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1. INTRODUCTION:
The financial risk faced by companies has increased tremendously over the last two decades and the payoffs of managing risk successfully are very high. In response to this increased risk and the incentive to manage it, older instruments of risk management such as forwards and futures have been expanded in scope, and many new instruments devised. The process of adaptation of existing financial instruments and processes to develop new ones, in order that financial market participants can effectively cope with the changing situation, is known as financial engineering (Marshall,1992:xv). Financial engineering is well on the way to becoming an independent discipline with its own professional bodies. An example is the American Association of Financial Engineers (AAFE), set up in 1991 (Marshall, 1992:61).
In this paper, we take a look at risk, the fundamental tools/methods of risk management, and the role of financial engineering in today's world.
2. FINANCIAL RISK:
The term "financial risk" covers the range of risks affecting financial outcomes, faced by a firm. Financial risk is essentially of two kinds: systematic and unsystematic. Systematic risk is that portion of risk which cannot be diversified away. Some of its components are listed below.
i. Business risk is the risk of fluctuations in sales revenue. It arises from macroeconomic factors such as economic swings and deregulation, and demand factors such as seasonality of demand. This risk is not totally systematic, however, and some of it can be reduced by diversification of the firm's operations. The risk of property loss, and product liability suits, can be insured against (Shapiro,1986: 215).
ii. Financing risk arises from leverage. It is possible to minimise it by restricting the amount of debt in the firm, even though there may be tax advantages to borrowing (Shapiro,1986:215).
iii. Inflation risk arises from unanticipated inflation. In international trade, it arises from movement away from purchasing power parity (PPP). Hedging is difficult in this case (Walsh,1990:56).
iv. Default, or credit risk is the risk of default of payment by debtors of the firm. Large banks use credit rating agencies, such as Moody's Investor Services and Standard and Poor's Corporation, to rate borrowers. Though this risk is mostly systematic, it can be diversified in some cases (e.g., by banks holding a large portfolio). Some forms of credit risk can be insured against, e.g., export credit (Shapiro, 1986: 225).
v. When it is difficult to buy or sell a financial instrument at its market price, then there is a marketability, or liquidity risk associated with it. This risk is undiversifiable and also completely systematic. Some insurance companies insure this risk to some extent (Shapiro,1986:225).
vi. Operating risk: Operating leverage is the commitment of the firm to fixed production charges (fixed costs). The greater the operating leverage, the greater the risk to the firm. Reducing operating leverage wherever possible, helps (Shapiro,1986:226) .
vii. Political risk can be both domestic and foreign; it is particularly high when operating in some politically unstable Third World countries. This risk is highly systematic and undiversifiable (Walsh,1990:55).
Unsystematic risk comprises primarily of price risks.
i. Interest rate risk arises both from fixed and floating rate debt. Unanticipated changes in floating interest rates can cause costs to rise. However, Putnam (1986) shows that the real interest rate on floating-rate debt is more or less fixed, while it is floating in case of fixed-rate debt. Thus the real interest costs are known with certainty in case of floating-rate debt. Effectively, therefore, floating-rate debt offers a long-run hedge against inflation risk (Putnam, 1986:241). It is clear that inflation and interest rate risks are closely related. At the same time, a fixed rate debt can cause financial difficulties in case interest rates drop. This is therefore a major risk faced by almost all companies. It can be hedged against in many ways.
ii. Currency (or foreign exchange) risk arises when cash inflows or outflows take place in foreign currency. This risk can be either diversified or hedged.
iii. Commodity price risk arises from unanticipated changes in commodity prices and can be hedged.
3. PRINCIPLES OF MANAGING RISK:
Financial literature has concerned itself mainly with the systematic risk of a firm, measured through its beta. In fact, as per the capital asset pricing model, not managing unsystematic risk does not increase the rate of return required by investors. However, by significantly lowering the level of the firm's expected cash flows, it can and does, in practice, reduce the value of the firm. It is necessary therefore to manage unsystematic risk in cases where it could adversely impact on a firm's existence (Shapiro,1986:216). Total risk is the sum of the systematic and unsystematic risks. Shapiro and Titman (1986) advocate a total risk approach to risk management. Total risk, being the sum of systematic and unsystematic risks, should be considered by the firm. The objective of the shareholders would then be to search for an optimal risk profile, where the marginal cost of bearing risk equals the marginal cost of managing it.
Risk management requires the identification of the risks to which the firm is exposed, quantification of these exposures - wherever possible, determination of the desired outcomes, and engineering a strategy to achieve these outcomes (Marshall,1992:239). A look at the coverage ratios is a good first step. But for detailed identification of risk, a series of cash budgets must be prepared using different economic variables and considering the use of different risk-reducing mechanisms (Shapiro,1986:222). Each time, the risk must be identified/ evaluated in terms of the probability of not being able to meet essential payments/ obligations.
Wherever possible, risk should be quantified. Non-financial companies can carry out a sensitivity analysis by making a computer model which determines the relationship of inputs/ outputs/ sales, etc., to different prices, such as interest rates (Marshall,1992:261). By varying prices, their effect on pre-tax income can be determined. Alternatively, the historical sensitivity of the company's equity value to changes in prices can be measured. The coefficients of a simple linear regression are used to estimate the sensitivity of the value of the firm to changes in the respective variables (Smith,1990:42). This approach is similar in some ways to determining the beta under CAPM.
Financial companies can measure the degree of interest rate risk through gap and duration analysis. Gap is the difference between RSA and RSL, where RSA is the market value of the rate sensitive assets and RSL is the value of the rate sensitive liabilities. Using gap, the impact on the firm of changes in the interest rate is given by _NII = gap x _r, where NII is the net interest income, and _r represents the change in interest rate (Smith, 1990:36).
The measure, duration, which was developed in 1938 by Frederick Macaulay, is the most widely used measure of interest-rate sensitivity of an asset, and is the effective maturity of an asset/liability expressed in units of time. The Macaulay duration is given by:
D = -(dS/S)
(dR/R)
where S is the instrument's spot price and R equals 1 plus the asset's yield (for example, yield to maturity). Thus, D measures the response of price to a proportional change in the interest rate(Martin,1988:529). If V is the value of the firm and _ represents the change operator, then,
_V/V = _(1+r)/(1+r) x D (Smith,1990:38)
In this process of risk measurement, it is essential to understand the underlying determinants of the risk. In case of interest rate risk, the underlying factor would largely comprise of inflation. Therefore, the management of interest rate risk and inflation risk will have to go together (Putnam,1986). As emphasised earlier, more important is to place the risk in perspective. If the company is not threatened by bankrupcty if prices move, "then a more passive strategy, involving perhaps a periodic monitoring of overall corporate exposure, is probably sufficient" (Putnam, 1986:242). These considerations will help the firm to determine the desired outcomes of risk management.
3.1 Designing a suitable strategy: The final step is the design of an appropriate strategy. There are three fundamental ways of managing risk: insurance, asset/ liability management, and hedging. We discuss these below.
i. Insurance is available against some risks (but not, generally, against price risks). However, there are usually other cheaper alternatives to insurance available. This is because insurance companies have to return a profit after taking into account things like moral hazard and adverse selection which steeply raise their costs (Marshall,1992:154).
ii. On-balance sheet asset/ liability management: In this method, the firm has to hold the right combination of on-balance sheet assets and on-balance sheet liabilities, based on the principle of immunization (Marshall,1992:155). Immunization was proposed by F.M.Redington in the early 1950s. To immunize risk, one has to select assets so that not only the present value, but also their duration equals those of the liabilities, such that:
Duration x Market value = Duration x Market value
of assets of assets of liabilities of liabilities
There is problem associated with immunization. As prices change, the same process of asset/liability adjustment has again to be carried out, which can prove extremely expensive, especially during periods of extremely volatile interest rates (Martin,1988:530). Further, hedges often do much better (Marshall,1992: 164).
Apart from immunization, some price risks, such as foreign exchange exposure resulting from overseas competition, can also be managed by directly borrowing in the competitor's currency or by moving production abroad. These are also on-balance sheet, but in general, these are costly solutions (Smith,1990:43).
iii. Off-balance sheet hedging: In hedging, ideally, there have to be two investments (say, A and B) that are perfectly correlated; one takes a temporary position by buying one and selling the other, so that the net position is absolutely safe. Though similar in some ways to asset/liability management, hedging is primarily off-balance sheet. Sometimes, however, a hedge can take the form of an on-balance sheet position (Marshall,1992:165). The following equation holds:
Expected change = a + _ ( Change in )
in value of A ( value of B )
Here _ measures the sensitivity of changes in A to changes in the value of B, and is called the hedge ratio. The view that states that Ideally _ should equal 1 is now viewed unfavourably and is called the naive view.
But Johnson (1960) and Stein (1961) took a portfolio approach to hedging. In the case of futures, for example, the goal of hedging, they felt, should be to minimise the variance of the profit associated with the combined cash and futures position. Ederington extended this approach further in 1979. In the Johnson/ Stein/ Ederington (JSE) method, the spot price is regressed against the futures price using an ordinary least squares regression. The risk minimising or the minimum variance hedge ratio is then given by the slope of the regression line (Marshall,1992:517).
In this paper we focus on hedging as the chief method of risk management.
3.2 Hedging and financial engineering: Financial engineering has been defined as "the design, the development, and the implementation of innovative financial instruments and processes, and the formulation of creative solutions to problems in finance" (Marshall,1992:3). This is a very broad definition, but the primary objective of financial engineering (FE) is to meet the needs of risk management. FE takes a building block approach to the building of new instruments. This approach was first demonstrated by Black and Scholes (1973) in considering a call option as "a continuously adjusting portfolio of two securities: (1) forward contracts on the underlying asset and (2) riskless securities" (Smith,1990:50). Most of the hedges can be constructed from futures, forwards, options, and swaps, which are now known as the building blocks of financial engineering. By combining forwards, options, futures and swaps, with the underlying cash position, a firm's risk exposure can be manipulated in a practically infinite variety of ways.
4. THE BUILDING BLOCKS OF FINANCIAL ENGINEERING:
In this section we take a brief look at the building blocks, before going on to see how this approach is applied in practice.
4.1 Futures contracts: In futures contracts, the sale and purchase of a specified asset at some specified future date is contractually agreed to, at a price determined now. The buyer places a small initial margin, usually tendered in T-bills or other forms of security, with the broker. Essentially, therefore, a position can be taken without investment in the futures market, and they are therefore off-balance sheet transactions (Marshall,1992:281). Changes in the contract price are settled daily, with each trader marking his position to market (Copeland,1988:304). If the margin falls below a point, a margin call is made on the buyer. This process by and large eliminates credit risk. Whereas a few major instances of default have occurred, e.g., the default of silver contracts by Hunt Brothers, it is true that in general there is an extremely low default rate in futures (Ross,1990:656). Finally, at the time of delivery the buyer receives (wherever feasible) the asset which was purchased, by paying the contract price.
Futures can be used to hedge against commodity-price risk, interest-rate risk, and exchange-rate-risk (Marshall, 1992:283). The main types of futures are commodities futures, financial futures and futures on indices. The first organised commodity futures market was the Chicago Board of Trade (CBT), established in 1848. The first financial futures contract was introduced on October 20, 1975, by the CBT. Financial futures markets are now much larger than traditional commodity futures markets (Martin,1988:519).
Financial futures are used primarily to trade interest rate risk. The markets for financial futures are very liquid; and of course there is no cost of storage. Most financial futures contracts fall into three categories:
i. Interest rate futures: These include futures on interest bearing instruments such as T-bills, T-notes, T-bonds, certificates of deposit, Eurodollars, etc., are a popular and useful method of hedging interest rate risk. These contracts enable borrowers to lock in interest rates for some future period.
ii. Foreign currency futures: These are available in all major currencies, and are used for hedging foreign exchange risk.
iii. Share price index futures: The first of these was introduced in the U.S.A. only in 1982 (Van Horne, 1990:725). They are traded on the Standard and Poor's 500 index, the New York Stock Exchange Composite index, and the Value Line index (Copeland,1988:316). These are obviously non-deliverable. Instead, these are settled in cash by marking to the market "at the closing value of the respective underlying spot stock market index on the last trading day" (Martin,1988:522).
Some issues of interest relating to futures contracts are dealt with in Annexure II (1).
4.2 Forward contracts: These are similar to futures. Here the owner of the forward contract is obliged to buy a specified asset on a specified date at a the exercise price specified in the contract. No payment is made at any time at the commencement or during the term of the contract, making it an off-balance sheet instrument (Smith,1990:45). Forwards seem to have a flaw. "Whichever way the price of the deliverable instrument moves, one party has an incentive to default. There are many cases where defaults have occurred in the real world"(Ross,1990:655). Therefore, forward contracts usually involve counterparties who have prior knowledge of each other.
Though the oldest among financial instruments hedging risk, forward markets continue to thrive inspite of the subsequent emergence of futures markets - which are very similar to futures in many ways - because of different clienteles and other reasons. First, forward contracts are tailored to fit the needs of the customer. Second, futures do not exist for all commodities and on all financials. Third, there is a difference in accounting treatment between futures and forwards in some countries. And lastly, there is the likelihood of a possible mismatch between the length of the hedger's hedging horizon and the maturity date of the futures. Forwards take care of this. There are many interesting differences between futures and forwards. These are discussed in Annexure II.
The forward markets in currencies are the most highly developed of all the forwards markets. Large banks buy and sell forward currency, usually for periods up to 1 year ahead. In the case of the major currencies forward contracts of upto 5 years or more are now common (Brealey,1988:618).
4.3 Swaps: The term "swap" covers a range of transactions "where two or more entities exchange or swap cash flows in the same or in two or several different currencies and/or interest rate bases for a predetermined length of time" (Das,1989:17). Swaps are used primarily to hedge against interest rate and foreign exchange risks. The first currency swap was introduced in 1976, and interest rate swap only in 1981. But inspite of this, swap markets now overwhelm any other financial innovation by the sheer volume of transactions. A survey undertaken by the Federal Reserve Bank of the USA in 1989 (Eiteman,1992:91) showed that 64% of all interbank foreign exchange transactions were spot transactions, a massive 27% were swap transactions, and only 4.2% were forward transactions. Interest rate swaps now dominate the market for swaps. In this type of swap, the two different interest rates determine the cash flows.
Swap financing transactions can be classifed into four (Das,1989:17). The first category is the parallel or back-to-back loans. The second is swap transactions, comprising, inter alia, of currency swaps, currency coupon swaps, interest rate swaps, basis rate swaps, commodity swaps, swaps with timing mismatches, swaps with option-like payoffs (swaptions, also called contingent swaps or option swaps), deferred swaps, forward swaps, circus swaps, principal only swaps, amortising swaps, zero coupon swaps, and long-dated or long-term foreign exchange contracts (LTFX). The third category is the forward rate agreements (FRAs), and lastly we have the caps, collars and floors. A further discussion on swaps is given in Annexure II (3).
4.4 Options: In an options contract, "one party has the right, but not the obligation, to do something - usually to buy or sell some underlying asset" (Marshall,1992:338). Of course, the seller of the options contract has an absolute obligation. When the buyer has a right to buy, then it is a call option, and when the right is to sell, it is a put. The price paid for the option is in the form of a flat up-front sum called premium. Options that can be exercised only on the maturity date are called European options, and those which can be exercised at any time are called American options. Most of the traded options are American options.
Trading in call options began on the Chicago Board Options Exchange (CBEO) in April 1973. The paper by Black and Scholes (1973) appeared at about the same time (Weston, 1989: 479). Thereafter there has been a phenomenal growth in option trading. Much of this has been fuelled by the standardisation of contracts and the consequent lowering in transaction costs. The fundamental use of options is in trading risk in an asymmetric manner.
Apart from single-period options such as calls and puts, there are many others. Multiperiod options - which include interest rate caps, interest rate floors, and interest rate collars - are important because they are easily combined with other instruments, such as swaps, to achieve very specialised solutions to some problems of hedging (Marshall,1992:366). Additionally, there are options on caps, called captions, and options on swaps, called swaptions (which are also classified sometimes under swaps). Further, multiperiod currency options have been introduced and multiperiod commodity options are about to be introduced (Marshall, 1992:366). There are also compound options which are options on options; e.g., debt is a compound option to equity holders (Marshall,1992:382). Similarly, risky bonds, common stock, leases and life insurance policies can be visualised as compound options. We note in the passing that the simple Options Pricing Model does not accurately price compound options (Copeland,1983:257).
Some of the properties of options, and their pricing, etc., are looked into briefly in the Annexure II (4).
5. APPLICATION OF THE BUILDING BLOCK APPROACH:
There are three major methods of actually working on the building block approach: (i) to look at the risk and payoff profiles, (ii) to look at time-line cash flow diagrams and (iii) lastly, there is the arithmetic approach recently introduced by Donald J. Smith. The boxed cash flow diagrams approach is also sometimes used (Marshall,1992: 535).
In each of these approaches, the process is essentially the same. First of all a graphical or mathematical view of the current risk exposure is projected. This picture is overlayed with the cash flows associated with the hedging instruments under consideration. Then the residual or net cash flows are examined. Ultimately, by varying the delivery months and the strike prices, etc., the risk exposure is manipulated in the desired manner. To facilitate the calculations and analysis, spreadsheets and special software packages are put to use (Marshall,1992:540). It is usually possible to achieve the objective using different combinations of hedging instruments. The combination or strategy which is least costly is then accepted (Marshall,1992: 535). The securities resulting from this process are often given special names, or simply called synthetic securities.
We look below at some examples of synthetic securities. This list is only illustrative; the actual range of products, as can well be imagined, is almost infinite. The figures referred to in the following discussion are given in Annexure I to this paper. The detailed method of building or synthesising the listed securities is not provided, for want of space.
5.1 Payoff profiles method: In this method, the risk and payoff profiles of the instrument are drawn, and the combinations of some of the simpler instruments can be seen in this way. In Figure 1 we look at the payoff profile of a forward contract and a call and put option.
i. Synthetic future: A forward/future can be synthesised by "snapping together" a European call and a European with the same time to maturity and exercise price. This is shown in Figure 2 (from Copeland,1988:323).
ii. Swaps with optionlike characteristics: Swaps can be constructed to have option-like provisions which limit the range of outcomes. These include the floating floor-ceiling and the fixed floor-ceiling swaps. This is illustrated in Figure 3 (from Smith,1986:254).
5.2 Time-line cash flow method: The time-line cash flow diagrams are very intuitive and easy to grasp. Usually, the direction of the arrows represents the direction of the cash flows; the long arrow denotes the principal, and short arrows the exchange of other cash flows. A denotes fixed interest rate and ~ denotes floating interest rate. The following examples illustrate this approach.
i. Reverse floater: In a reverse or inverse floater, the coupon payment on an inverse floater decreases as LIBOR increases. It can be synthesised in many ways, one of which is show in Figure 4 (from Smith,1990:64).
ii. Synthesis of a deep-discount dollar bond: This is illustrated in Figure 5 (from Smith,1986:257).
iii. Synthetic dual currency bond: This is illustrated in Figure 6 (from Marshall,1992:592).
iv. A forward swap: This instrument is also called a delayed start swap, and combines forwards with a swap, or two swaps. This is illustrated in Figure 7 (from Smith,1990:57).
v. Foreign-pay zero: This is illustrated in Figure 8 (from Marshall,1992:594).
5.3 Arithmetic approach: The notation of the arithmetic approach is illustrated by: A = B + C, where A, B, and C represent expected cash flows from these securities. The " = " sign represents identical cash flows in terms of amount, currency and timing. A " + " indicates a long position and a " - " indicates a short position (Smith, D.J.). The following examples are based on this approach.
i. Synthetic fixed rate debt: This is given by the following combination (Smith,D.J.:405). Here FRN stands for fixed rate note.
Typical Interest
- FRN = - FRN + Rate Swap + Floor
Swap fixed LIBOR + 0.25% pay fixed, 4.75%
rate + 0.25% min. 5% rec. LIBOR
ii. Asset Swaps: In asset swaps, the cash flow characteristics of the underlying asset are changed. If the usual FRN is taken as the asset, then an asset swap could look like this (Smith,D.J.:406):
Typical Interest
+ FRN = + FRN - Rate Swap - Floor
Swap fixed LIBOR + 0.25% rec. fixed, 4.75%
rate+0.25% min. 5% pay LIBOR
iii. Mini-max or "collared" floater: This is basically a typical FRN with the addition of a maximum coupon rate, and is synthesised as follows (Smith,D.J.:407):
Mini-Max Unrestricted
+ FRN = + FRN + Annuity - Cap + Floor
LIBOR LIBOR 0.5% 8.5% 4.5%
+ 0.5%
min. 5%
max. 9%
iv. Inverse floater: Discussed earlier as a reverse floater, this can be synthesised in many ways, one of which is illustrated below (Smith,D.J.:408):
- Inverse = - Two + Unrestricted - Cap
floater FRNs FRN
16%-LIBOR 8% LIBOR 16%
v. Participation agreement: The outcome of a participation agreement is that the buyer "has the benefit of a ceiling on LIBOR but makes settlement payments at a constant fraction of the rate differential when LIBOR is below the ceiling" (Smith,D.J.:409). It is synthesised as follows (where NP is the notional principal, NP* is the given amount of interest rate protection, and PR, or the participation rate, is 62.5%):
Participation
+ Agreement = + Cap - Floor
10% ceiling 10% 10%
NP = NP* NP = NP* NP = .375 NP*
Others examples of financial engineering: Listed below are some other common examples of the building block approach to financial engineering.
i. Synthetic options: In Section 3.2 of this paper we have seen how Black and Scholes (1973) showed that a call option can be synthesised from forward contracts and riskless securities.
ii. Bonds with embedded options: Bonds with warrants/ convertible bonds/ callable bonds have options embedded in them. In a convertible bond, the bondholder has the right (but not the obligation) to convert the bond into some specified asset of the issuer. In a callable bond the issuer has the right (but not the obligation) to call the bond for redemption prior to maturity. Varieties of other types of bonds have also been synthesised, which given the bondholder an option (Smith,1990:65).
iii. Synthetic futures: These can be built from forward contracts. We can also use an appropriate combination of single-period options to synthesise a futures contract (Marshall,1992:535).
iv. Synthetic swaps: Since the payoff profile of swaps is similar to that of a forward contract, they can easily be synthesised from forwards (Smith,1986). A swap can also be synthesised from an appropriate strip of futures or from a strip of futures-like option combinations (Marshall,1992:535).
6. REASONS FOR RAPID GROWTH IN FINANCIAL ENGINEERING:
Since the 1950s and 1960s, and particularly in the last decade, the global and financial environment has changed rapidly. In particular, the breakdown of the Bretton Woods agreement in 1972 which ultimately led to floating exchange rates, has led to major increases in volatility and competition (Smith,1990:33). Technology has improved dramatically in this period. Government debt has also increased in most countries. Marshall (1992:20) has classified the causes of increasing risk into two: environmental and intra-firm. We use this classification here to analyse the reasons why the increase in risk and major developments in finance, taken together, created the right environment for rapid growth in financial engineering.
6.1 Environmental factors:
i. Increase in price volatility: The term "price" here includes the price of money, foreign exchange, stocks, and commodities. The currency floats have meant that the stability of exchange rates is a thing of the past. Interest rates have been very volatile too, e.g., in June 1982, AA bonds were yielding 15.3 percent. In May 1986 the same bonds yielded 8.9 percent and in April, 1989, 10.2 percent (Brigham, 1990:604). Oil prices are the best example of dramatic commodity price volatility, and the October, 1987 stock crash illustrates the volatility in stock prices. There was also a major volatility in overall prices, i.e., inflation, over the past three decades. This all-round increase in volatility has led to tremendous increases in the risks which companies face, and enhanced the need for hedging the risks.
ii. Globalisation of the world economy and competition: Commerce has grown very rapidly in the past two decades. This has increased the size of markets and greatly enhanced competition (Marshall,1992:658).
iii. Deregulation and increase in competition: Initially, investment banks were the only ones which could offer various services regarding risk management. Deregulation of the financial markets has brought in new entrants into the financial markets, particularly NBFIs, who have aggressively competed with the traditional banking sector, by introducing new products and services. In return, banks were forced to come out with innovative ways to compete with NBFIs by taking recourse to off-balance sheet transactions.
iv. Advances in technology and communication: Funds can be transferred from ATMs and telephones now. Computers have entered the field of finance in a big way.
v. Development of new markets and market linkages: There has been an explosive growth of futures and options exchanges worldwide. 24-hour trading has become possible on futures and options exchanges across the globe. The Chicago Exchange has developed a computer system on which trade can now be carried out at any time, replacing human activity on the floor (Marshall, 1992:665).
vi. Dramatic decline in information and transactions costs: There has been a tremendous decline in transaction costs and spreads, e.g., the cost of transacting a share of $100 has declined from $1 in the 1970s to under 2 cents in the 1990s (Marshall,1992:38). Computerised databases of financial transactions are available to subscribers. Information asymmetry has considerably declined.
vii. Advances in financial theory: Developments in finance theory have contributed immensely to the development of new hedging techniques. The OPM is a case in point.
viii.Tax asymmetries: Taxes differ across industries and countries, over time. Also, some firms have sufficient tax credits/ write-offs which give them an advantage over other firms. For example, zero coupon yen bonds were treated liberally in Japan. In the USA, the abolition, in 1984, of the withholdings tax on interest payments to overseas investors in the domestic securities of the USA influenced the growth of interest rate swaps (Das,1989:170).
ix. Arbitrage opportunities: The globalisation of the financial markets has meant that arbitrage opportunities across different capital markets could be identified and exploited. In theory, exploiting these differentials through arbitrage should eventually lead to their disappearance.
x. Completing markets: Often there have been gaps in the financial markets which have been identified and filled up with new kinds of instruments. For example, at one time there were no interest rate forward contracts; interest rate swaps were then designed to fill this gap. Thus, swaps complete markets (Smith,1986).
xi. Standardisation: There has been an increasing standardisation of financial instruments, e.g., in futures, options and swaps. This has expanded the market.
xii. Low documentation costs: Many of the new financial instruments require little documentation, and no prospectus, etc. This has made them attractive to companies.
6.2 Intrafirm factors:
i. Liquidity needs: Companies need liquidity of their "free cash flows". To make use of funds temporarily not needed, money markets and sweep markets have developed rapidly (Marshall,1992:39). The same purpose in the longer term is served by FRNs (floating rate notes), adjustable rate preferred stock, etc.
ii. Risk aversion: The risk aversion of firms to the increasing risks has been an important driving force in motivating innovations.
iii. Agency costs: Marshall (1992:42) shows how leveraged buyouts were motivated by the desire to reduce agency costs. The financing of such activity required new forms of financing, including junk bonds.
iv. Quantitative sophistication of management training: The increase in the quantitative skills possessed by managers has led to a demand for better tools of financial management.
v. Accounting objectives: At times, financial innovation has been fuelled by the desire to improve accounting figures.
Many forms of financial innovation, including eurobonds, eurodollars, electronic funds transfer, etc., have arisen from these factors. The development of financial engineering is perhaps the most important of the outcomes of the changes discussed above.
7. CONCLUSION:
Financial engineering has proved extremely effective in managing the increased financial risk witnessed over the past few decades, and particularly in the last decade. "It's rare that a day goes by in the financial markets without hearing of at least one new or hybrid product" (Smith,1990:64). Using a building block approach, it appears that almost all requirements of risk management can be met by a suitable product. These instruments and their ever-expanding markets also seem to be playing a role in increasing efficiency in capital markets. Cox (1976) has suggested that "futures trading increases market information and thereby increases the efficiency of spot prices. By "efficiency" he meant that spot prices provide more accurate signals for resource allocation when the given commodity has a futures market" (Martin,1988:546).
In summation, we note that financial engineering as a major discipline within finance is playing an important role and has come to stay.
References:
Brealey, R.A. and Myers, S.C. (1988). Principles of Corporate Finance. 3rd edn. McGraw-Hill Publishing Co., New York.
Brigham, E.F., and Gapenski, L.C. (1990). Intermediate Financial Management. 3rd edn. The Dryden Press, Chicago.
Coopers and Lybrand (1987). A Guide to Financial Instruments. Euromoney Publications, London.
Copeland, T.E., and Weston, J.F. (1983). Financial Theory and Corporate Policy. 2nd edn. Addison-Wesley Publishing Co.
Copeland, T.E., and Weston, J.F. (1988). Financial Theory and Corporate Policy. 3rd edn. Addison-Wesley Publishing Co.
Das, Satyajit (1989). Swap Financing. The Law Book Company Ltd., Melbourne.
Eiteman, D. K., Stonehill, A. I. and Moffett, M.H. (1992). Multinational Business Finance. 6th edn. Addison-Wesley Publishing Co., Massachussets.
Juttner, D.Johannes (1991) Financial Markets, Interest Rates and Monetary Economics. 2nd edn. Longman Cheshire, Melbourne.
Marshall, John F., and Bansal, Vipul K. (1992). Financial Engineering: A Complete Guide to Financial Innovation. New York Institute of Finance, New York.
Martin, J.D., Cox, S.H.,Jr., and MacMinn, R.D. (1988). The Theory of Finance: Evidence and Applications. The Dryden Press, Chicago.
Putnam, B. (1986). "Managing Interest Rate Risk: An Introduction to Financial Futures and Options" in Stern, J.M. and Chew, Jr., D.H. (eds.) (1986), The Revolution in Corporate Finance. Basil Blackwell.
Ross, S.A., Westerfield, R.W., and Jaffe, J.F. (1990) Corporate Finance. Irwin, Boston.
Shapiro, A. and Titman, S. (1986). "An Integrated Approach to Corporate Risk Management" in Stern, J.M. and Chew, Jr., D.H. (eds.) (1986), The Revolution in Corporate Finance. Basil Blackwell.
Smith, Clifford W.,Jr., Smithson, Charles W. and Wakeman, Lee Macdonald (1986). "The Evolving Market for Swaps" in The Midland Corporate Financial Journal. Winter 1986.
Smith, Clifford W.,Jr., Smithson, Charles W. and Wilford, D.S. (1990). "Managing Financial Risk" in The Handbook of Financial Engineering. Harper Business Books, New York.
Smith, Donald J. "The Arithmetic of Financial Engineering." (distributed in class).
Smith, Roy C., and Walter, Ingo (1990). Global Financial Services. Harper Business, New York.
Van Horne, J., Davis, K., Nicol,R., and Wright, Ken.(1990). Financial Management and Policy in Australia. 3rd edn. Prentice Hall, New York.
Walsh, David (1990). International Finance Handbook. Curtin University of Technology.
Weston, J.F., and Copeland, T.E. (1989). Managerial Finance. 8th edn. with tax update. The Dryden Press, Chicago.
ANNEXURE II:
1) MORE ON FUTURES:
Commodity futures: Hedgers are prepared to pay speculators a premium to bear the risk of interest. This is because most hedgers wish to short in a commodity, and they wish to attract speculators to take on the risk. Keynes termed this phenomenon normal backwardation. Such a risk premium would be subtracted from the expected spot price to yield the futures price.
Futures price = Expected future spot price - risk
premium
We should therefore see futures prices that are below expected spot prices. Many empirical studies have failed to find normal backwardation, but the issue is not yet settled (Martin,1988:545).
Contango is the opposite of normal backwardation. This happens when the futures price is above the expected spot price (Copeland, 1988: 318).
Pricing of futures: Cox, Ingersoll, and Ross (1981) showed that the futures price, F(t,d), is the value at time t of a contract that pays at time d the following amount:
S(d)RtRt+1...Rd-1
where d is the maturity of the futures contract, S(d) the price at time d of the financial instrument on which the contract is written, Rt is 1 plus the spot interest rate prevailing from time to time t+1, etc (Martin,1988:533).
The pricing of commodities contracts are however, more complex. This is because of storage costs involved. Further, spot markets may be too thin for arbitrage. The two approaches for explaining these prices are (1) based on convenience yields and storage costs, in which the futures prices, and thus the basis, are determined by cost of purchasing the item in the spot market and carrying it to the delivery date, and (2) based on risk premium such as the CAPM beta (Copeland,1988:317). Note: The basis is the gap between the futures and spot price.
2) MORE ON FORWARDS:
Difference between futures and forwards: We look at the major difference between futures and forwards below (compiled from Marshall (1992:277) and Walsh (1990:88).
* Clientele: Forwards are mostly transacted by large bank. Futures markets handle less frequent, and smaller investors, and also speculators.
* Liquidity/ size of the markets: In dollar terms, forwards markets are many times larger than futures markets.
* Location/timing of trading: Forward contracts trade in over-the-counter dealer-type markets, through any bank, at almost any time, anywhere. Futures contracts trade on futures exchanges, while the exchange is open.
* Standardisation and identification of counterparties: Forward contracts are negotiated between the contracting parties, with each party being directly responsible to the other. Consequently, the identities of the counterparties are important. Futures contracts are highly standardised, with all contract terms, including size and maturity dates, (except price) defined by the exchange on which they trade. A clearing association stands between the parties to a futures contract, and consequently, the identities of the counterparties are irrelevant.
* Pricing: Forward quotes are bid/ask from a bank. Futures prices are determined by open outcry, which may be more efficient.
* Regulation: Forward markets, in general, are not regulated. But futures markets are regulated by the Commodity Futures Trading Commission (CFTC) in the US.
* Margins and credit risk: Market makers in the forward market tend to limit their contracting to parties who are well-known to them because of credit risk. In the futures market, credit risk is looked after by requiring each party to a contract to post a margin, which is adjusted through a daily mark-to-market process.
* Marketability risk: Forward contracts are very difficult to terminate. Therefore they are usually settled at the end of the contract, on the settlement date. Futures, on the other hand, are very easy to terminate or settle through simple offsetting transactions, or by marking to market.
* Transaction costs: Forwards costs are based on bid/ask spreads, so the investor is wise to shop around. Futures costs are a percentage of the size of the contract, but these costs do not change much between brokers. Shopping around between brokers will be based on the research ability of the brokers and the quality of advice that they provide.
3) MORE ON SWAPS:
The following table illustrates the phenomenal growth seen in swap markets in the last ten years.
Table 1: Estimate of volume of swaps (in billion US$)
Type of swap 1982 1983 1984 1985 1986 1987 1988
------------------------------------------------------------
Currency 3 5 19 50 100 150 175 Interest rate 2 30 90 175 190 388 568
Total 5 35 109 225 290 538 743
Source: International Swap Dealers Association, etc.
(Smith and Walter,1990:418)
Brief description of some swaps:
The credit swap was the first kind of swap undertaken by governments. It involved the exchange of currencies between a business firm and a bank (often the central bank) of a foreign country, which was then reversed at a predetermined future date. These swaps have been used for more than half a century to satisfy temporary government needs for foreign exchange (Eiteman,1992:217).
The parallel loans evolved in the early 1970s. In these loans, one firms say A, lends an amount in its home currency to the subsidiary of a foreign firm B operating in the home country of A, in exchange for the receipt of an equivalent amount in foreign currency by its subsidiary operating in the foreign country from where B operates. Thus, a parallel loan is a set of two loan agreements and it is obligatory for one counterparty to fulfil its part of the agreement even though the other side may default. This is due to the legal position regarding agreements (Walsh,1990:97)
A back-to-back loan involves the direct exchange of their own home currency loans between A and B. This represents one single loan agreement, but creates two sets of rights and obligations, very similar to those obtaining in the case of a parallel loan. The advantages of parallel and back-to-back loans were unfortunately offset by the risks of default by one party (credit risk). This risk was overcome by the evolution of currency swaps between firms. Further, "After the ... adoption of floating exchange rates, controls governing the international transfer of funds became obsolete and began to be removed... Parallel loans were no longer necessary, and immediately went into decline" (Smith and Walter,1990:419)
Currency swaps are very similar to a back-to-back loan, except that these do not appear on a firm's balance sheet and these eliminate credit risk to a great extent. In a currency swap, two firms agree to exchange an equivalent amount of two different currencies for a specified period of time. Due to the change in exchange rate fluctuations, a fee may have to be paid by one counterparty to the other to compensate for the interest differential (Eiteman:216). The first currency swap took place in Europe between the Dutch Guilder and the British pound in 1976. These were initially customised swaps in which the intermediaries arranging these swaps themselves undertook no capital risk, but this has now changed.
Interest rate swaps, also called coupon swaps, are the most diversified of all. "Interest rate swaps are simply an exchange of fixed and floating assets or liabilities between two firms" (Walsh:99). The first interest rate swap was transacted in 1981, and the first such swap in Australian dollars was transacted in 1983. What is termed as a `plain vanilla' interest rate swap is an agreement between two borrowers to exchange fixed-rate for floating-rate financial obligations. "The basis for an interest rate swap is a notional underlying principal amount of loan and deposit, between two counterparties, whereby one counterparty agrees to pay to the other agreed sums referred to as `interest payments'. These sums are calculated as though they were interest on the principal amount of the notional loan and deposit, in a specified currency, during the life of the contract through the application of predetermined formulae, based on the interest rate pricing structure of each other's underlying liabilities. In addition to the basic `plain vanilla' swap, there are many other types of interest rate swaps. Interest rate swaps have now become standardised and homogeneous and are a high volume, low margin business (Smith,1986). Intermediaries, usually commercial banks, tend to accept swap contracts without a counterparty and take on risk. This is the process of "warehousing" (Coopers,1987: 123).
FRAs (Forward Rate Agreements): As per Das's classification (discussed in the main body of the paper), FRAs are akin to swaps and could therefore be classified in this group (some others classify these under forwards).
A FRA is essentially a forward interest-rate contract, used by borrowers or lenders to hedge against future interest rate movements. FRAs were originally introduced by some banks in 1983, and British banks remain the principal market makers. FRAs are offered by some banks and other financial institutions. In this, "the buyer and seller agree to exchange, on the settlement date, an amount of money calculated by reference to the interest rate differential existing between a reference rate of interest and the interest rate agreed upon in the FRA contract (applied to the principal sum involved in the FRA). The FRA does not involve any commitment to borrow or lend funds" (Van Horne,1990:724). "FRAs have become very important in global banking" (Marshall,1992:292).
Current status of swaps markets: The swap market has considerably matured now, in the view of Smith and Walter (1990:433): "An active secondary market has developed that permits swaps to be sold and transferred to others, voluntarily terminated or nullified by entering into reversing transactions." Spot, futures, and options all exist for swaps. However, the problem of credit risk of swaps seems to be in a fluid stage of development. There is some uncertainty about the legal standing of swaps (Smith,1986) and doubts about what will happen "after the first major default."
4) MORE ON OPTIONS:
Some different kinds of options:
* We can get varieties of resultant securities by combining options in different ways. Examples are: spread, straddle, straps and strips (Copeland,1983: 238).
* Caps (interest rate caps): "The writer of a cap pays the cap holder each time the contract's reference rate is above the contract's ceiling rate on a settlement date. By this structure, a cap provides a multiperiod hedge against increases in interest rates" (Marshall, 1992: 367).
* Floors (interest rate floors): This "is a multiperiod interest rate option identical to a cap except that the floor writer pays the floor purchaser when the reference rate drops below the contract rate, called the floor rate" (Marshall,1992:373).
* Collars (interest rate collars): This "is a combination of a cap and a floor in which the purchaser of the collar buys a cap and simultaneously sells a floor. Collars can be constructed from two separate transactions (one involving a cap and one involving a floor) or they can be combined into a single transaction. This is sometimes called locking into a band, or swapping into a band" (Marshall,1992:377).
* Managers of mutual or pension funds can protect themselves against a downward movement in the prices by buying a put option on an index, also called share price index options.
* Options on futures: Futures options are options on futures contracts (both commodity and financial), and require the delivery of the underlying futures contract when the option is exercised. All of these of the American type (Martin,1988: 541). Papers by Ramaswamy and Sundaresan (1986), Stoll and Whaley (1986), and Barone-Adesi and Whaley (1987) have offered solutions for valuing American futures options (Martin,1988: 541). There are also options on swaps called swaptions (Smith,1990: 63).
Some mathematical representations:
Let St be the price of the underlying asset at time t, X the exercise price, c the purchase price of the call, and yt the profit/loss to the call buyer at time t. Then:
yt = - (c+X) + St if St > X
= - c if St < X
For the call writer,
yt = (c+X) - St if St > X
= c if St < X
Bounds on value of options: Assuming the call to be European, and if S is the price of the underlying asset, rf is the risk-free interest rate (for the period until expiration date), then it can be shown that the upper and lower bounds on the call price are:
S c Max [0, S - X/(1+rf)]
Put-call parity is a fixed relationship between the price of put and call options with the same maturity date which are written on a single underlying security (Stoll,1969). This relationship holds in case of European options only. Consider a European call. Let the subscript 0 stand for current market price, and P be the price of a put. Then the following can be proved (Copeland,1983:239).
c0 - P0 = S0 - X/(1+rf)
Pricing options: Most option valuation models focus on European options because they have a fixed exercise date. Take a European call option. There are two basic methods to option pricing (i) the Binomial approach, derived by Cox, Ross and Rubenstein (1979), or (ii) the traditional Black and Scholes approach (1973). It has been shown by Cox, Ross and Rubenstein, that the Black and Scholes model is a limiting case of the more general Binomial model (Copeland,1983:255). The binomial formula approaches the Black and Scholes formula as n, the number of trials, increases (Copeland,1983: 259). The Black and Scholes is more accurate in most cases.
In the Black and Scholes options pricing model (OPM), the price of an option is a function of five variables: the value of the underlying share (S), the exercise or strike price of the option (X), the instantaneous variance of the underlying share (2), the remaining term to maturity (T), and the risk-free rate (rf). Thus, c = f(S, X, 2, T, rf). Figures for S, X, and T, are published by the financial media; rf can be proxied by the yield on Treasury Bills with maturity equal to the expiration of the option under consideration. The only parameter left is 2, which has to be estimated. This is done by taking the ex-post stock price data and calculating the ex-post variance. However, there is no guarantee that the stock variability will remain constant in the future. This means that option valuation is subject to statistical errors (Ross:578). The following relationship holds for the partial derivatives:
_c _c _c _c _c
-- > 0, -- < 0, -- > 0, -- > 0, -- > 0
_S _X _2 _T _rf
The Black and Scholes formula is:
c = SN(d1) - Xe-rfTN(d2)
where
d1 = ln(S/X) + rfT + 1 ʹT
ʹT 2
and d2 = d1 - ʹT
A common American call option is not more valuable than a European call. This is because it does not pay to exercise an American option before maturity (Copeland, 1983:243). The early exercise feature of American options is only valuable when the common stock makes dividend payments. In such a case, the solutions found by Roll (1977) and Geske (1979) are used (Copeland,1983:261).
To price European put options, the standard call option pricing formula and the put-call parity is used (Copeland, 1983:262). For American put options, the put-call parity does not hold, and these have to be evaluated directly. Solutions have been provided by Parkinson (1977), Brennan and Schwartz (1977), and Cox, Ross and Rubenstein (1979) involving computerised numerical methods. The binomial approach to option pricing can also be employed to value American puts on nondividend paying common stock (Copeland, 1983:262).
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