FINANCIAL INSTRUMENTS 1

5.2 FINANCIAL INSTRUMENTS 1

There are a variety of financial instruments that may be used for multiple purposes, such as hedging, speculating, investing, and ‘money multiplying’ or leveraging. Their development and use require the ingenuity of financial engineers and the

1 This section is partly based on a paper written by students at ESSEC, Bernardo Dominguez, C´edric Lespiau and Philippe Pages in the Master of Finance programme. Their help is gratefully acknowledged.

DERIVATIVES FINANCE

care of practising investors. Financial instruments are essentially contracts of various denominations and conditions on financial assets. Contracts by definition, however, are an agreement between two or more parties that involves an exchange. The terms of the contract depend on the purpose of contracting, the contractees, the environment and the information available to each of the parties. Examples of contracts abound in business, and more generally in society. For example, one theory holds that a firm is nothing more than a nexus of contracts both internal and external in nature.

Financial contracts establish the terms of exchange between parties mostly for the purpose of managing contractors’ and contract holders’ risks. Derivative assets or derivative contracts are special forms of contract that derive their value from an underlying asset. Such assets are also called contingent claim assets, as their price is dependent upon the state of the underlying asset. For example, warrants, convertible bonds, convertible preferred stocks, options and forward contracts, etc. are some well-known derivatives. They are not the only ones, however. The intrinsic value of these assets depends on the objectives and the needs of the buyer and the seller as well as the right and obligations these assets confer on each of the parties. When the number of buyers and (or) sellers is very large, these contingent assets are often standardized to allow their free trading on an open market. Many derivatives remain over-the-counter (OTC) and are either not traded on a secondary market or are in general less traded and hence less liquid than their market counterparts. The demand for such trades has led to the creation of special stock exchanges (such as the Chicago, London, and Philadelphia commodities and currency exchanges) that manage the transactions of such assets. A number of such contingent assets and financial instruments are defined next.

5.2.1 Forward and futures contracts

A futures contract gives one side, the holder of the contract, the obligation to buy or sell a commodity, a foreign currency etc. at some specified future time at

a specified price, place, quantity, location and quality, according to the contract specification. The buyer or long side has at the end of the contract, called the maturity, the option to buy the underlying asset at a predetermined price and sell it back at the market price if he wishes to do so. The seller or short side (provider), however, has the obligation to sell the underlying asset at the predetermined price. In futures contracts, the exchange of the underlying asset at a predetermined price is between anonymous parties which is not the case in OTC forward contracts. Financial futures are used essentially for trading, hedging and arbitrage.

Futures contracts can be traded on the CBOT (the Chicago Board of Trade) and the CME (the Chicago Mercantile Exchange), as well as on many trading floors in the world. Further, many commodities, currencies, stocks etc. are traded daily in staggering amounts (hundreds of billions of dollars). A futures price at time t with delivery at time T can be written by F(t, T ). If S(t) is the spot price, then clearly if t = T , we have by definition F(t, t) = S(t) and S(t) ≥ F(t, T ), T≥t .

115 The difference between the spot assets to be pledged in a future contract and

FINANCIAL INSTRUMENTS

its futures price is often called the ‘basis risk’ and is given by b(t, T ) = S(t) −

F (t, T ). It is the risk one suffers when reversing a futures contracts position. Imagine we need to buy in 3-month pork for a food chain. We may buy futures contracts today that deliver the asset at a predetermined price in 6 months. After

3 months, we reverse or sell our futures position. The payoff is thus the change in the futures price less the price paid for the underlying asset, or F(3, 6) −

F (0, 6) − S(3). If we were at maturity, only −F(0, 6) would remain. That is, the price of the underlying asset is set by a delayed physical transaction using futures contracts. However, if there remains a basis risk in the payoff, then −F(0, 6) +

b (3, 6) would remain. If the futures contract does not closely match the price of the underlying asset then the effectiveness of our hedging strategy will be reduced.

Futures contracts like forwards can be highly speculative instruments because they require no down payment since no financial exchange occurs before either maturity or the reversal of the position. Traders in the underlying assets can therefore use these markets to enhance their positions in the underlying asset either short or long. Unsurprisingly, a position in these contracts is considered levered or a borrowed position in the underlying asset, as the price of a forward and futures contract is nothing more than an arbitrage with the asset bought today using borrowed funds and delivered at maturity. There are differences between futures and forwards involving liquidity, marking to market, collaterals and delivery options, but these differences are generally glossed over.

The leverage implied in a futures contract explains why collaterals are required for forwards and marking to market for futures. In their absence, defaults would

be much more likely to happen. For example, for a short futures contract, when prices fall, the investor is making a virtual loss since he would have to sell at

a higher price than he started with (should he terminate his contract) and take an offsetting position by buying a futures contract. This is reflected in a ‘futures market’ when the bank adjusts the collateral account of the trader, called the margin. The margin starts at an initial level in, generally, the form of Treasury bills. It is adjusted every day to reflect the day’s gains or losses. Should the margin fall below a maintenance level, the trader will ask the investor to add funds to meet margin requirements. If the investor fails to meet such requirements, the trader cuts his losses by reversing the position.

A forward rate agreement (FRA) is an agreement made between two parties seeking generally to protect or hedge themselves against a future interest-rate or price movement, for a specific hedging period, by fixing the future interest rate or price at which they will buy or sell for a specific principal sum in a specified currency. It requires that settlement be effected between the parties in accordance with an established formula. Typically, forward contracts, unlike futures contracts are not traded and can therefore be tailored to specific needs. This means that contracts tend to be much higher in size, far less liquid and less competitively priced, but suffer from no basis risk. The price at time t of a forward contract at time T in the future can be written by p(t, T ) or by p(t, t + x), x = T − t and is defined by the (delivery) price for which the contract value is null at delivery

DERIVATIVES FINANCE

under risk neutral pricing.

E(Future spot rate − Forward rate) = 0

Of course, p(T , T ) = 1 and therefore the derivative of the price with respect to T (or x) is necessarily negative, reflecting the lower value of the asset in the future

compared to the same asset in the present. The relationship between forward rates and spot prices is a matter of intensive research and theories. For example, the theory of rational expectations suggests that we equate the expected future spot rate to the current forward rate, that is (see also the next chapter):

Forward rate = E (Future spot rate)

For example, if s t is the logarithm of the spot price of a currency at time t and f t is the logarithm of the 1 month forward price, the expectation hypothesis means that:

f t = E(s t +1 )

Note that if S t t =S t +1 −S t , then the rate of change,

t ) with s t = log S t . Empirical research has shown, at least for currencies forward, that it is mis- leading and therefore additional and alternative theories are often devised which introduce concepts of risk premium as well as the expected rate of depreciation to explain the incoherence between spot and forward market values and risk-neutral pricing.

Forward and futures contracts are not only used in financial and commodities markets. For example, a transport futures exchange has been set up on the In- ternet to help solve forward-planning problems faced by truckers and companies shipping around the world. The futures exchange enables companies to purchase transport futures, helping them to plan their freight requirements and shipments by road, rail and, possibly, barge. The exchange allows truckers and manufacturers to match transport capacity to their shipments and to match their spot requirements, buy and sell forward, and speculate on future movements of the market. This mar- ket completes other markets where one can buy and sell space on ocean-going ships. For example, London’s Baltic Exchange handles spot trades in dry cargo carriers and tankers.

5.2.2 Options

Options are instruments that let the buyer of the option (the long side) the right to exercise , for a price, called the premium, the delivery of a commodity, a stock,

a foreign currency etc. at a given price, called the strike price, at (within) a given time period, also called the exercise date. Such an option is called a European (American) CALL for the buyer. The seller of such an option (the short side), has by contrast the obligation to sell the option at the stated strike and exercise date.

A PUT option (the long side) provides an option to sell while for the short seller

117 this is an obligation to buy. There are many types of options, however. Below are

FINANCIAL INSTRUMENTS

a selected few (in the next two chapters we shall consider a far larger number of option contracts):

r Call option (long) (on foreign exchange (FX), deposit or futures etc.): an option contract that gives the holder the right to buy a specified amount of the

commodity, stock or foreign currency for a premium on or before an expiration date as stated above. A call option (short), however, is an obligation to maintain the terms of this contract.

r Put option (long) (on FX, commodity etc.): gives the right to sell a specified amount at the strike price on (or before, for an American option) a specific

expiration date. The short side of such a contract is an obligation, however, to meet the terms of this contract.

r Swaps (for interest rates, currency and cross-currency swaps, for example): transactions between two unrelated and independent borrowers, borrowing

identical principal amounts for the same period from different lenders and with an interest rate calculated on a different basis. The borrowers agree to make payments to each other based on the interest cost of the other’s borrowing. It is used both for arbitrage and to manage firm’s liabilities. It can facilitate access of funding in a particular currency, provide export credits or other credits in

a particular currency, provide access to various capital markets etc. These contracts are used intensively by banks and traders and will be discussed at length in the next chapter.

r Caps : a contract in which a seller pays a buyer predetermined payments at prespecified dates, with an interest (cap) rate calculated at later dates. If the

rate of reference (the variable rate) is superior to a guaranteed rate, then the cap rate becomes effective, meaning that the largest interest rate is applied.

r Floors : products consisting in buying a cap and at the same time selling another product at a price compensating exactly the buying price of the cap. In this case,

the floor is a contract in which the seller pays to the buyer for a predetermined period with a rate calculated at the fictive date. If the reference rate (the variable rate) is inferior to the guaranteed rate by the floor (rate), then the lower rate is applied.

Options again

Trading in options and other derivatives is not new. Derivative products were used by Japanese farmers and traders in the Middle Ages, who effectively bought and sold rice contracts. European financial markets have traded equity options since the seventeenth century. In the USA, derivative contracts initially started to trade in the CBOT (Chicago Board of Trade) in 1973. Derivatives were thus used for

a long time without stirring up much controversy. It is not the idea that is new, it is the volume of trade, the large variety of instruments and the significant and growing number of users trading in financial markets that has made derivatives a topic that attracts permanent attention.

Today, the most active derivative market is the CBOT, while the CME (Mercantile Stock Exchange) ranks second. Other active exchanges are the CBOE,

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PHLX, AMEX, NYSE and TSE (Toronto Stock Exchange). In Montreal a stock exchange devoted to derivatives was also started in 2001. In Europe the most active markets are LIFFE (London International Financial Futures Exchange), MATIF (March´e `a Terme International de France), DTB (Deutsche Terminbrose), and the EOE (Amsterdam’s European Options Exchange). The most voluminous markets in East Asia include TIFFE (Tokyo International Financial Futures Exchange), the Hong Kong Futures Exchange and SIMEX (Singapore International).

Options contracts in particular are traded on many trading floors and, mostly, they are defined in a standard manner. Nevertheless, there are also ‘over-the- counter options’ which are not traded in specific markets but are used in some contracts to fit specific needs. For example, there are ‘Bermudan and Asian op- tions’. The former option provides the right to exercise the option at several specific dates during the option lifetime while the latter defines the exercise price of the option as an average of the value attained over a certain time interval. Of course, each option, defined in a different way, will lead to alternative valuation formulas. More generally, there can be options on real assets, which are not traded but used to define a contract between two parties. For example, an airline com- pany contracts the acquisition (or the option to acquire) a new (technology) plane at some future time. The contract may involve a stream or a lump sum payment to the contractor (Boeing or Airbus) in exchange for the delivery of the plane at a specified time. Since payments are often made prior to the delivery of the plane,

a number of clauses are added in the contract to manage the risks sustained by each of the parties if any of the parties were to deviate from the contract stated terms (for example, late deliveries, technological obsolescence etc.). Similarly,

a manufacturer can enter into binding bilateral agreements with a supplier by which agreed (contracted) exchange terms are used as a substitute for the free market mechanism. This can involve future contractual prices, delivery rates at specific times (to reduce inventory holding costs) and, of course, a set of clauses intended to protect each party against possible failures by the other in fulfilling the terms of the contract. Throughout the above cases the advantage resulting from negotiating a contract is to reduce, for one or both parties, the uncertainty concerning future exchange operating and financial conditions. In this manner, the manufacturer will be eager to secure long-term sources of supplies, and their timely availability, while the investor, buyer of options, would seek to avoid too large a loss implied by the acquisition of a risky asset, currency or commodity, etc. Since for each contract there, necessarily, needs to be one (or many) buyer and one (or many) seller, the price of the contract can be interpreted as the outcome of a negotiation process where both parties have an inducement to enter into a contractual agreement. For example, the buyer and the seller of an option can

be conceived of as being involved in a game, the benefits of which for each of the players are deduced from premium and risk transfer. Note that the utility of entering into a contractual agreement is always positive ex-ante for all parties; otherwise there would not be any contractual agreement (unless such a contract were to be imposed on one of the parties!). When the number of buyers and sellers of such contracts becomes extremely large, transactions become ‘imper- sonal’ and it is the ‘market price’ that defines the value of the contract. Strategic

119 behaviours tend to break down the larger the group and prices tend to become

HEDGING AND INSTITUTIONS

more efficient.

Making decisions with options

We shall see in Chapter 7, ‘Options and Practice’, some approaches using options in hedging and in speculating. Decisions involving options are numerous, e.g.:

r Buy and sell; on the basis of the stock price and the remaining time to its exercise.

r Buy and sell; on the basis of estimated volatility of the underlying or related statistics.

r Use options to hedge downside risk. r Use stock options to motivate management and employees. r Use options and stock options for tax purposes. r Use options to raise money for investments.

These problems clearly require a competent understanding of options theory and financial markets and generally the ability to construct and compounds assets, options and other contracts into a portfolio of desirable characteristics. This is also called financial engineering and is also presented in the next chapter.

We shall use a theoretical valuation of options based on ‘risk-neutral proba- bilities’. ‘Uncertainty’, defined by ‘risk-neutral probabilities’, unlike traditional (historical) probabilities, determined by interacting market forces, reflects the market resolution of demand and supply (equilibrium) for assets of various risks. This difference contrasts two cultures. It is due to economic and financial as- sumptions that current market prices ‘endogenize’ future prices (states and their best forecast based on available information). If this is the case, and it is so in markets we call complete markets, the current price ought to be determined by an appropriate discounting of expected future values. In other words, it is the market that determines prices and not uncertainty. We shall calculate explicitly these ‘probabilities’ in the next chapter when we turn to the technical valuation of options.