency NDFs as well. In 2003, six Asian Currencies the Korean Won, Chinese Renminbi, New Taiwan Dollar, Indonesian Rupiah, Philippine Peso, and the Indian Rupee constituted a majority of global NDF markets with the remaining volume coming largely from Latin American currencies and the Russian Rubble. For the Indian Rupee, NDFs are traded primarily in Singapore and Hong Kong with Dubai and Bahrain with comparatively low volume. The NDF market for the Indian Rupee started back in the 1990 s when it provided the foreign investors in India the only avenue of hedging currency risk, in the presence of severe exchange restrictions in a scenario where the Rupee was expected to have a secular decline. Foreign investors would generally sell the NDF Rupee contracts to hedge their underlying positions. The 54

5 opposite side would typically be taken by Indian trading companies and exporters who could make arbitrage profits as they had access to both the onshore currency markets as well as Dollar flows outside the country. Multinationals also use the Indian Rupee NDF market to hedge their exposure. There is also a demand from arbitrageurs playing the two forward markets. Onshore financial institutions are prohibited from participating in the NDF market. Several major multinational banks like Deutsche Bank, UBS, and Citibank are active traders in the Rupee NDF market. The activity there has risen by over 7.5 times in the last few years while total foreign investment in India has roughly trebled during the period and with easing currency restrictions. Table 4.1: Currency wise access to onshore forward market by non-residents 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 requirements 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 Source: Ma Guonam et al., HSBC (2003); national data. Generally participants take position in the INR NDF market based on their view on where the INR spot will be, after a certain time period in the on shore market. Entities who have access to both the market take advantage of the arbitrage opportunities, if available between both the markets. Arbitrage opportunity is generally available between the INR NDF market and the on shore market. Rupee dealers in India also keep track of the INR NDF market before taking a view on the INR. Though no authentic data are available, the daily average volume in INR NDF market is estimated to be around USD million. Reference: BIS ( Example of NDF Assume on 5 January 2009, Hind Corporation sells INR mio. NDF to Cosmic Bank threemonths forward for value 6 April 2009, at the NDF rate of USD/INR Rate fixing date 5 th April By transacting the above, Hind has locked-in the 3-month forward INR selling rate at USD/INR 48.50, which is equivalent to Hind buying USD 1 mio. (INR mio.). On 5th April 2009, the fixing date, both parties will compare the NDF rate with the prevailing USD/INR fixing rate as RBI USD/INR reference spot rate. There are 3 possible scenarios:- a) The prevailing USD/INR rate is equal to the NDF rate or b) The prevailing USD/INR rate is higher than the NDF rate or c) The prevailing USD/INR rate is lower than the NDF rate. 55

6 Now after 3 months the prevailing USD/INR is on 5 th April In this instance, the INR has weakened and there is a difference of 3 INR. Hence Cosmic Bank will pay the difference to Hind Corporation on the settlement date (6 th April 2009) As the settlement is in USD, Cosmic Bank will have to pay Hind Corporation the difference in USD; this can be worked out by the following method. On 5/1/2009 Hind sells INR mio = USD 1,000, (as USD/INR 48.50) On 5/4/2009 the dollar equivalent will be (for INR mio = USD 941, ) (As the exchange rate is USD/INR 51.50) It yields the profit of USD 58, to the party (Difference) Hence on 6/4/09, Cosmic Bank pays USD 58, to Hind Corporation and the NDF is settled. Assuming the rate other than the realized rate If the USD/INR exchange rate were on 5th April In this instance INR has strengthened and there is a difference of 5 INR. Hence Hind Corporation will pay the difference to Cosmic Bank on the settlement date (6 th April 2009). On 5/1/09 Hind sells INR mio = USD 1,000, USD/INR On 5/4/09 INR mio = USD 11,14, (as the rate is USD/INR 43.50) Thus there will be loss to the party of USD (Difference) Hence on 6/4/09, Hind Corporation pays USD to Cosmic Bank and the NDF would have been settled for the given exchange rate. 4.2 SWAPS: Introduction: Swap is a derivative instrument. It is a transaction in which two parties agree to pay each other a series of cash flows over a specified period of time. The four popular kinds of swaps are currency swap, interest rate swap, equity swap and commodity swap. Over the years many varieties of swaps have evolved. The common types of swap involve one party making a series of fixed payments and receiving a series of floating payments. In some swap both the parties make floating payment with different bases. Swaps can be used to hedge certain risks such as interest rate risk, or to speculate on changes in the underlying prices. Most swaps are traded Over The Counter (OTC), "tailor-made" for the counter parties. Some types of swaps are also exchanged on futures markets, for instance Chicago Mercantile Exchange Holdings Inc., the largest U.S. futures market, the Chicago Board Options Exchange and Frankfurt-based Eurex AG. The Bank for International Settlements (BIS) publishes statistics on the notional amounts outstanding in the OTC Derivatives market. At the end of 2006, this was USD trillion (that is, more than 8.5 times the 2006 gross world product). The majority of this (USD trillion) was due to interest rate swaps. These split by currency is as follows: 56

7 Table: 4.2 Currency wise notional amounts outstanding in the OTC Derivatives market from 2000 to Notional outstanding (Year End) in USD trillion Currency Euro US dollar Japanese yen Pound sterling Swiss franc (Source: If a swap transaction involves exchange of interest payments then it is known as an interest rate swap. The first interest rate swap took place in London in 1979 and further in 1981, Salomon Brothers negotiated a benchmark currency swap between IBM and the World Bank. Later in1984 banks started developing warehousing whereby a single counter party would approach bank and bank would play a role of counter party. A temporary hedge would be taken in the bond or futures market with opposite exposure until a suitable counter party could be found. Standard terms introduced by ISDA and BBA in 1985 also helped in growth in swap market. Introduction of swaps in India: OTC rupee derivatives in the form of Forward Rate Agreements (FRAs)/Interest Rate Swaps (IRS) - were introduced by RBI in India in July These derivatives enable banks, primary dealers (PDs) and all-india financial institutions (FIs) to hedge interest rate risk for their own balance sheet management and for market-making purposes. Banks/PDs/FIs can undertake different types of plain vanilla FRAs/IRS. Swaps having explicit/implicit option features such as caps/floors/collars are not permitted Interest Rate Swap: There are two parties in a swap transaction, fixed rate payer/ receiver and floating rate receiver/ payer. A fixed rate payer is the provider of floating rate funds and vice a versa. The following illustration will explain this point: Suppose two firms A and B have been offered the following rates per annum on a Rs. 1 million five years loan from the market: Table 4.3: Interest rates combination to two firms Firm Fixed Rate Floating rate A 12% MIBOR % B 14% MIBOR % 57

8 Firm A requires a floating rate loan and Firm B needs a fixed rate loan. Initially we will assume a direct dealing between these two parties; then after we will consider swap with intermediation of Bank. The first step in designing the swap deal is to calculate the quality differential spread as per absolute advantage or as per comparative advantage. Table 4.4: Calculation of QSD for the Swap deal Firm Fixed Rate Floating rate A 12% MIBOR % B 14% MIBOR % QSD 02 % - 01% = 1 % Here there is comparative advantage to firm B in floating rate compared to fixed rate. Therefore the difference in both rates will be deducted to arrive at the spread differentials. If we pass on the benefits of swap equally between these two parties then each party would get a benefit of 0.5%. Therefore the net cost to firm B should be 14% - 0.5% = 13.5%. Similarly to firm A cost should be (MIBOR + 1%) 0.5% = MIBOR + 0.5%. The swap can be structured as follows; Diagram 4.1: Swap deal between Firm A and Firm B. FIRM A MIBOR + 0.5% 12% FIRM B 12% MIBOR+ 2% Market Market In the diagram Firm A borrows from the market Rs. 1 12% which is other than their objective i.e. floating rate loan and Firm B MIBOR + 2% (floating) even though their objective is in Fixed loan. Now the firm A agrees to pay MIBOR + 0.5% to firm B in exchange of firm B s acceptance of paying 12% fixed to firm A. which is the rate at which firm A has borrowed from the Market. Thus the net cost to firm A will be [-12% + 12% -(MIBOR + 0.5%)] = MIBOR + 0.5%. Similarly firm B pays to firm A 12% and receives MIBOR + 0.5% which will net their cost to 12% +(MIBOR + 0.5%) (MIBOR +2%) = 13.5% which is less by 0.5% compared to 14% rate, if they individually go for loan borrowing in the market. Interest rate swap with intermediation of Bank: Generally the bank s intermediation is required to design any swap deal. In that case the Bank charges its commission. In the above example suppose Bank charges 0.2% p.a. as commission and both parties will share the 58

9 remaining spread equally i.e. 0.4% each, then the swap can be restructured as follows (other things are assumed as it is.) Diagram 4.2: Swap deal between Firm A and Firm B with intermediary of Bank MIBOR+ 0.6 % MIBOR+ 2 % FIRM A BANK FIRM B 12% 13.6 % 12% MIBOR+ 2% Market Market Table 4.5: Calculation of the net gain to the Bank: BANK Fixed Floating RECEIPT 13.6% MIBOR+0.6% PAYMENT 12% MIBOR + 2 % NET + 1.6% - (1.4%) = (+0.2%) Thus Bank is getting 0.2% commission from the spread and each party gets 0.4% of spread each. This swap is known as plain-vanilla swap. Other categories of swap are floating to floating or fixed-to- fixed (in different currencies). 59

10 4.2.3 Currency Swap: Currency swaps are used for yield enhancement as well as for risk containment. This can be explained from the following hypothetical situation. Suppose an Indian firm establishes one subsidiary in U.S. and one U.S. firm has one subsidiary in India. Now both these subsidiaries want funds for expansion/diversification. If the U.S. parent manages the funds of its subsidiary then it will borrow US$ and converts it into rupees at the prevailing exchange rate. The opposite will be the situation with Indian firm. If we assume that the requirement of funds of both the firms is equivalent, then they can avoid exchange rate risk by entering into swap agreement. This is because every year the subsidiary will generate revenues in the currency, where they are established. But the interest payment will have to be made in the currency of parent country and also the repayment of loan would also be done in parent country s currency. This exposes both the subsidiary firms to exchange rate risk. Moreover if the subsidiary gets loan from the host country and if it is not very much known in the host country then they have to pay higher rate of interest than what rate is offered to the domestic company. Considering this situation if the Indian parent company borrows rupee loan for the U.S. subsidiary and similarly if the U.S. parent borrows loan for Indian subsidiary in US$ and then they swap the amounts to each other s subsidiary. Thus both the firms could get benefit of this contract. Firstly they avoid exchange rate risk because there is no transition of funds cross border and secondly the domestic companies are offered loans at cheaper rates. After the exchange of principal, the U.S. subsidiary will pay regular rupee interest to the Indian firm and the Indian subsidiary will pay US$ interest amount regularly to the U.S. parent out of its revenue which is also in US$. At the end there will be re-exchange of principal amounts by both subsidiaries. Thus a currency swap generally involves the following steps: Initial exchange of principal Exchange of interest rate Re-exchange of the principal at the end of the contract. A numerical example explaining the above situation is given below: Suppose company A is an Indian manufacturer, wishes to borrow U.S. $ at a fixed rate of interest for its business in California. Company B is a U.S. manufacturer established in Ahmedabad Special Economy Zone (SEZ) wishes to borrow rupees at a fixed rate of interest. Indian firm needs U.S.$ 10,00,000 while U.S. manufacturer wants Rs. 5,00,00,000 when the exchange rate is 1 US$ = INR They have been quoted the following rates per annum: Table 4.6: Interest rates offered to two firms COMPANY RUPEE (%) DOLLAR (%) A 14.00% 7.00 % B 13.00% 4.80 % Suppose the bank acting as an intermediary wants 20 basis points as swap charges and each party would share benefit equally. The swap can be designed as below. 60

11 Table 4.7: Calculation of QSD for the Swap deal: COMPANY RUPEE (%) DOLLAR (%) A 14.00% 7.00 % B 13.00% 4.80 % QSD 1.00 % % = (1.20%) In this case, the U.S. Company (i.e. Company B) is in a dominant position as they are offered less interest in both the currencies. So comparative advantage theory is applicable and the spread would be considered as the difference (and not the addition) of two differences between the rates. Here the bank is charging 20 basis points i.e. 0.2% of total spread of 1.20% then each party /company would gain 50 basis points i.e. 0.5% each. Therefore the net cost to company A would be 6.50 % $ instead of 7% which is offered to them by U.S. market if they borrow on their own. Similarly company B would have a net cost of 12.5% INR. The swap deal can be explained with the following diagram. Diagram 4.3: Currency Swap deal between Firm A and Firm B with intermediary of Bank 6.50 %($) 4.8%($) COMPANY A BANK COMPANY B 14% (Rs.) 12.5 %(Rs.) 14% (Rs) 4.8 %($) MARKET MARKET Table 4.8: Calculation of the net gain to the Bank for currency Swap BANK INR (%) US$(%) RECEIPT % 6.50 % PAYMENT % 4.80 % NET (-1.5 %) + (1.7%) = 0.2 % Thus Bank is gaining its agreed charges of 20 basis points while each company is gaining 50 basis points each in terms of cost reduction with swap. Many firms enter into swap agreement with notional principal without any direct hedging purpose but for the yield gain of spread from the swap. 61

12 4.2.4 Limitations of Swap: It is difficult to choose the opposite party to the swap transaction for the swap dealer when one party approaches him. The swap deal can not be terminated without the agreement of the parties involved in the transaction. The default party risk prevails, as no mark to marking is there in swap. Less growth of the secondary market for swap, that reduces liquidity. The swap market is not exchange controlled and it is an OTC market. Therefore assessment of creditworthiness requires extra time and cost Valuation of Swaps: The value of a swap is the net present value (NPV) of all future cash flows. Initially, the terms of a swap contract are such that the NPV of all future cash flows is equal to zero. In a plain vanilla fixed-to-floating interest rate swap, where Company A pays a fixed rate and Company B pays a floating rate. In such an agreement the fixed rate would be such that the present value of future fixed rate payments by Company A are equal to the present value of the expected future floating rate payments (i.e. the NPV is zero). Where this is not the case, an Arbitrageur, X, will: 1. Assume the position with the lower present value of payments, and borrow funds equal to this present value 2. Meet the cash flow obligations on the position by using the borrowed funds, and receive the corresponding payments - which have a higher present value 3. Use the received payments to repay the debt on the borrowed funds 4. Earn the difference - where the difference between the present value of the loan and the present value of the inflows is the arbitrage profit. Thus a swap can be assumed as the portfolio of borrowing and lending. A firm which converts its fixed rate obligations into floating rate can be compared with a firm that has raised bonds with a fixed coupon rate and then invest in the floating rate deposits.(chance Don, 2004) The valuation of a currency swap can be explained with numerical example as follows: Suppose an American firm has an existing swap agreement with a British firm. The original exchange rate was US$ 1.35 = 1. Now currency exchange rate is US$ 1.30 = 1. The fixed interest rates for the swap are 8% for Sterling and 5% for US$. Interest payments are annual and such payment has just been exchanged. The swap has a remaining life of four years. The American firm is a recipient of sterling ( ) and a payer of dollars. The original amounts agreed were US$ 13.5 million and 10 million. At present the interest rate in US$ is 4% and in sterling is 6%. From this information we can calculate the value of the swap to both the firms by calculating the present values of their cash inflows and cash outflows. Then by calculating their difference in 62

13 one currency we can comment on the profit or loss to both these parties. As it is a zero sum deal, the profit of one firm will become loss to the other firm. We consider the payoff from the U.S. firm s point of view. As they are recipient of sterling ( ), their cash inflows are in terms while outflows are in US$ terms. The following table shows these calculations: Table 4.9: Inflows and outflows from Currency Swap YEAR INFLOWS ( ) In millions OUTFLOWS ($) In millions Calculations of Present value of inflows (Discount factor will be 6% which is the current rate of interest in ): P.V. of inflow = [(0.8)/ (1.06) + (0.8/(1.06) 2 + (0.8)/ (1.06) 3 + (0.8)/ (1.06) 4 + (10)/ (1.08) 4 ] = millions P.V. of outflow = [0.675 * PVIFA (4%, 4 yrs.) * PVIF (4%, 4 yrs.) ] = US $ millions. If we convert millions in $ at the current exchange rate i.e. 1.3 $ per pound sterling then we would get $ millions. Now the value of swap to the American firm would be difference between the P.V. of inflow and outflows. i.e. US$ ( millions) = $ approximately. The same will be the profit for British firm in the swap. Thus the swap valuation depends on the present rates of interest in two underlying currencies as well as the prevailing currency exchange rate Pricing of Interest Rate Swap: The pricing of swap means derivation of fixed rate (agreed upon rate) for the one leg of swap. Here we have to use the term structure of interest rate at the contract initiation date. For pricing a swap firstly the present value of both future fixed and floating rate payments are found out. To avoid arbitrage, the present value of fixed and floating rate cash flow must be same. In order to find out the present value of fixed rate payments, term structure of interest rates is considered for appropriate period. The cash flow for floating rate payment is known for one period only. Therefore the present value of single cash flow is only calculated in case of floating rate payment. It is considered as 1. Because the LIBOR for the interest calculation and LIBOR used for discounting are same at the beginning of payment period and also at the end of payment period. (Chance Don, 2008) 63

14 For simplicity of calculations, portfolio of two bonds is considered. The investor has short sold the fixed rate paying Bond and invested the proceeds in Floating rate paying Bond. The following formula shows the stepwise calculations for swap pricing. The assumed agreed rate for fixed leg of swap is assumed as R, which is to be derived. Assume the principal of Re. 1 for interest calculations. 1. Value of Floating Rate Bond can be worked out by the following formula. 2. At the beginning or at end of any payment period V ( FLRTB) =1. V ( FLRTB ) t1 1+ L0( t 1 ) 360 = t1 t 1+ Lt( t1 ) 360 (Between payment dates 0 and 1: i.e. at time t) Here V ( FLRTB) = Present Value of floating rate payments of Bond. Value of fixed rate bond: n ti ti 1 3. VFXRTB = R B0( ti) + B0( tn) i= Where B ( 1) = 0 t t1 1+ L0( t1 ) And B0( ) = tn t1 1+ L0( tn ) 360 Formula for calculating fixed rate for swap can be written as follows: n ( ) 0( ) 0( ) V = R q B + B FXRTB ti tn i= 1 Where ( t( ) t i ( i 1) ) q = Which remains constant e.g. ( ) = ( )

15 Now, the (V FLRTB ) and (V FXRTB ) should be same for no arbitrage. n 1 = R( q) B0( t ) + B0( t ) i= 1 i n R and q are constant over here, therefore the formula can be re-written as follows: n 1 = R* ( q) B0( ti) + B0 ( tn) i= 1 This can be re-arranged as follows: n = n i i= 1 ( 1 B0 ( t )) n R = n ( q) B0 ( ti ) i= 1 1 B ( ) R* 0 ( q t ) B0 ( t ) ( 1 B0( t )) R = 1 n n q B0( ti ) i= 1 This is the formula for calculating the Fixed agreed upon rate for a interest rate swap contract. The following example explains the application of the derived formula for interest swap pricing. Example: A company enters into a two year Rs. 50,00,000 notional principal interest rate swap. It promises to pay a fixed rate and receive LIBOR. The payments are made every six months. Assuming 180 days period for each interest payment and considering 360 days basis, the term structure of interest rate is given below: Table 4.10: Interest rates offered at different maturity periods Time period Rates annualized (%) 180 days days days days 12 65

16 By applying the formula for R we will get the following answer 1 ( 1 B0( )) tn R = =» R = n q *(100) = B ( ti ) i= 1 The excel calculations give the following results: Table 4.11: Calculation of the Fixed agreed upon rate for interest rate swap contract Discounted Bond Annualized Rates Time period price (Bo) values of Principal Re fixed rate of swap R = % By solving with Excel worksheet we get R = %. This rate is the fixed rate for plain vanilla swap. 66

17 4.3 FUTURES: Introduction: A futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future at a certain price. Future contracts are standardized and exchange traded. To provide enough liquidity in the futures contract, the exchange specifies certain standard features of the contract. It is a standardized contract with standard underlying instrument, standard quantity and quality of the underlying instrument that can be delivered and a standard timing of such settlement. The futures contracts are generally offset prior to maturity by entering into an equal and opposite transaction. As per NSE data more than 99% of futures transactions are offset this way. Distinction between futures and forwards can be summarized as follows: Table 4.12: Distinction between futures and forwards Futures Forwards Trading on an organized exchange Over the counter in nature Standardized contract terms Customized contract terms More liquid Less liquid Requires margin payments No margin payment Follows daily settlement Settlement happens only at end of period (Source: NCFM Derivatives Market (Dealers) module) Pricing of Futures: The relationship between futures price and spot price can be written in terms of cost of carry. This measures the storage cost plus the interest paid to finance the asset less the income earned on the asset. For non-dividend paying stock, the cost of carry is r (rate of interest) because there are no storage costs and no income is earned. For an equity index, it is r-q (where q is dividend earned on stock portfolio of underlying index) as income is earned at rate q on the asset. For a currency, it is r- r f, where r f is interest on foreign currency, For a commodity with storage cost that are a proportion u of price, it is r + u; and likewise. Defining cost of carry as c for an investment asset, the futures price is F 0 = S 0 e ct 67

18 For a consumption asset, it is F 0 = S 0 e (c-y) T Where y is the convenience yield. (Source: Futures and options markets by John C. Hull) The effective price of the underlying asset can be found out by using futures as follows: Suppose Sp 1 is the spot price at time T 1 Sp 2 is the spot price at time T 2 F t1 is the futures price at time T 1 F t2 is the futures price at time T 2 Sp 1 - F t1 = Basis at time T 1 = b 1 Sp 2 - F t2 = Basis at time T 2 = b 2 Assume that an exporter is going to receive foreign exchange at time T 2. Therefore to hedge his position (to avoid the unfavorable movement of exchange rate i.e. expecting the appreciation of home currency at that time) he enters into short currency futures contract at time T 1 for price F t1 He closes his position at time T 2 by going long in currency futures. The payoff will be calculated as F t1 - F t2 (i.e. the difference between the selling and purchase price of futures.) He will actually sell the foreign exchange in the market at ongoing exchange rate at time T 2 i.e. Sp 2. The effective price at which the foreign exchange sold is; = Sp 2 + ( F t1 - F t2 ) = Ft 1 + ( Sp 2 - F t2 ) = F t1 + b 2 Where b 2 represents basis at time T 2 as defined earlier. As b 2 is unknown, the futures transaction is exposed to risk. If basis remains constant i.e. b 1 = b 2, then the effective price will be Ft 1 + ( Sp 1 - F t1 ) = Sp 2. 68

19 Here the risk is completely eliminated and the home currency inflow will be exactly as price of underling at T 1. It means you have freezed the spot rate for future execution Concept of Hedge ratio: The market is exposed to basis risk, as the abovementioned situation does not always work; the hedge ratio is to be found out because the exposure in futures has to be different than the exposure in the underlying asset. A hedger has to determine the number of futures contracts that provide best hedge for his exposure. It helps the hedger to determine the number of contracts that must be entered into for minimizing the risk of the combined cash-futures position. The hedge ratio is defined as the number of futures contracts to hold for a given position in the underlying asset. Futures Position Hedge Ratio = Underlying Asset Position The Minimum Variance Hedge Ratio: A portfolio theory is used to derive the mathematical model for defining minimum variance hedge ratio as the proportion of the futures to the cash position that minimizes the net price change risk. If h stands for minimum variance hedge ratio then: F*σS p h= σf t p F p = Coefficient of correlation between S p and F t σs p = Standard deviation of S p σf t = Standard deviation of F t S p = Change in the spot price during the period of hedging F t = Change in the futures price during the period of hedging The following example explains the concept of hedging using currency futures. Assume a U.S. based exporter is exporting goods to his U.K. based client. On November3 2008, the exporter got the confirmation from the U.K. importer that the payment of Pound sterling 6,25,000 will be made on January Thus the U. S. exporter is exposed to the risk due to currency fluctuations. The depreciation of pound sterling will create loss on the dollar receivables. To hedge this risk the exporter can sell GBP future contracts on the exchange. It can be performed as follows: Spot market rate on November 3 is (US$/ per GBP) is (as per cross rate on RBI reference rates). Expected cash inflows are (6, 25,000* = US$ 10,23,125 US$. If he were able to convert GBP into US$. But he cannot do so as he did not receive the GBP. Therefore he decided to go short on futures on GBP. 69

20 Futures market: Assuming one contract is of GBP 1, 25,000, he has to enter into five sell contracts on GBP. Suppose the rate is for expiry February So the equivalent notional amount in US$ will be 10,25,000 ( i.e. 6,25,000 * ) On January 30, 2009 SPOT MARKET Dollar has appreciated and the spot rate is (US$ / per GBP). The dollar value of GBP 6,25,000 now is US$ 8,90,187. Thus the loss on spot position is (10, 23,125 8,90,187 = US$ 1,32,938) On January 30, 2009 FUTURES MARKET Buy five February GBP futures contracts. Let the futures rate be It gives the exporter the notional right to buy GBP 6,25,000 by paying US$ 8,92,063.( i.e. 6,25,000* ) Thus profit on the futures contract is (US$ 10,25,000 8,92,063) = US$ 1,32,938. The loss in the spot market arising from the appreciation of US$, is set off by the profit in the futures contract. Here in this example the exporter finally receives the payment as per the rate on November 3, This has happened because of the same basis change in spot and futures market, i.e. No basis risk. But generally, because of basis risk, the exposure in the futures contract should be different than the exposure in the spot market. For that the concept of hedge ratio is applied as explained earlier. Thus we can summarize the hedging procedure as follows: Hedging in the futures market involves a two step process. Depending upon the cash/spot market position, a hedger initially either buys or sells futures. For example, an investor who owns or plans to purchase equity stock will sell futures to hedge this cash position. A long hedge involves purchasing futures to protect itself a price increase in the underlying, prior to purchasing it either in the spot or forward market. In the second step, once cash market transaction materializes, the futures position is closed out i.e. if the person has gone short a futures contract will now go long on the same contract. It is worth noting that both futures transactions should have same size and expiry/ delivery month. Application of Futures as Speculation: For this if you are bullish on the security then you buy futures. Suppose a speculator who has a view of bullish trend of the market. He believes that a particular security that trades at Rs. 500 is undervalued and expects the price to go up in the next two months. 70

21 If he buys 200 shares then his investment would be Rs. 1,00,000. Suppose after two months if the price moves up to Rs. 510 in two months, then his portfolio value enhances to Rs. (510*200 = Rs. 1,02,000) i.e. a 12% annual basis return. If he purchases stock futures instead of stock purchase then the return can be calculated as follows: Suppose the futures, currently trades at Rs If the minimum contract value is Rs. 1,00,000 then he buys 200 security futures (lot size) for which he pays margin of Rs. 20,000. After two months, the price of futures increases to Rs. 510 in two months period. On the day of expiration, the futures price converges to the spot price and he earns a profit of Rs. (( ) * 200) Rs This will be equal to annual return of 24%. Thus because of the leverage on futures the security futures form an attractive means for speculation. If the view of investor becomes wrong and the price of underlying stock declines then the losses will be manifold compare to cash position in stock. Similarly for speculation on bearish stock, the opposite strategy can be adopted. If the investor can t do short selling in a particular stock then he cannot take advantage of his bearish view of the market price. He can at most go for intra-day short selling. But with futures, he can always go short at the on going futures price and after a month or two, he can square up the position by going long, or can exercise it on expiry Stock index futures: a) Meaning: When the underlying is any stock composite index, i.e. sensex or nifty in India, then it is called Stock Index Futures. Index futures offer ease of use for hedging any portfolio of its composition. They are cash settled and hence do not suffer from any settlement delays and problems related to delivery. The contract specifications for S & P Nifty Futures are given below: Table 4.13: The contract specifications for S & P Nifty Futures Underlying index S & P CNX Nifty Exchange of Trading NSE India Ltd. Contract Size Permitted lot size is 100 (Minimum value Rs. 2,00,000) Price steps Re Price bands Not applicable Trading Cycle Maximum 3 months trading cycle Expiry day Last Thursday of the month Settlement basis Mark to market and final settlement will be cash settled on T+1 basis Settlement price Daily settlement price will be the closing price of futures for the trading day and the final settlement price shall be the closing value of the underlying index on the last trading day. (Source: nseindia) 71

22 b) Pricing Of Index Futures: The price can be decided as follows: Consider an investor who wants to hold a portfolio of market index for a period of one year. During the period of his holding in one year, he receives dividends, and at the end of the year, he will have capital gain / loss by selling the portfolio. Suppose the current market index is Io and at expiration its value is I t and the dividends received are D t then, the rupee return earned by the investor can be written as ( I t I o ) + D t If an alternative of index futures is considered then, he will buy the index futures contract and invest all his money into risk free securities. (Margin money is ignored here). If the current futures price is F o, the expiration day price as F t and the interest earned in rupees as R f, the rupee return from index futures to the investor will be ( F t F o ) + R f If the investor has to be neutral between the two alternatives then both these rupee returns should be same i.e. ( I t I o ) + D t = ( F t F o ) + R f As on expiry the spot and futures prices converge, F t = I t Thus the equation will be reduced to F o = I o + (R f - D t ) Therefore the current index futures price must be equal to the index value plus the difference between the risk free interest and dividends expected over the life of the contract. The difference of interest and dividend is called the cost of carry. This cost of carry is generally positive. 72

23 c) Application of Index Futures: Index futures can be used for arbitrage and hedging purposes. In the stock market, an arbitrage opportunity arises when the same scrip trades at different prices in different markets. In such a situation, investors buy the stock in one market at a lower price and sell it in the other for more, cashing in on the difference, net of the transaction cost. However, such an opportunity vanishes quickly as investors rush in to take advantage of this price difference. Thus, the arbitrage process helps correct the discrepancies in pricing. The same principle can be applied to index futures. Being a derivative product, index futures derive their value from the stocks that constitute the index (either the Sensex or the Nifty). At the same time, the index futures value is linked to the stock index value. Application Of Stock Index Futures For Arbitrage: On 30 th April the Nifty is traded at The risk free rate is 6.5% p.a., the annual dividend yield is suppose 3.5% p.a., and the July Nifty futures contract i.e. 90 days from here onwards is at The lot size for Nifty futures is 50. The theoretical index futures pricing can be arrived at as follows: F o = [(3330* 0.065* 0.25)] [3330*0.035*0.25] = = Here the index future is overpriced than the calculated theoretical price. Arbitrage strategy: 1. Short Nifty futures at Long cash Nifty at Now the investor will earn risk less profit of Rs. [ ( * 50 = Rs ], whether the bullish or bearish trend prevails. We can consider two extreme situations on expiry of July futures. 1. Suppose the Nifty closes at 3030,then arbitrageur s profit can be calculated as follows: 73

24 Table 4.14: Calculation of arbitrage profit from nifty futures in bearish trend Particulars Profit from short sell of Nifty futures [ ] *50 Cash dividend 3.5% [( 3330 * * 0.25)] * 50 Less: Loss on sale of stock portfolio index [ ] *50 Interest foregone [3330*0.065*50*0.25] Total pay-off (ignoring transaction cost) Rs 19, , Suppose Nifty closes at 3663 on expiry of futures contract: Table 4.15: Calculation of arbitrage profit form nifty futures in bullish trend Particulars Loss from short sell of Nifty futures [ ] *50 Cash dividend 3.5% [( 3330 * * 0.25)] * 50 Profit on sale of stock portfolio index [ ] *50 Interest foregone [3330*0.065*50*0.25] Total pay-off (ignoring transaction cost) Rs , The annual return is [ /(50* 3330)] *4 = = 7.81% This return exceeds the risk free rate of 6.5%. Application of Stock Index Futures for Hedging: The basic Principle is: "If long in cash underlying: Short Future; If short in cash underlying: Long Future" This is illustrated in the following example. Example: If you have bought 500 shares of company A and want to hedge against market movements, you should short an appropriate amount of Index Futures. This will reduce your overall exposure to events affecting the whole market (systematic risk). Given this situation if 74

25 the entire market falls (most likely including Company A), then your loss in company A would be offset by the gains in your short position in Index Futures. Some instances where hedging strategies are useful include: Reducing the equity exposure of a Mutual Fund by selling Index Futures; Investing funds raised by new schemes in Index Futures so that market exposure is immediately taken. Another usage of futures is for portfolio beta management as explained below with numerical example. d) Beta Management: Stock index futures can be used to hedge an equity portfolio If P = Current value of the portfolio A = Current value of the stocks underlying one futures contract If the portfolio is identical to the index then a hedge ratio of 1 will be appropriate. The formula for number of futures contract is N * = (P / A) Suppose the index is representative of the market as a whole then appropriate hedge ratio can be written as * N P = β A Here β measures systematic risk. Hedging the exposure to the Price of an individual stock: An investor holds 1400 Infosys Technology equity shares. He is concerned about the volatility of the market during next month due to Parliamentary election results to be announced in May The current price( ) is Rs The current level of Nifty (Market Index) is 3380, and the June future price of Nifty is 3400.The beta of Infosys is 1.2. The lot size of Nifty is 50. Strategy: 1. Short 14 June futures contracts on Nifty (i.e. * N P = β = [1.2 * ((19,60,000)/ (3400*50)) ] = 14 approx.) A 75