No copyright infrigement intended all belongs to its due authors A Unique Instrument First, we would like to introduce the equivalent of the integer zero, in finance. Remember the property of zero in algebra.Adding (subtracting) zero to any other real number leaves this number the same. There is a unique financial instrument that has the same property with respect to market and credit risk. Consider the cash flow diagram in Figure 1-1. Here, the time is continuous and the t0, t1, t2 represent some specific dates. Initially we place ourselves at time t0. The following deal is struck with a bank. At time t1 we borrow USD100, at the going interest rate of time t1, called the Libor and denoted by the symbol Lt1 . We pay the interest and the principal back at time t2. The loan has no default risk and is for a period of δ units of time.1 Note that the contract is written at time t0, but starts at the future date t1. Hence this is an example of forward contracts. The actual value of Lt1 will also be determined at the future date t1. Now, consider the time interval from t0 to t1, expressed as t ∈ [t0, t1]. At any time during this interval, what can we say about the value of this forward contract initiated at t0? It turns out that this contract will have a value identically equal to zero for all t ∈ [t0, t1] regardless of what happens in world financial markets. Perceptions of future interest rate 1 The δ is measured in proportion to a year. For example, assuming that a “year” is 360 days and a “month” is always 30 days, a 3-month loan will give δ = 1 4 . 12 C HAPTER 1. Introduction t 2 t 1 t 0 Contract initiation Proceeds received Interest and Principal paid 1 100 2 100 2Lt 1 d100 FIGURE 1-1 movements may go from zero to infinity, but the value of the contract will still remain zero. In order to prove this assertion, we calculate the value of the contract at time t0. Actually, the value is obvious in one sense. Look at Figure 1-1. No cash changes hand at time t0. So, the value of the contract at time t0 must be zero. This may be obvious but let us show it formally. To value the cash flows in Figure 1-1, we will calculate the time t1-value of the cash flows that will be exchanged at time t2. This can be done by discounting them with the proper discount factor. The best discounting is done using the Lt1 itself, although at time t0 the value of this Libor rate is not known. Still, the time t1 value of the future cash flows are P Vt1 = Lt1 δ100 (1 + Lt1 δ) + 100 (1 + Lt1 δ) (1) At first sight it seems we would need an estimate of the random variableLt1 to obtain a numerical answer from this formula. In fact some market practitioners may suggest using the corresponding forward rate that is observed at time t0 in lieu of Lt1 , for example. But a closer look suggests a much better alternative. Collecting the terms in the numerator P Vt1 = (1 + Lt1 δ)100 (1 + Lt1 δ) (2) the unknown terms cancel out and we obtain: P Vt1 = 100 (3) This looks like a trivial result, but consider what it means. In order to calculate the value of the cash flows shown in Figure 1-1, we don’t need to know Lt1 . Regardless of what happens to interest rate expectations and regardless of market volatility, the value of these cash flows, and hence the value of this contract, is always equal to zero for any t ∈ [t0, t1]. In other words, the price volatility of this instrument is identically equal to zero. This means that given any instrument at time t, we can add (or subtract) the Libor loan to it, and the value of the original instrument will not change for all t ∈ [t0, t1]. We now apply this simple idea to a number of basic operations in financial markets. 1.1. Buying a Default-Free Bond For many of the operations they need, market practitioners do not “buy” or “sell” bonds. There is a much more convenient way of doing business.1. A Unique Instrument 3 1100 2100 Pay cash Receive interest and principal t2 t1 t0 1r t0 d100 FIGURE 1-2. Buying default-free bond. The cash flows of buying a default-free coupon bond with par value 100 forward are shown in Figure 1-2. The coupon rate, set at time t0, is rt0 . The price is USD100, hence this is a par bond and the maturity date is t2. Note that this implies the following equality: 100 = rt0 δ100 (1 + rt0 δ) + 100 (1 + rt0 δ) (4) which is true, because at t0, the buyer is paying USD100 for the cash flows shown in Figure 1-2. Buying (selling) such a bond is inconvenient in many respects. First, one needs cash to do this. Practitioners call this funding, in case the bond is purchased. When the bond is sold short it will generate new cash and this must be managed.2 Hence, such outright sales and purchases require inconvenient and costly cash management. Second, the security in question may be a registered bond, instead of being a bearer bond, whereas the buyer may prefer to stay anonymous. Third, buying (selling) the bond will affect balance sheets, called books in the industry. Suppose the practitioner borrows USD100 and buys the bond. Both the asset and the liability sides of the balance sheet are now larger. This may have regulatory implications.3 Finally, by securing the funding, the practitioner is getting a loan. Loans involve credit risk. The loan counterparty may want to factor a default risk premium into the interest rate.4 Now consider the following operation. The bond in question is a contract. To this contract “add” the forward Libor loan that we discussed in the previous section. This is shown in Figure 1-3a. As we already proved, for all t ∈ [t0, t1], the value of the Libor loan is identically equal to zero. Hence, this operation is similar to adding zero to a risky contract. This addition does not change the market risk characteristics of the original position in any way. On the other hand, as Figure 1-3a and 1-3b show, the resulting cash flows are significantly more convenient than the original bond. The cash flows require no upfront cash, they do not involve buying a registered security, and the balance sheet is not affected in any way. Yet, the cash flows shown in Figure 1-3 have exactly the same market risk characteristics as the original bond. Since the cash flows generated by the bond and the Libor loan in Figure 1-3 accomplish the same market risk objectives as the original bond transaction, then why not package them as a separate instrument and market them to clients under a different name? This is an Interest Rate 2 Short selling involves borrowing the bond and then selling it. Hence, there will be a cash management issue. 3 For example, this was an emerging market or corporate bond, the bank would be required to hold additional capital against this purchase. 4 If the Treasury security being purchased is left as collateral, then this credit risk aspect mostly disappears.4 C HAPTER 1. Introduction (a) (b) 2100 2100 1100 1100 t 2 t 1 t 0 t 0 t 1 t 2 1Lt 0 d100 2Lt 1 d100 Received fixed Add vertically Interest rate swap Pay floating t 2 t 1 t 0 1st 0 d100 2L t1 d100 FIGURE 1-3 Swap (IRS). The party is paying a fixed rate and receiving a floating rate. The counterparty is doing the reverse. IRSs are among the most liquid instruments in financial markets. 1.2. Buying Stocks Suppose now we change the basic instrument. A market practitioner would like to buy a stock St at time t0 with a t1 delivery date. We assume that the stock does not pay dividends. Hence, this is, again, a forward purchase. The stock position will be liquidated at time t2. Also, assume that the time-t0 perception of the stock market gains or losses is such that the markets are demanding a price St0 = 100 (5) for this stock as of time t0. This situation is shown in Figure 1-4a, where the ΔSt2 is the unknown stock price appreciation or depreciation to be observed at time t2. Note that the original price1. A Unique Instrument 5 1100 1100 2100 2100 (If Iosses) t 2 t 1 t 0 t 2 t 0 t 1 DSt 2 DSt 2 2Lt 1 d100 (a) (b) Equity and commodity swap Pay if losses DS t 2 Libor Pay Libor and any losses Receive any gains (Note the there will be either gains or losses, not both as shown in the graph) t 2 t 1 t 0 FIGURE 1-4 being 100, the time t2 stock price can be written as St2 = St1 + ΔSt2 = 100 + ΔSt2 (6) Hence the cash flows shown in Figure 1-4a. It turns out that whatever the purpose of buying such a stock was, this outright purchase suffers from even more inconveniences than in the case of the bond. Just as in the case of the Treasury bond, the purchase requires cash, is a registered transaction with significant tax implications, and immediately affects the balance sheets, which have regulatory implications. A fourth inconvenience is a very simple one. The purchaser may not be allowed to own such a stock.5 Last, but not least, there are regulations preventing highly leveraged stock purchases. Now, apply the same technique to this transaction. Add the Libor loan to the cash flows shown in Figure 1-4a and obtain the cash flows in Figure 1-4b. As before, the market risk 5 For example, only special foreign institutions are allowed to buy Chinese A-shares that trade in Shanghai.6 C HAPTER 1. Introduction characteristics of the portfolio are identical to those of the original stock. The resulting cash flows can be marketed jointly as a separate instrument. This is an equity swap and it has none of the inconveniences of the outright purchase. But, because we added a zero to the original cash flows, it has exactly the same market risk characteristics as a stock. In an equity swap, the party is receiving any stock market gains and paying a floating Libor rate plus any stock market losses.6 Note that if St denoted the price of any commodity, such as oil, then the same logic would give us a commodity swap.7 1.3. Buying a Defaultable Bond Consider the bond in Figure 1-1 again, but this time assume that at time t2 the issuer can default. The bond pays the coupon ct0 with rt0 < ct0 (7) where rt0 is a risk-free rate. The bond sells at par value, USD100 at time t0. The interest and principal are received at time t2 if there is no default. If the bond issuer defaults the investor receives nothing. This means that we are working with a recovery rate of zero. Figure 1-5a shows this characterization. (a) (b) No default Default 1100 2100 t 2 t 1 t 0 t 2 t 2 t 1 t 0 Libor loan 2100 1100 Ct 0 d100 2Lt 1 d100 FIGURE 1-5 6 If stocks decline at the settlement times, the investor will pay the Libor indexed cash flows and the loss in the stock value. 7 To be exact, this commodity should have no other payout or storage costs associated with it, it should not have any convenience yield either. Otherwise the swap structure will change slightly. This is equivalent to assuming no dividend payments and will be discussed in Chapter 3.1. A Unique Instrument 7 This transaction has, again, several inconveniences. In fact, all the inconveniences mentioned there are still valid. But, in addition, the defaultable bond may not be very liquid. 8 Also, because it is defaultable, the regulatory agencies will certainly impose a capital charge on these bonds if they are carried on the balance sheet. A much more convenient instrument is obtained by adding the “zero” to the defaultable bond and forming a new portfolio. Visualized together with a Libor loan, the cash flows of a defaultable bond shown in Figure 1-5a change as shown in Figure 1-5b. But we can go one step further in this case. Assume that at time t0 there is an interest rate swap (IRS) trading actively in the market. Then we can add this interest rate swap to Figure 1-5b and obtain a much clearer picture of the final cash flows. This operation is shown in Figure 1-6. In fact, this last step eliminates the unknown future Libor rates Lti and replaces them with the known swap rate st0 . The resulting cash flows don’t have any of the inconveniences suffered by the defaultable bond purchase. Again, they can be packaged and sold separately as a new instrument. Letting the st0 denote the rate on the corresponding interest rate swap, the instrument requires receipts of a known and constant premium ct0 − st0 periodically. Against this a floating (contingent) cash flow is paid. In case of default, the counterparty is compensated by USD100. This is similar to buying and selling default insurance. The instrument is called a credit default swap (CDS). Since their initiation during the 1990s CDSs have become very liquid instruments and completely changed the trading and hedging of credit risk. The insurance premium, called the CDS spread cdst0 , is given by cdst0 = ct0 − st0 (8) This rate is positive since the ct0 should incorporate a default risk premium, which the defaultfree bond does not have.9 No default Default 2100 t 2 t 1 t 0 2Lt 1 2Lt 1 1Ct 0 (Assuming d 5 1) FIGURE 1-6 8 Many corporate bonds do not trade in the secondary market at all. 9 The connection between the CDS rates and the differential ct0 − st0 is more complicated in real life. Here we are working within a simplified setup.8 C HAPTER 1. Introduction 1.4. First Conclusions This section discussed examples of the first method of financial engineering. Switching from cash transactions to trading various swaps has many advantages. By combining an instrument with a forward Libor loan contract in a specific way, and then selling the resulting cash flows as separate swap contracts, the financial engineer has succeeded in accomplishing the same objectives much more efficiently and conveniently. The resulting swaps are likely to be more efficient, cost effective and liquid than the underlying instruments. They also have better regulatory and tax implications. Clearly, one can sell as well as buy such swaps. Also, one can reverse engineer the bond, equity, and the commodities by combining the swap with the Libor deposit. Chapter 5 will generalize this swap engineering. In the next section we discuss another major financial engineering principle: the way one can build synthetic instruments. We now introduce some simple financial engineering strategies. We consider two examples that require finding financial engineering solutions to a daily problem. In each case, solving the problem under consideration requires creating appropriate synthetics. In doing so, legal, institutional, and regulatory issues need to be considered. The nature of the examples themselves is secondary here. Our main purpose is to bring to the forefront the way of solving problems using financial securities and their derivatives. The chapter does not go into the details of the terminology or of the tools that are used. In fact, some readers may not even be able to follow the discussion fully. There is no harm in this since these will be explained in later chapters. 2. A Money Market Problem Consider a Japanese bank in search of a 3-month money market loan. The bank would like to borrow U.S. dollars (USD) in Euromarkets and then on-lend them to its customers. This interbank loan will lead to cash flows as shown in Figure 1-7. From the borrower’s angle, USD100 is received at time t0, and then it is paid back with interest 3 months later at time t0 + δ. The interest rate is denoted by the symbol Lt0 and is determined at time t0. The tenor of the loan is 3 months. Therefore δ = 1 4 (9) and the interest paid becomes Lt0 1 4 . The possibility of default is assumed away.10 t 1 5 t 01 d t 1 t 0 Borrow (Receive USD) Cash inflow Cash outflow Pay back with interest 1100 USD 2100 (1 1 Lt 0 d) FIGURE 1-7. A USD loan. 10 Otherwise at time t0 + δ there would be a conditional cash outflow depending on whether or not there is default.2. A Money Market Problem 9 The money market loan displayed in Figure 1-7 is a fairly liquid instrument. In fact, banks purchase such “funds” in the wholesale interbank markets, and then on-lend them to their customers at a slightly higher rate of interest. 2.1. The Problem Now, suppose the above-mentioned Japanese bank finds out that this loan is not available due to the lack of appropriate credit lines. The counterparties are unwilling to extend the USD funds. The question then is: Are there other ways in which such dollar funding can be secured? The answer is yes. In fact, the bank can use foreign currency markets judiciously to construct exactly the same cash flow diagram as in Figure 1-7 and thus create a synthetic money market loan. The first cash flow is negative and is placed below the time axis because it is a payment by the investor. The subsequent sale of the asset, on the other hand, is a receipt, and hence is represented by a positive cash flow placed above the time axis. The investor may have to pay significant taxes on these capital gains. A relevant question is then: Is it possible to use a strategy that postpones the investment gain to the next tax year? This may seem an innocuous statement, but note that using currency markets and their derivatives will involve a completely different set of financial contracts, players, and institutional setup than the money markets. Yet, the result will be cash flows identical to those in Figure 1-7. 2.2. Solution To see how a synthetic loan can be created, consider the following series of operations: 1. The Japanese bank first borrowslocalfunds in yen in the onshore Japanese money markets. This is shown in Figure 1-8a. The bank receives yen at time t0 and will pay yen interest rate LY t0 δ at time t0 + δ. 2. Next, the bank sells these yen in the spot market at the current exchange rate et0 to secure USD100. This spot operation is shown in Figure 1-8b. 3. Finally, the bank must eliminate the currency mismatch introduced by these operations. In order to do this, the Japanese bank buys 100(1 + Lt0 δ)ft0 yen at the known forward exchange rate ft0 , in the forward currency markets. This is the cash flow shown in Figure 1-8c. Here, there is no exchange of funds at time t0. Instead, forward dollars will be exchanged for forward yen at t0 + δ. Now comes the critical point. In Figure 1-8, add vertically all the cash flows generated by these operations. The yen cash flows will cancel out at time t0 because they are of equal size and different sign. The time t0 + δ yen cash flows will also cancel out because that is how the size of the forward contract is selected. The bank purchases just enough forward yen to pay back the local yen loan and the associated interest. The cash flows that are left are shown in Figure 1-8d, and these are exactly the same cash flows as in Figure 1-7. Thus, the three operations have created a synthetic USD loan. The existence of the FX-forward played a crucial role in this synthetic. 2.3. Some Implications There are some subtle but important differences between the actual loan and the synthetic. First, note that from the point of view of Euromarket banks, lending to Japanese banks involves a principal of USD100, and this creates a credit risk. In case of default, the 100 dollars lent may not be repaid. Against this risk, some capital has to be put aside. Depending on the state of money10 C HAPTER 1. Introduction 1 1 t 0 t 1 Borrow yen... (a) USD Pay borrowed yen 1 interest Buy spot dollars with the yen... (b) 2USD ...Buy the needed yen forward. Adding vertically, yen cash flows cancel... (c) 1Yen USD The result is like a USD loan. 2USD (d) t 0 t 1 t 0 t 1 t 0 t 1 FIGURE 1-8. A synthetic USD loan. markets and depending on counterparty credit risks, money center banks may adjust their credit lines toward such customers. On the other hand, in the case of the synthetic dollar loan, the international bank’s exposure to the Japanese bank is in the forward currency market only. Here, there is no principal involved. If the Japanese bank defaults, the burden of default will be on the domestic banking system in Japan. There is a risk due to the forward currency operation, but it is a counterparty risk and is limited. Thus, the Japanese bank may end up getting the desired funds somewhat easier if a synthetic is used. There is a second interesting point to the issue of credit risk mentioned earlier. The original money market loan was a Euromarket instrument. Banking operations in Euromarkets are considered offshore operations, taking place essentially outside the jurisdiction of national banking authorities. The local yen loan, on the other hand would be subject to supervision by Japanese authorities, obtained in the onshore market. In case of default, there may be some help from the Japanese Central Bank, unlike a Eurodollar loan where a default may have more severe implications on the lending bank.3. A Taxation Example 11 The third point has to do with pricing. If the actual and synthetic loans have identical cash flows, their values should also be the same excluding credit risk issues. If there is a value discrepancy the markets will simultaneously sell the expensive one, and buy the cheaper one, realizing a windfall gain. This means that synthetics can also be used in pricing the original instrument.11 Fourth, note that the money market loan and the synthetic can in fact be each other’s hedge. Finally, in spite of the identical nature of the involved cash flows, the two ways of securing dollar funding happen in completely different markets and involve very different financial contracts. This means that legal and regulatory differences may be significant. 3. A Taxation Example Now consider a totally different problem. We create synthetic instruments to restructure taxable gains. The legal environment surrounding taxation is a complex and ever-changing phenomenon, therefore this example should be read only from a financial engineering perspective and not as a tax strategy. Yet the example illustrates the close connection between what a financial engineer does and the legal and regulatory issues that surround this activity. 3.1. The Problem In taxation of financial gains and losses, there is a concept known as a wash-sale. Suppose that during the year 2007, an investor realizes some financial gains. Normally, these gains are taxable that year. But a variety of financial strategies can possibly be used to postpone taxation to the year after. To prevent such strategies, national tax authorities have a set of rules known as wash-sale and straddle rules. It is important that professionals working for national tax authorities in various countries understand these strategies well and have a good knowledge of financial engineering. Otherwise some players may rearrange their portfolios, and this may lead to significant losses in tax revenues. From our perspective, we are concerned with the methodology of constructing synthetic instruments. Suppose that in September 2007, an investor bought an asset at a price S0 = $100. In December 2007, this asset is sold at S1 = $150. Thus, the investor has realized a capital gain of $50. These cash flows are shown in Figure 1-9. Dec. 2007 $50 $100 invest 2$100 Liquidate and realize the capital gains Jan. 2007 Jan. 2008 Sept. 2007 FIGURE 1-9. An investment liquidated on Dec. 2007. 11 However, the credit risk issues mentioned earlier may introduce a wedge between the prices of the two loans.12 C HAPTER 1. Introduction One may propose the following solution. This investor is probably holding assets other than the St mentioned earlier. After all, the right way to invest is to have diversifiable portfolios. It is also reasonable to assume that if there were appreciating assets such as St, there were also assets that lost value during the same period. Denote the price of such an asset by Zt. Let the purchase price be Z0. If there were no wash-sale rules, the following strategy could be put together to postpone year 2007 taxes. Sell the Z-asset on December 2007, at a price Z1, Z1 < Z0, and, the next day, buy the same Zt at a similar price. The sale will result in a loss equal to Z1 − Z0 < 0 (10) The subsequent purchase puts this asset back into the portfolio so that the diversified portfolio can be maintained. This way, the losses in Zt are recognized and will cancel out some or all of the capital gains earned from St. There may be several problems with this strategy, but one is fatal. Tax authorities would call this a wash-sale (i.e., a sale that is being intentionally used to “wash” the 2007 capital gains) and would disallow the deductions. 3.1.1. Another Strategy Investors can find a way to sell the Z-asset without having to sell it in the usual way. This can be done by first creating a synthetic Z-asset and then realizing the implicit capital losses using this synthetic, instead of the Z-asset held in the portfolio. Suppose the investor originally purchased the Z-asset at a price Z0 = $100 and that asset is currently trading at Z1 = $50, with a paper loss of $50. The investor would like to recognize the loss without directly selling this asset. At the same time, the investor would like to retain the original position in the Z-asset in order to maintain a well-balanced portfolio. How can the loss be realized while maintaining the Z-position and without selling the Zt? The idea is to construct a proper synthetic. Consider the following sequence of operations: • Buy another Z-asset at price Z1 = $50 on November 26, 2007. • Sell an at-the-money call on Z with expiration date December 30, 2007. • Buy an at-the-money put on Z with the same expiration. The specifics of call and put options will be discussed in later chapters. For those readers with no background in financial instruments we can add a few words. Briefly, options are instruments that give the purchaser a right. In the case of the call option, it is the right to purchase the underlying asset (here the Z-asset) at a prespecified price (here $50). The put option is the opposite. It is the right to sell the asset at a prespecified price (here $50). When one sells options, on the other hand, the seller has the obligation to deliver or accept delivery of the underlying at a prespecified price. For our purposes, what is important is that short call and long put are two securities whose expiration payoff, when added, will give the synthetic short position shown in Figure 1-10. By selling the call, the investor has the obligation to deliver the Z-asset at a price of $50 if the call holder demands it. The put, on the other hand, gives the investor the right to sell the Z-asset at $50 if he or she chooses to do so. The important point here is this: When the short call and the long put positions shown in Figure 1-10 are added together, the result will be equivalent to a short position on stock Zt. In fact, the investor has created a synthetic short position using options. Now consider what happens as time passes. If Zt appreciates by December 30, the call will be exercised. This is shown in Figure 1-11a. The call position will lose money, since the investor has to deliver, at a loss, the original Z-stock that cost $100. If, on the other hand, the Zt3. A Taxation Example 13 Gain Loss Long position in Zt Purchase another Z-asset Synthetic short position in Z-asset Long put with strike 50 Short call with strike 50 K 5 50 Strike price Zt Z1 5 50 Zt Gain Loss FIGURE 1-10. Two positions that cancel each other. decreases, then the put position will enable the investor to sell the original Z-stock at $50. This time the call will expire worthless.12 This situation is shown in Figure 1-11b. Again, there will be a loss of $50. Thus, no matter what happens to the price Zt, either the investor will deliver the original Z-asset purchased at a price $100, or the put will be exercised and the investor will sell the original Z-asset at $50. Thus, one way or another, the investor is using the original asset purchased at $100 to close an option position at a loss. This means he or she will lose $50 while keeping the same Z-position, since the second Z, purchased at $50, will still be in the portfolio. The timing issue is important here. For example, according to U.S. tax legislation, wash-sale rules will apply if the investor has acquired or sold a substantially identical property within a 31- day period. According to the strategy outlined here, the second Z is purchased on November 26, while the options expire on December 30. Thus, there are more than 31 days between the two operations.13 3.2. Implications There are at least three interesting points to our discussion. First, the strategy offered to the investor was risk-free and had zero cost aside from commissions and fees. Whatever happens 12 For technical reasons, suppose both options can be exercised only at expiration. They are of European style. 13 The timing considerations suggest that the strategy will be easier to apply if over-the-counter (OTC) options are used, since the expiration dates of exchange-traded options may occur at specific dates, which may not satisfy the legal timing requirements.14 C HAPTER 1. Introduction Z Z Dec. 30 Short call If Zt appreciates short call will be exercised, with a loss of 50. Receive $50, deliver Z with cost $100. Zt (a) K 5 50 Long put Receive $50, deliver the Z with cost $100, the loss is again 50. Dec. 30 Zt (b) If Zt declines, the put is exercised. K 5 50 1 2 1 2 FIGURE 1-11. The strategy with the Z initially at 50. Two ways to realize loss. to the new long position in the Z-asset, it will be canceled by the synthetic short position. This situation is shown in the lower half of Figure 1-10. As this graph shows, the proposed solution has no market risk, but may have counterparty, or operational risks. The second point is that, once again, we have created a synthetic, and then used it in providing a solution to our problem. Finally, the example displays the crucial role legal and regulatory frameworks can play in devising financial strategies. Although this book does not deal with these issues, it is important to understand the crucial role they play at almost every level of financial engineering. 4. Some Caveats for What Is to Follow A newcomer to financial engineering usually follows instincts that are harmful for good understanding of the basic methodologies in the field. Hence, before we start, we need to lay out some basic rules of the game that should be remembered throughout the book. 1. This book is written from a market practitioner’s point of view. Investors, pension funds, insurance companies, and governments are clients, and for us they are always on the other side of the deal. In other words, we look at financial engineering from a trader’s, broker’s, and dealer’s angle. The approach is from the manufacturer’s perspective rather than the viewpoint of the user of the financial services. This premise is crucial in understanding some of the logic discussed in later chapters.5. Trading Volatility 15 2. We adopt the convention that there are two prices for every instrument unless stated otherwise. The agents involved in the deals often quote two-way prices. In economic theory, economic agents face the law of one price. The same good or asset cannot have two prices. If it did, we would then buy at the cheaper price and sell at the higher price. Yet for a market maker, there are two prices: one price at which the market participant is willing to buy something from you, and another one at which the market participant is willing to sell the same thing to you. Clearly, the two cannot be the same. An automobile dealer will buy a used car at a low price in order to sell it at a higher price. That is how the dealer makes money. The same is true for a market practitioner. A swap dealer will be willing to buy swaps at a low price in order to sell them at a higher price later. In the meantime, the instrument, just like the used car sold to a car dealer, is kept in inventories. 3. It is important to realize that a financial market participant is not an investor and never has “money.” He or she has to secure funding for any purchase and has to place the cash generated by any sale. In this book, almost no financial market operation begins with a pile of cash. The only “cash” is in the investor’s hands, which in this book is on the other side of the transaction. It is for this reason that market practitioners prefer to work with instruments that have zero-value at the time of initiation. Such instruments would not require funding and are more practical to use.14 They also are likely to have more liquidity. 4. The role played by regulators, professional organizations, and the legal profession is much more important for a market professional than for an investor. Although it is far beyond the scope of this book, many financial engineering strategies have been devised for the sole purpose of dealing with them. Remembering these premises will greatly facilitate the understanding of financial engineering. 5. Trading Volatility Practitioners or investors can take positions on expectations concerning the price of an asset. Volatility trading involves positions taken on the volatility of the price. This is an attractive idea, but how does one buy or sell volatility? Answering this question will lead to a third basic methodology in financial engineering. This idea is a bit more complicated, so the argument here will only be an introduction. Chapter 8 will present a more detailed treatment of the methodology. In order to discuss volatility trading, we need to introduce the notion of convexity gains. We start with a forward contract. Let us stay within the framework of the previous section and assume that Ft0 is the forward dollar-yen exchange rate.15 Suppose at time t0 we take a long position in the U.S. dollar as shown in Figure 1-15. The upward sloping line is the so-called payoff function. 16 For example, if at time t0 + Δ the forward price becomes Ft0+Δ, we can close the position with a gain: gain = Ft0+Δ − Ft0 (11) It is important, for the ensuing discussion, that this payoff function be a straight line with a constant slope. 14 Although one could pay bid-ask spreads or commissions during the process. 15 The et0 denotes the spot exchange rate USD/JPY, which is the value of one dollar in terms of Japanese yen at time t0. 16 Depending on at what point the spot exchange rate denoted by eT , ends up at time T, we either gain or lose from this long position.16 C HAPTER 1. Introduction Now, suppose there exists another instrument whose payoff depends on the FT . But this time the dependence is nonlinear or convex as shown in Figure 1-12 by the17 convex curve C(Ft). It is important that the curve be smooth, and that the derivative ∂C(Ft) ∂Ft (12) exist at all points. Finally suppose this payoff function has the additional property that as time passes the function changes shape. In fact as expiration time Tapproaches, the curve becomes a (piecewise) straight line just like the forward contract payoff. This is shown in Figure 1-13. 5.1. A Volatility Trade Volatility trades depend on the simultaneous existence of two instruments, one whose value moves linearly as the underlying risk changes, while the other’s value moves according to a convex curve. First, suppose {Ft1 ,. . .Ftn } are the forward prices observed successively at times t < t1,. . .,tn < T as shown in Figure 1-12. Note that these values are selected so that they oscillate around Ft0 . Ft4 Ft 2 Ft 0 Ft 1 Ft 3 Slope D4 Slope D3 Slope D1 Slope D0 Slope D2 FIGURE 1-12 At time t, t 0,t ,T Ft0 At expiration FIGURE 1-13 17 Options on the dollar-yen exchange rate will have such a pricing curve. But we will see this later in Chapter 8.5. Trading Volatility 17 F1 F0 D 0 D 1 Ignore the movement of the curve, assumed small. Note that as the curve moves down slope changes Sell |D02 D1| units at F1 Buy |D02 D1| units at F0 FIGURE 1-14 Gain at time t, t 0,t ,T before expiration Expiration gain Expiration loss e T eT Ft 0 Ft Ft Slope 5 11 FIGURE 1-15 Second, note that at every value of Fti we can get an approximation of the curve C(Ft) using the tangent at that point as shown in Figure 1-12. Clearly, if we know the function C(.), we can then calculate the slope of these tangents. Let the slope of these tangents be denoted by Di. The third step is the crucial one. We form a portfolio that will eliminate the risk of directional movements in exchange rates. We first buy one unit of the C(Ft) at time t0. Note that we do need cash for doing this since the value at t0 is nonzero. 0 < C(Ft0 ) (13) Simultaneously, we sell D0 units of the forward contract Ft0 . Note that the forward sale does not require any upfront cash at time t0. Finally, as time passes, we recalculate the tangent Di of that period and adjust the forward sale accordingly. For example, if the slope has increased, sell Di − Di−1 units more of the18 C HAPTER 1. Introduction forward contracts. If the slope has decreased cover Di − Di−1 units of the forwards.18 As Fti oscillates continue with this rebalancing. We can now calculate the net cash flows associated with this strategy. Consider the oscillations in Figures 1-12 and 1-13, (Fti−1 = F0) → (Ft1 = F1) → (Fti = F0) (14) with F0 < F1. In this setting if the trader follows the algorithm described above, then at every oscillation, the trader will 1. First sell Di – Di−1 additional units at the price F1. 2. Then, buy the same number of units at the price of F0. For each oscillation the cash flows can be calculated as gain = (D1 − D0)(F1 − F0) (15) SinceF0 < F1 and D0 < D1, this gain is positive as summarized in Figure 1-14. By hedging the original position in C(.) and periodically rebalancing the hedge, the trader has in fact succeeded to monetize the oscillations of Fti (see also Figure 1-15). 5.2. Recap Look at what the trader has accomplished. By holding the convex instrument and then trading the linear instrument against it, the trader realized positive gains. These gains are bigger, the bigger the oscillations. Also they are bigger, the bigger the changes in the slope terms Di. In fact the trader gains whether the price goes down or up. The gains are proportional to the realized volatility. Clearly this dynamic strategy has resulted in extracting cash from the volatility of the underlying forward rate Ft. It turns out that one can package such expected volatility gains and sell them to clients. This leads to volatility trading. It is accomplished by using options and, lately, through volatility swaps. 6. Conclusions This chapter uses some examples in order to display the use of synthetics (or replicating portfolios as they are called in formal models). The main objective of this book is to discuss methods that use financial markets, instruments, and financial engineering strategies in solving practical problems concerning pricing, hedging, risk management, balance sheet management, and product structuring. The book does not discuss the details of financial instruments, although for completion, some basics are reviewed when necessary. The book deals even less with issues of corporate finance. We assume some familiarity with financial instruments, markets, and rudimentary corporate finance concepts. Finally, the reader must remember that regulation, taxation, and even the markets themselves are “dynamic” objects that change constantly. Actual application of the techniques must update the parameters mentioned in this book. 18 This means buy back the units.Suggested Reading 19 Suggested Reading There are excellent sources for studying financial instruments, their pricing, and the associated modeling. An excellent source for instruments and markets is Hull (2008). For corporate finance, Brealey and Myers (2000) and Ross et al. (2002) are two well-known references. Bodie and Merton (1999) is highly recommended as background material. Wilmott (2000) is a comprehensive and important source. Duffie (2001) provides the foundation for solid asset pricing theory.20 C HAPTER 1. Introduction CASE STUDY: Japanese Loans and Forwards You are given the Reuters news item below. Read it carefully. Then answer the following questions. 1. Show how Japanese banks were able to create the dollar-denominated loans synthetically using cash flow diagrams. 2. How does this behavior of Japanese banks affect the balance sheet of the Western counterparties? 3. What are nostro accounts? Why are they needed? Why are the Western banks not willing to hold the yens in their nostro accounts? 4. What do the Western banks gain if they do that? 5. Show, using an “appropriate” formula, that the negative interest rates can be more than compensated by the extra points on the forward rates. (Use the decompositions given in the text.) NEW YORK, (Reuters) - Japanese banks are increasingly borrowing dollar funds via the foreign exchange markets rather than in the traditional international loan markets, pushing some Japanese interest rates into negative territory, according to bank officials. The rush to fund in the currency markets has helped create the recent anomaly in shortterm interest rates. For the first time in years, yields on Japanese Treasury bills and some bank deposits are negative, in effect requiring the lender of yen to pay the borrower. Japanese financial institutions are having difficulty getting loans denominated in U.S. dollars, experts said. They said international banks are weary of expanding credit lines to Japanese banks, whose balance sheets remain burdened by bad loans. “The Japanese banks are still having trouble funding in dollars,” said a fixed-income strategist at Merrill Lynch & Co. So Japan’s banks are turning to foreign exchange transactions to obtain dollars. The predominant mechanism for borrowing dollars is through a trade combining a spot and forward in dollar/yen. Japanese banks typically borrow in yen, which they have no problem getting. With a threemonth loan, for instance, the Japanese bank would then sell the yen for dollars in the spot market to, say, a British or American bank. The Japanese bank simultaneously enters into a three-month forward selling the dollars and getting back yen to pay off the yen loan at the stipulated forward rate. In effect, the Japanese bank has obtained a three-month dollar loan. Under normal circumstances, the dealer providing the transaction to the Japanese bank should not make anything but the bid-offer spread. But so great has been the demand from Japanese banks that dealers are earning anywhere from seven to 10 basis points from the spot-forward trade. The problem is that the transaction saddles British and American banks with yen for three months. Normally, international banks would place the yen in deposits with Japanese banks and earn the three-month interest rate. But mostWestern banks are already bumping against credit limits for their banks on exposure to troubled Japanese banks. Holding the yen on their own books in what are called NOSTRO accounts requires holding capital against them for regulatory purposes. So Western banks have been dumping yen holdings at any cost—to the point of driving interest rates on Japanese Treasury bills into negative terms. Also, large western banks such as Barclays Plc and J.P. Morgan are offering negative interest rates on yen deposits—in effect saying no to new yen-denominated deposits.Case Study 21 Western bankers said they can afford to pay up to hold Japanese Treasury bills—in effect earning negative yield—because their earnings from the spot-forward trade more than compensate them for their losses on holding Japanese paper with negative yield. Japanese six-month T-bills offer a negative yield of around 0.002 percent, dealers said. Among banks offering a negative interest rate on yen deposits was Barclays Bank Plsc, which offered a negative 0.02 percent interest rate on a three-month deposit. The Bank of Japan, the central bank, has been encouraging government-lending institutions to make dollar loans to Japanese corporations to overcome the problem, said [a market professional]. (Reuters, November 9, 1998). chapter 2 Introduction This chapter takes a step back and reviews in a nutshell the prerequisite for studying the methods of financial engineering. Readers with a good grasp of the conventions and mechanics of financial markets may skip it, although a quick reading would be preferable. Financial engineering is a practice and can be used only when we define the related environment carefully. The organization of markets, and the way deals are concluded, confirmed, and carried out, are important factors in selecting the right solution for a particular financial engineering problem. This chapter examines the organization of financial markets and the way market practitioners interact. Issues related to settlement, to accounting methods, and especially to conventions used by market practitioners are important and need to be discussed carefully. In fact, it is often overlooked that financial practices will depend on the conventions adopted by a particular market. This aspect, which is relegated to the background in most books, will be an important parameter of our approach. Conventions are not only important in their own right for proper pricing, but they also often reside behind the correct choice of theoretical models for analyzing pricing and risk management problems. The way information is provided by markets is a factor in determining the model choice. While doing this, the chapter introduces the mechanics of the markets, instruments, and who the players are. A brief discussion of the syndication process is also provided. 2. Markets The first distinction is between local and Euromarkets. Local markets are also called onshore markets. These denote markets that are closely supervised by regulators such as central banks and financial regulatory agencies. There are basically two defining characteristics of onshore markets. The first is reserve requirements that are imposed on onshore deposits. The second is the formal registration process of newly issued securities. Both of these have important cost, liquidity, and taxation implications. In money markets, reserve requirements imposed on banks increase the cost of holding onshore deposits and making loans. This is especially true of the large “wholesale” deposits that 2324 C HAPTER 2. An Introduction to Some Concepts and Definitions banks and other corporations may use for short periods of time. If part of these funds are held in a noninterest-bearing form in central banks, the cost of local funds will increase. The long and detailed registration process imposed on institutions that are issuing stocks, bonds, or other financial securities has two implications for financial engineering. First, issue costs will be higher in cases of registered securities when compared to simpler bearer form securities. Second, an issue that does not have to be registered with a public entity will disclose less information. Thus, markets where reserve requirements do not exist, where the registration process is simpler, will have significant cost advantages. Such markets are called Euromarkets. 2.1. Euromarkets We should set something clear at the outset. The term “Euro” as utilized in this section does not refer to Europe, nor does it refer to the Eurozone currency, the Euro. It simply means that, in terms of reserve requirements or registration process we are dealing with markets that are outside the formal control of regulators and central banks. The two most important Euromarkets are the Eurocurrency market and the Eurobond market. 2.1.1. Eurocurrency Markets Start with an onshore market. In an onshore system, a 3-month retail deposit has the following life. A client will deposit USD100 cash on date T. This will be available the same day. That is to say, “days to deposit” will equal zero. The deposit-receiving bank takes the cash and deposits, say, 10 percent of this in the central bank. This will be the required reserves portion of the original 100.1 The remaining 90 dollars are then used to make new loans or may be lent to other banks in the interbank overnight market.2 Hence, the bank will be paying interest on the entire 100, but will be receiving interest on only 90 of the original deposit. In such an environment, assuming there is no other cost, the bank has to charge an interest rate around 10 percent higher for making loans. Such supplementary costs are enough to hinder a liquid wholesale market for money where large sums are moved. Eurocurrency markets eliminate these costs and increase the liquidity. Let’s briefly review the life of a Eurocurrency (offshore) deposit and compare it with an onshore deposit. Suppose a U.S. bank deposits USD100 million in another U.S. bank in the New York Eurodollar (offshore) market. Thus, as is the case for Eurocurrency markets, we are dealing only with banks, since this is an interbank market. Also, in this example, all banks are located in the United States. The Eurodeposit is made in the United States and the “money” never leaves the United States. This deposit becomes usable (settles) in 2 days—that is to say, days to deposit is 2 days. The entire USD100 million can now be lent to another institution as a loan. If this chain of transactions was happening in, say, London, the steps would be similar. 2.1.2. Eurobond Markets A bond sold publicly by going through the formal registration process will be an onshore instrument. If the same instrument is sold without a similar registration process, say, in London, and if it is a bearersecurity, then it becomes essentially an off-shore instrument. It is called a Eurobond. 1 In reality the process is more complicated than this. Banks are supposed to satisfy reserve requirements over an average number of days and within, say, a one-month delay. 2 In the United States this market is known as the federal funds market.2. Markets 25 Again the prefix “Euro” does not refer to Europe, although in this case the center of Eurobond activity happens to be in London. But in principle, a Eurobond can be issued in Asia as well. A Eurobond will be subject to less regulatory scrutiny, will be a bearer security, and will not be (as of now) subject to withholding taxes. The primary market will be in London. The secondary markets may be in Brussels, Luxembourg, or other places, where the Eurobonds will be listed. The settlement of Eurobonds will be done through Euroclear or Cedel. 2.1.3. Other Euromarkets Euromarkets are by no means limited to bonds and currencies. Almost any instrument can be marketed offshore. There can be Euro-equity, Euro-commercial paper (ECP), Euro mediumterm note (EMTN), and so on. In derivatives we have onshore forwards and swaps in contrast to off-shore nondeliverable forwards and swaps. 2.2. Onshore Markets Onshore markets can be organized over the counter or as formal exchanges. Over-the-counter (OTC) markets have evolved as a result of spontaneous trading activity. An OTC market often has no formal organization, although it will be closely monitored by regulatory agencies and transactions may be carried out along some precise documentation drawn by professional organizations, such as ISDA, ICMA.3 Some of the biggest markets in the world are OTC. A good example is the interest rate swap (IRS) market, which has the highest notional amount traded among all financial markets with very tight bid-ask spreads. OTC transactions are done over the phone or electronically and the instruments contain a great deal of flexibility, although, again, institutions such as ISDA draw standardized documents that make traded instruments homogeneous. In contrast to OTC markets, organized exchanges are formal entities. They may be electronic or open-outcry exchanges. The distinguishing characteristic of an organized exchange is its formal organization. The traded products and trading practices are homogenous while, at the same time, the specifications of the traded contracts are less flexible. A typical deal that goes through a traditional open-outcry exchange can be summarized as follows: 1. A client uses a standard telephone to call a broker to place an order. The broker will take the order down. 2. Next, the order is transmitted to exchange floors or, more precisely, to a booth. 3. Once there, the order is sent out to the pit, where the actual trading is done. 4. Once the order is executed in the pit, a verbal confirmation process needs to be implemented all the way back to the client. Stock markets are organized exchanges that deal in equities. Futures and options markets process derivatives written on various underlying assets. In a spot deal, the trade will be done and confirmed, and within a few days, called the settlement period, money and securities change hands. In futures markets, on the other hand, the trade will consist of taking positions, and 3 The International Securities Market Association is a professional organization that among other activities may, after lengthy negotiations between organizations, homogenize contracts for OTC transactions. ISDA is the International Swaps and Derivatives Association. NASD, the National Association of Securities Dealers in the United States, and IPMA, the International Primary Market Association, are two other examples of such associations.26 C HAPTER 2. An Introduction to Some Concepts and Definitions settlement will be after a relatively longer period, once the derivatives expire. The trade is, however, followed by depositing a “small” guarantee, called an initial margin. Different exchanges have different structures and use different approaches in market making. For example, at the New York Stock Exchange (NYSE), market making is based on the specialist system. Specialists run books on stocks that they specialize in. As market makers, specialists are committed to buying and selling at all times at the quoted prices and have the primary responsibility of guaranteeing a smooth market. 2.2.1. Futures Exchanges EUREX, CBOT, CME, and TIFFE are some of the major futures and options exchanges in the world. The exchange provides three important services: 1. A physical location (i.e., the trading floor and the accompanying pits) for such activity, if it is an open-outcry system. Otherwise the exchange will supply an electronic trading platform. 2. An exchange clearinghouse that becomes the real counterparty to each buyer and seller once the trade is done and the deal ticket is stamped. 3. The service of creating and designing financial contracts that the trading community needs and, finally, providing a transparent and reliable trading environment. The mechanics of trading in futures (options) exchanges is as follows. Two pit traders trade directly with each other according to their client’s wishes. One sells, say, at 100; the other buys at 100. Then the deal ticket is signed and stamped. Until that moment, the two traders are each other’s counterparties. But once the deal ticket is stamped, the clearinghouse takes over as the counterparty. For example, if a client has bought a futures contract for the delivery of 100 bushels of wheat, then the entity eventually responsible (they have agents) for delivering the wheat is not the “other side” who physically sold the contract on the pit, but the exchange clearinghouse. By being the only counterparty to all short and long positions, the clearinghouse will lower the counterparty risk dramatically. The counterparty risk is actually reduced further, since the clearinghouse will deal with clearing members, rather than the traders directly.4 An important concept that needs to be reviewed concerning futures markets is the process of marking to market. When one “buys” a futures contract, a margin is put aside, but no cash payment is made. This leverage greatly increases the liquidity in futures markets, but it is also risky. To make sure that counterparties realize their gains and losses daily, the exchange will reevaluate positions every day using the settlement price observed at the end of the trading day.5 Example: A 3-month Eurodollar futures contract has a price of 98.75 on day T. At the end of day T + 1 , the settlement price is announced as 98.10. The price fell by 0.65, and this is a loss to the long position holder. The position will be marked to market, and the clearinghouse—or more correctly—the clearing firm, will lower the client’s balance by the corresponding amount. 4 In order to be able to trade, a pit trader needs to “open an account” with a clearing member, a private financial company that acts as clearing firm that deals with the clearinghouse directly on behalf of the trader. 5 The settlement price is decided by the exchange and is not necessarily the last trading price.4. The Mechanics of Deals 27 The open interest in futures exchanges is the number of outstanding futures contracts. It is obtained by totaling the number of short and long positions that have not yet been closed out by delivery, cash settlement, or offsetting long/short positions. 3. Players Market makers make markets by providing days to delivery, notice of delivery, warehouses, etc. Market makers must, as an obligation, buy and sell at their quoted prices. Thus for every security at which they are making the market, the market maker must quote a bid and an ask price. A market maker does not warehouse a large number of products, nor does the market maker hold them for a long period of time. Traders buy and sell securities. They do not, in the pure sense of the word, “make” the markets. A trader’s role is to execute clients’ orders and trade for the company given his or her position limits. Position limits can be imposed on the total capital the trader is allowed to trade or on the risks that he or she wishes to take. A trader or market maker may run a portfolio, called a book. There are “FX books,” “options books,” “swap books,” and “derivatives books,” among others. Books run by traders are called “trading books”; they are different from “investment portfolios,” which are held for the purpose of investment. Trading books exist because during the process of buying and selling for clients, the trader may have to warehouse these products for a short period of time. These books are hedged periodically. Brokers do not hold inventories. Instead, they provide a platform where the buyers and sellers can get together. Buying and selling through brokers is often more discreet than going to bids and asks of traders. In the latter case, the trader would naturally learn the identity of the client. In options markets, a floor-broker is a trader who takes care of a client’s order but does not trade for himself or herself. (On the other hand, a market maker does.) Dealers quote two-way prices and hold large inventories of a particular instrument, maybe for a longer period of time than a market maker. They are institutions that act in some sense as market makers. Risk managers are relatively new players. Trades, and positions taken by traders, should be “approved” by risk managers. The risk manager assesses the trade and gives approvals if the trade remains within the preselected boundaries of various risk managers. Regulators are important players in financial markets. Practitioners often take positions of “tax arbitrage” and “regulatory arbitrage.” A large portion of financial engineering practices are directed toward meeting the needs of the practitioners in terms of regulation and taxation. Researchers and analysts are players who do not trade or make the market. They are information providers for the institutions and are helpful in sell-side activity. Analysts in general deal with stocks and analyze one or more companies. They can issue buy/sell/hold signals and provide forecasts. Researchers provide macrolevel forecasting and advice. 4. The Mechanics of Deals What are the mechanisms by which the deals are made? How are trades done? It turns out that organized exchanges have their own clearinghouses and their own clearing agents. So it is relatively easy to see how accounts are opened, how payments are made, how contracts are purchased and positions are maintained. The clearing members and the clearinghouse do most of these. But how are these operations completed in the case of OTC deals? How does one buy a bond and pay for it? How does one buy a foreign currency?28 C HAPTER 2. An Introduction to Some Concepts and Definitions Trading room Reuters, Bloomberg etc . . . . Deal goes to back office Back office clerical, desks Middle office initial verification a) Trade ticket is written b) Entered in front office computers c) Rerouted to middle office SWIFT manages Payments, Receipt Confirmations Reconciliation, audit department Outgoing trades Final verification, settlement Reconcile bank accounts (nostros) Reconcile custody accounts Report problems FIGURE 2-1. How trades are made and confirmed. Turning to another detail, where are these assets to be kept? An organized exchange will keep positions for the members, but who will be the custodian for OTC operations and secondary market deals in bonds and other relevant assets? Several alternative mechanisms are in place to settle trades and keep the assets in custody. A typical mechanism is shown in Figure 2-1. The mechanics of a deal in Figure 2-1 are from the point of view of a market practitioner. The deal is initiated at the trading or dealing room. The trader writes the deal ticket and enters this information in the computer’s front office system. The middle office is the part of the institution that initially verifies the deal. It is normally situated on the same floor as the trading room. Next, the deal goes to the back office, which is located either in a different building or on a different floor. Back-office activity is as important for the bank as the trading room. The back office does the final verification of the deal, handles settlement instructions, releases payments, and checks the incoming cash flows, among other things. The back office will also handle the messaging activity using the SWIFT system, to be discussed later. 4.1. Orders There are two general types of orders investors or traders can place. The first is a market order, where the client gets the price the market is quoting at that instant. Alternatively parties can place a limit order. Here a derived price will be specified along the order, and the trade will go through only if this or a better price is obtained. A limit order is valid only during a certain period, which needs to be specified also. A stop loss order is similar. It specifies a target price at which a position gets liquidated automatically.4. The Mechanics of Deals 29 Processing orders is by no means error-free. For example, one disadvantage of traditional open-outcry exchanges is that in such an environment, mistakes are easily made. Buyer and seller may record different prices. This is called a “price out.” Or there may be a “quantity out,” where the buyer has “bought 100” while the seller thinks that he has “sold 50.” In the case of options exchanges, the recorded expiration dates may not match, which is called a “time out.” Out-trades need to be corrected after the market close. There can also be missing trades. These trades need to be negotiated in order to recover positions from counterparties and clients.6 4.2. Confirmation and Settlement Order confirmation and settlement are two integral parts of financial markets. Order confirmation involves sending messages between counterparties, to confirm trades verbally agreed upon between market practitioners. Settlement is exchanging the cash and the related security, or just exchanging securities. The SWIFT system is a communication network that has been created for “paperless” communication between market participants to this end. It stands for the Society for Worldwide Financial Telecommunications and is owned by a group of international banks. The advantage of SWIFT is the standardization of messages concerning various transactions such as customer transfers, bank transfers, Foreign Exchange (FX), loans, deposits. Thousands of financial institutions in more than 100 countries use this messaging system. Another interesting issue is the relationship between settlement, clearing, and custody. Settlement means receiving the security and making the payment. The institutions can settle, but in order for the deal to be complete, it must be cleared. The orders of the two counterparties need to be matched and the deal terminated. Custody is the safekeeping of securities by depositing them with carefully selected depositories around the world. A custodian is an institution that provides custody services. Clearing and custody are both rather complicated tasks. FedWire, Euroclear, and Cedel are three international securities clearing firms that also provide some custody services. Some of the most important custodians are banks. Countries also have their own clearing systems. The best known bank clearing systems are CHIPS and CHAPS. CHAPS is the clearing system for the United Kingdom, CHIPS is the clearing system for payments in the United States. Payments in these systems are cleared multilaterally and are netted. This greatly simplifies settling large numbers of individual trades. Spot trades settle according to the principle of DVP—that is to say, delivery versus payment— which means that first the security is delivered (to securities clearing firms) and then the cash is paid. Issues related to settlement have another dimension. There are important conventions involving normal ways of settling deals in various markets. When a settlement is done according to the convention in that particular market, we say that the trade settles in a regular way. Of course, a trade can settle in a special way. But special methods would be costly and impractical. Example: Market practitioners denote the trade date by T, and settlement is expressed relative to this date. U.S. Treasury securities settle regularly on the first business day after the trade—that is to say, on T+1. But it is also common for efficient clearing firms to have cash settlement— that is to say, settlement is done on the trade date T. 6 As an example, in the case of a “quantity out,” the two counterparties may decide to split the difference.30 C HAPTER 2. An Introduction to Some Concepts and Definitions Corporate bonds and international bonds settle on T+3. Commercial paper settles the same day. Spot transactions in stocks settle regularly on T+3 in the United States. Euromarket deposits are subject to T+2 settlement. In the case of overnight borrowing and lending, counterparties may choose cash settlement. Foreign exchange markets settle regularly on T+2. This means that a spot sale (purchase) of a foreign currency will lead to two-way flows two days after the trade date, regularly. T+2 is usually called the spot date. It is important to expect that the number of days to settlement in general refers to business days. This means that in order to be able to interpret T + 2 correctly, the market professional would need to pin down the corresponding holiday convention. Before discussing other market conventions, we can mention two additional terms that are related to the preceding dates. The settlement date is sometimes called the value date in contracts. Cash changes hands at the value date. Finally, in swap-type contracts, there will be the deal date (i.e., when the contract is signed), but the swap may not begin until the effective date. The latter is the actual start date for the swap contract and will be at an agreed-upon later date. 5. Market Conventions Market conventions often cause confusion in the study of financial engineering. Yet, it is very important to be aware of the conventions underlying the trades and the instruments. In this section, we briefly review some of these conventions. Conventions vary according to the location and the type of instrument one is concerned with. Two instruments that are quite similar may be quoted in very different ways. What is quoted and the way it is quoted are important. As mentioned, in Chapter 1 in financial markets there are always two prices. There is the price at which a market maker is willing to buy the underlying asset and the price at which he or she is willing to sell it. The price at which the market maker is willing to buy is called the bid price. The ask price is the price at which the market maker is willing to sell. In London financial markets, the ask price is called an offer. Thus, the bid-ask spread becomes the bid-offer spread. As an example consider the case of deposits in London money and foreign exchange markets, where the convention is to quote the asking interest rate first. For example, a typical quote on interest rates would be as follows: Ask (Offer) Bid 5 1 4 5 1 8 In other money centers, interest rates are quoted the other way around. The first rate is the bid, the second is the ask rate. Hence, the same rates will look as such: Bid Ask (Offer) 5 1 8 5 1 4 A second characteristic of the quotes is decimalization. The Eurodollar interest rates in London are quoted to the nearest 1 16 or sometimes 1 32 . But many money centers quote interest5. Market Conventions 31 rates to two decimal points. Decimalization is not a completely straightforward issue from the point of view of brokers/dealers. Note that with decimalization, the bid-ask spreads may narrow all the way down to zero, and there will be no minimum bid-ask spread. This may mean lower trading profits, everything else being the same. 5.1. What to Quote Another set of conventions concerns what to quote. For example, when a trader receives a call, he or she might say, “I sell a bond at a price of 95,” or instead, he or she might say, “I sell a bond at yield 5%.” Markets prefer to work with conventions to avoid potential misunderstandings and to economize time. Equity markets quote individual stock prices. On the New York Stock Exchange the quotes are to decimal points. Most bond markets quote prices rather than yields, with the exception of short-term T-bills. For example, the price of a bond may be quoted as follows: Bid price Ask (Offer) price 90.45 90.57 The first quote is the price a market maker is willing to pay for a bond. The second is the price at which the market maker dealer is willing to sell the same bond. Note that according to this, bond prices are quoted to two decimal points, out of a par value of 100, regardless of the true denomination of the bond. It is also possible that a market quotes neither a price nor a yield. For example, caps, floors, and swaptions often quote “volatility” directly. Swap markets prefer to quote the “spread” (in the case of USD swaps) or the swap rate itself (Euro-denominated swaps). The choice of what to quote is not a trivial matter. It affects pricing as well as risk management. 5.2. How to Quote Yields Markets use three different ways to quote yields. These are, respectively, the money market yield, the bond equivalent yield, and the discount rate.7 We will discuss these using default-free pure discount bonds with maturity T as an example. Let the time-t price of this bond be denoted by B(t, T). The bond is default free and pays 100 at time T. Now, suppose R represents the time-t yield of this bond. It is clear that B(t, T) will be equal to the present value of 100, discounted using R, but how should this present value be expressed? For example, assuming that (T − t) is measured in days and that this period is less than 1 year, we can use the following definition: B(t, T) = 100 (1 + R)( T−t 365 ) (1) where the ( T −t 365 ) is the remaining life of the bond as a fraction of year, which here is “defined” as 365 days. 7 This latter term is different from the special interest rate used by the U.S. Federal Reserve System, which carries the same name. Here the discount rate is used as a general category of yields.32 C HAPTER 2. An Introduction to Some Concepts and Definitions But we can also think of discounting using the alternative formula: B(t, T) = 100 (1 + R( T −t 365 )) (2) Again, suppose we use neither formula but instead set B(t, T) = 100 − R T − t 365 100 (3) Some readers may think that given these formulas, (1) is the right one to use. But this is not correct! In fact, they may all be correct, given the proper convention. The best way to see this is to consider a simple example. Suppose a market quotes prices B(t, T) instead of the yields R. 8 Also suppose the observed market price is B(t, T) = 95.00 (4) with (T − t) = 180 days and the year defined as 365 days. We can then ask the following question: Which one of the formulas in (1) through (3) will be more correct to use? It turns out that these formulas can all yield the same price, 95.00, if we allow for the use of different Rs. In fact, with R1 = 10.9613% the first formula is “correct,” since B(t, T) = 100 (1 + .109613)( 180 365 ) (5) = 95.00 (6) On the other hand, with R2 = 10.6725% the second formula is “correct,” since B(t, T) = 100 (1 + .106725( 180 365 )) (7) = 95.00 (8) Finally, if we let R3 = 10.1389%, the third formula will be “correct”: B(t, T) = 100 − .101389 180 365 100 (9) = 95.00 (10) Thus, for (slightly) different values of Ri, all formulas give the same price. But which one of these is the “right” formula to use? That is exactly where the notion of convention comes in. A market can adopt a convention to quote yields in terms of formula (1), (2) or (3). Suppose formula (1) is adopted. Then, once traders see a quoted yield in this market, they would “know” that the yield is defined in terms of formula (1) and not by (2) or (3). This convention, which is only an implicit understanding during the execution of trades, will be expressed precisely in the actual contract and will be 8 Emerging market bonds are in general quotes in terms of yields. In treasury markets, the quotes are in terms of prices. This may make some difference from the point of view of both market psychology, pricing and risk management decisions. Exercises 1. Suppose the quoted swap rate is 5.06/5.10. Calculate the amount of fixed payments for a fixed payer swap for the currencies below in a 100 million swap. • USD. • EUR. Now calculate the amount of fixed payments for a fixed receiver swap for the currencies below in a 100 million swap. • JPY. • GBP. 2. Suppose the following stock prices for GE and Honeywell were observed before any talk of merger between the two institutions: Honeywell (HON) 27.80 General Electric (GE) 53.98 Also, suppose you “know” somehow that GE will offer 1.055 GE shares for each Honeywell share during any merger talks. (a) What type of “arbitrage” position would you take to benefit from this news? (b) Do you need to deposit any of your funds to take this position? (c) Do you need to and can you borrow funds for this position? (d) Is this a true arbitrage in the academic sense of the word? (e) What (if any) risks are you taking? 3. Read the market example below and answer the following questions that relate to it. Proprietary dealers are betting that Euribor, the proposed continental European-based euro money market rate, will fix above the Euro BBA Libor alternative... The arbitrage itself is relatively straightforward. The proprietary dealer buys the Liffe September 1999 Euromark contract and sells the Matif September 1999 Pibor contract at roughly net zero cost. As the Liffe contract will be referenced to Euro BBA Libor and the Matif contract