Fixed-Income Analysis for the Global Financial Market: Money Market, Foreign Exchange, Securities, and Derivatives / Edition 1

by Giorgio S. Questa

Overview

This comprehensive new book explains and clarifies the essential building blocks underlying the pricing and risk analysis of fixed-income securities and derivatives - using mathematics lightly, to make things easier, not harder. The emphasis throughout is on how-to-do, on building operational knowledge from the ground up. There are more than 300 examples and exhibits based on current market data. You will find essential information on:
* The global money market
* Foreign exchange transaction and foreign exchange derivatives
* Bonds and zero coupon bonds - including a risk management-driven discussion of duration and convexity
* Interest rate swaps, currency swaps, and exchange-traded futures
* Stochastic models and option pricing
* Stochastic models of the yield curve

Product Details

ISBN-13:	9780471246534
Publisher:	Wiley
Publication date:	07/22/1999
Series:	Frontiers in Finance Series , #10
Pages:	368
Product dimensions:	7.40(w) x 10.30(h) x 1.15(d)

About the Author

GIORGIO S. QUESTA is a senior consultant at Pareto Partners, a quantitative institutional asset management firm with operations in the U.K., the U.S., and Australia. He teaches a number of graduate courses in finance, both in the U.S. and Europe. Previously, he was the CEO of IMI International, an investment banking and asset management firm with operations in New York, London, Frankfurt, and Luxembourg. He has also worked with Procter & Gamble and Andersen Consulting.

Read an Excerpt

Fixed-Income Analysis for the Global Financial Market: Money Market, Foreign Exchanges, and Derivative Securities

Giorgio S. Questa
0-471-24653-0

Note: The Figures and/or Tables mentioned in this sample chapter do not appear on the web.
Chapter 1
Background and Terminology

1-1 Quotations, Bid-Ask Spread, and Transaction Costs
1-2 Trade, Settlement, and Maturity Dates. Accrual Rules
1-3 Long and Short Positions; Short Selling Securities
1-4 Arbitrage-Free Pricing and the Law of One Price
1-5 Euromarket Time Deposits and LIBOR Reference Rate
1-6 Short-Term Discount Securities
1-7 Auctions

This is an introductory chapter. If you have a background in finance, you should be able to browse through it rather quickly; however, do not skip it altogether, because some relevant features covered here are not easily found in other reference books. The first four sections will introduce some of the basic concepts and terminology of fixed-income markets. The next two sections provide brief coverage of the two most pervasive short-term financial instruments, that is, bank deposits and short-term securities. Section 1-7 is an appendix dedicated to auctions, which are a widely used pricing and issuing mechanism (most government securities, including U. S. Treasury bills, notes, and bonds, are sold this way). Before we plunge into the subject matter of this chapter, it will be useful to spend a few words on terminology.

• The word securities is often used to indicate financial instruments, such as derivatives, that in fact are not securities.
• Coupon is a term originally associated only with bonds and notes, which, until book-entry securities became the norm, were printed carrying the appropriate number of coupons, one for each interest payment. Currently the word coupon also indicates periodic interest payments from fixed-income instruments that are not bonds, such as interest-rate or currency swaps; see Chapter 10.
• The word coupon is also used as a shorthand expression for coupon bonds and/ or notes. The expression U. S. Treasury coupons will therefore indicate T-bonds and T-notes, both of which pay interest semiannually.

  1-1 QUOTATIONS, BID-ASK SPREAD, AND TRANSACTION COSTS

  A number of important developments in modern finance are analyzed with reference to a frictionless world (zero transaction costs, continuous markets, identical lending and borrowing rates). This is justified by the necessity of presenting core ideas without the cumbersome mathematics that can be necessary to deal with a non-frictionless financial world. In real life, however, transaction costs play an important role.
  Most fixed-income and foreign exchange instruments trade over the counter (OTC), with market makers quoting two-way prices that are disseminated through computer networks. Deals are normally transacted over the phone, and their confirmation in writing can take place in a variety of ways, whenever possible taking ad-vantage of some specialized infrastructure, such as Fed Wire, Trax, or Swift. As a rule, OTC market makers keep a taped record of telephone deals.
  The most noticeable exception to OTC markets is represented by financial futures and options exchanges, some of which are committed to open-outcry trading, such as the Chicago Board of Trade and the Chicago Mercantile Exchange. The quotation mechanisms for futures and options exchanges will be examined within the appropriate context.
  The market rules examined in this paragraph should be sufficient to convey a basic understanding of the quotation mechanism in OTC markets. Further quotations systems will be covered in the relevant sections of this book. We operate in a very sophisticated and highly computerized environment. Yet a number of old, and often irrational, pricing and quoting traditions survive and are regularly utilized in everyday activity. Outdated as they might be, they are part of the terrain and must be clearly understood. An interesting example is the foreign-exchange quotation of the U. K. pound (£ or GBP), always in the form of foreign currency unit per 1 £, which still reflects the days in which the pound did not follow the decimal system and it was therefore inexpedient to quote a £ price for 1 unit of foreign currency (the same quotation applies to the Irish punt, I£, which, however, will soon disappear because the Republic of Ireland has joined the Euro).
  These quirks are by no means confined to old instruments. Forward rate agreements (FRAs) and exchange-traded interest rate futures are both quite recent (the 90-day T-bill future was introduced in 1976 and FRAs in 1984), but their quotations follow different rules (see Chapter 4). The following terminology is commonly accepted:

  Bid price = the price at which the market maker stands ready to buy
  Ask (offer) price = the price at which the market maker stands ready to sell
  Midprice = the arithmetic average of bid and ask prices
  Bid-ask spread = gross revenue margin for the market maker

  The quantities to which the bid-ask prices apply are subject to both lower and upper limits. Market makers usually do not deal in retail size. They also introduce upper limits to avoid being caught off-guard by large orders in moments of price volatility. Most of the quotations are only indicative for large volumes and have to be confirmed over the phone before a trade is finalized.

  Bonds and Notes

  Most fixed-income securities are quoted in terms of price (the bid is obviously lower than the ask), with reference to a face value of 100 currency units. In the United States,

  this quotation is known as dollar price. Prices are usually quoted clean, that is, without accrued coupon, which is paid on settlement over and above the clean price; see Section 1-2. There are, however, some oddities, the best known of which is represented by U. S. Treasury bonds, notes, and strips. For these securities the fractional number, separated by a colon or by a hyphen, is expressed in 32nds of 1% (see Exhibits 1-1 and 1-2).

  Short-Term Discount Securities

  Discount securities, such as Treasury bills (Exhibit 1-3) and commercial paper, do not carry add-on interest (coupon) and are issued and traded at a price that is lower than their redemption value (face value or maturity value). The interest paid by the issuer, over the time span from issue to maturity, is therefore equal to the difference between purchase price and face value. These securities are usually quoted in terms of the percent discount rate that is utilized to determine their price (also known as bank discount basis, see Section 1-6). In this case, due to the inverse relationship between price and discount rate, the bid rate is going to be higher than the ask rate. A common piece of jargon in the money market is basis point (bp), that is, 1% of 1% 4 0.01%.

  Quoting Bid-Ask Rates on Deposits

  Quotations are expressed in terms of the interest rate. The bid rate, which the bank is willing to pay on deposits (buy deposits), is obviously lower than the ask (offered) rate at which the bank will lend money (sell deposits). The Financial Times follows the London rule of quoting the offer rate first (see Exhibit 1-4). Note that live quotes on screens are now generally expressed in decimal form and that the bid-ask spread is usually lower than 4/ 32 of 1%.

  Foreign Exchange

  Foreign exchange (FX) quotations will be examined again in Chapter 4. For the moment let us note that there is a potential source of ambiguity: Buying $ against ¥ is the same transaction as selling ¥ against $.

  Spot sale of ¥ against $ = Spot purchase of $ against ¥

  To identify the bid and the ask, we must define, on a conventional basis, which currency is considered to be bought/ sold. The most widespread quoting rule in FX trades involving the $ is to consider the U. S. currency as the object of purchase or sale. Therefore ¥/$ 4 124.30/ 39 means that the FX dealer is buying $ at ¥ 124.30 (bid) and selling $ at ¥ 124.39 (ask, offer). We have seen that the £ is quoted in terms of units of currency per £. A $/£ quotation of 1.6328/ 38 entails that the market maker is willing to:

  • Buy £ at $1.6328 (4 sell $ at 0.6124 £ per $)
  • Sell £ at $1.6338 (4 buy $ at 0.6121 £ per $)

  Transaction Costs

  Transaction costs are commonly defined in terms of a roundturn, that is, buying a financial instrument and then selling it. For market-maker quotations, the cost of a roundturn equals the bid-ask spread-you open the position at the ask price and then you close it at the bid. In markets based on the open outcry system, each transaction has the same price for the buyer and for the seller, but both pay a commission to the broker( s) for executing the trade. The roundturn cost is simply the sum of the buy and sell commissions. In the futures markets, where open positions often have a very short life, brokers often quote commissions on a roundturn basis. The important concept of market liquidity is also defined in terms of transaction costs. A liquid market allows you to deal in volume, in a short time span, at low transaction costs. Thinking of transaction costs in terms of roundturn is usually accurate considering that, in most cases, investments are not held to maturity. When determining portfolio adjustments and switches between securities, you must factor in transaction costs.

  Example: You are an asset manager and you own $5 million, face value of the World Bank 6 3 ¤8 % global bond, maturity 21 July 2005 (bid-ask 4 95.75 1 95.875 on 3 July 1996). A securities dealer proposes a switch to bonds that yield a few basis points more and that are of the same quality (maturity, coupon, liquidity, high credit rating, etc. ). In deciding whether to accept the advice of the broker/ dealer, you should verify the yield advantage considering that you will be selling the World Bank bonds at the bid price and buying the proposed bonds at the ask.

  Selling a bond to buy another bond (one that presents more desirable risk/ return characteristics) was traditionally called a bond swap in Wall Street jargon. This can now be confusing because, since the beginning of the 1980s, swap has come to indicate a specific and very widely used derivative product. A new term, bond switch, is now being used as a substitute for bond swap. You should remember, however, that bond swap is still very much alive in Wall Street-speak.
  If you are a market maker, you face much lower transaction costs on the securities and instruments in which you are active. You can easily build up inventory by buying at the bid and waiting before selling. You are also at an advantage in selling short because you can go directly to your customers to borrow the necessary securities; see Section 1-3.

  1-2 TRADE, SETTLEMENT, AND MATURITY DATES. ACCRUAL RULES

  The settlement of fixed-income transaction hinges on a large set of market conventions. They are the province of operations and clearing specialists, and full coverage of their intricacies would require a separate book. In this section we shall therefore examine only those rules and examples that are necessary to build a satisfactory level of insight and to understand how to carry out fixed-income calculations.

  Trade Date

  The trade date is the date on which a commitment is made (to buy, sell, lend, borrow, swap, write an option, etc.). When securities are bought at an auction, the trade date coincides with the day on which the results of the auction are known and the bidders are told their allotments and invoice price( s). When securities are bought by members of an underwriting group (a common practice for corporate bonds and for Euromarket issues), the trade date coincides with the date on which the allotments are finalized by the lead manager( s) of the underwriting group.

  Settlement Date and Fail to Deliver

  The settlement date is the date on which the contract is fulfilled. The concept is better understood with reference to a few examples (see Exhibit 1-5).

  Spot Sale of Securities. Settlement date is when the buyer pays the price and the seller delivers the securities. Usually this takes place through some clearing organization, such as Fed Wire, Depository Trust Corporation, Euroclear, Cedel, and others, to guarantee delivery versus payment (DVP).
  When the seller cannot deliver the securities in due time, we have a fail to deliver. A complex set of rules governs fails-to-deliver in different markets and for different instruments. A common consequence, however, is that until the securities are delivered, the buyer does not have to pay for them, and therefore the seller loses the interest that would have accrued on these moneys. Fails that occur on a Friday are particularly disliked by sellers of securities (and liked by buyers) because they entail the loss of a minimum of three days of accrued interest.
  U. S. Treasury securities settle regular way on the first business day following the trade date (T `1 in settlement jargon). Corporate bonds and international bonds settle on the third business day after the trade date (T ` 3). The T ` 3 rule went into effect in mid 1995; before that, the rule was T ` 5. In the U. S. Treasury market it is not uncommon to agree on cash settlement, that is, settlement on the trade date (this is made possible by the high level of efficiency of Fed Wire).
  When a security is first issued, the settlement date is usually a few business days after the trade date (e. g., 13-and 26-week U. S. T-bills are auctioned on Monday and settle on the following Thursday).

  Time Deposits, such as Euromarket Deposits. Settlement means the delivery from the lender to the borrower of the contracted amount. Settlement in the Euromarkets is usually T ` 2. The contracting parties can agree, however, for settlement on the trade date (e. g., overnight deposits) or on the first business day following the trade date (e. g., for overnight deposits starting the day after the trade date- in jargon, TOMNEXT = tomorrow next). An overnight deposit settling (T ` 2) is known as SPOTNEXT.

  Foreign Exchange. Spot transactions settle regular way like Eurodeposits, that is, T ` 2. This involves two-way flows, as shown in Exhibit 1-6. The currency flows are in the form of sight deposits. Forward transactions settle on some contractually specified future date. A 3-month forward FX transaction will have the same two-way flows as a spot transaction, but these will take place 3 months after the settlement date of the spot transaction.

  Maturity Date; Days from Settlement to Maturity

  A number of fixed-income instruments (such as time deposits, T-bills, commercial paper, repos, FX swaps, zero coupon bonds, etc.) have only one maturity date, and day-count calculations are performed with reference to this single date. Other instruments (such as coupon-paying bonds, swaps, etc.) have more than one maturity date (in the case of a bond, the dates of the coupon payments plus the final maturity date when the bond is redeemed; the last coupon is usually paid on final maturity).
  Days from settlement to maturity (DSM) is obviously important for both interest accrual and present value and yield calculations. The generally accepted rule is that days are counted from the day of settlement (included) to the day of maturity (excluded). The logic underlying this rule is that payments have to be made early enough in the day to allow the receiver to use the funds to make other payments or to deposit them into a bank account, earning interest for the day. The settlement payment made by the buyer must therefore give him the right to any interest maturing on the fixed-income security on settlement day. The payment on maturity to the buyer gives him the availability of the funds for the maturity date and therefore must exclude interest accrual on the security for that day. You can compute DSM in two different ways.

  1. DSM 4 the actual number of days elapsing between settlement and maturity. This method is usually referred to by the abbreviation ACT (for actual). This is by far the most widely used method.
  2. The 30/ 360 rule, according to which every month is assumed to have 30 days, and consequently the year has 360 days. This method is utilized in some very large markets such as U. S. corporate bonds, and U. S. municipal bonds, but can be somewhat inaccurate at month's end (you add 2 days at the end of February and subtract 1 day for 31-day months).

  Days from Coupon to Settlement

  Coupon securities are usually quoted clean. Accrued interest is paid to the seller over and above the clean price. When we add the accrued coupon to the price of a bond, we obtain the invoice price, also know as the gross price or dirty price. We must therefore count the days from coupon to settlement (DCS)-the days between the first day of the coupon period (included) and the settlement date (excluded).
  The date on which a coupon is paid is excluded from the day count and is the first date of the following coupon period. Note that the parties in a securities trade can agree on a flat price because the payment of interest is uncertain- that is, when the issuer of the bond is in default.

  Three Commonly Adopted Accrual Rules

  Determining DSM or DCS is only the first step; you must also know which of the three main accrual rules is applicable:

  The Bank Method. Refer to Exhibit 1-7. The actual number of days (DSM = ACT) is divided by 360 instead of by 365 (or 366 in leap years); this method is also indicated as ACT/ 360. This rule is utilized to compute interest on Eurodeposits, which means that interest is a little higher than the quoted rate. A rate of 6% on a 365-day deposit would yield interest in the measure of 6.0833%. Note that for deposits and loans de-nominated in £ and in Belgian francs, the accrual rule is DSM/ 365. The bank method is also applied to discount securities, such as T-bills and commercial paper. The discount is calculated, however, on the face value instead (bank discount basis) and not on the amount invested.

  The ACT/ ACT Method. Refer to Exhibit 1-8. The actual number of days is divided by the actual number of days in the year (366 in leap years). It is adopted in a number of very important coupon-paying bond markets, such as the government bonds of the 11 countries that have adopted the Euro, and U. S. Treasury notes and bonds. When the ACT/ ACT rule is applied to semiannual coupon payments (e. g., U. S. Treasuries) the actual number of days from coupon to settlement is divided by the number of days in the relevant half-year.

  The 30/ 360 Rule. Refer to Exhibit 1-9. The 30/ 360 rule is an approximation of the ACT/ ACT method. It accrues a yearly coupon over 1 year (and a semiannual coupon over 6 months) but can be inaccurate at month's end. Prices and yields adjust to take this anomaly into account, as we shall see in Section 7-3. This method is adopted both in the U. S. corporate bond market and in some sectors of the Eurobond market.

  The Dated Date and Ex-Dividend Prices

  It can happen that a coupon-bearing bond or note is issued after the first accrual date. The 100-yr Walt Disney note (see Exhibit 7-1) had its first accrual date on 15 July 1993, while the issue date was 21 July 1993. In this case the bond is issued with accrued coupon (dirty price). The first accrual date is also known as the dated date. Within the first coupon period, days from coupon to settlement will always be computed with reference to the dated date. In some markets, coupon bonds trade ex-dividend (which means ex-coupon) starting a certain number of days before the coupon payment date (this practice, similar to that which is widespread for shares, does not appear to be very rational in a world of T ` 3 settlement). When a bond trades ex-dividend, the invoice price is adjusted with a negative coupon accrual from settlement date (included) to the payment date of the current coupon (excluded).

  1-3 LONG AND SHORT POSITIONS; SHORT SELLING SECURITIES

  The issues relating to long and short positions in interest rate and foreign-exchange instruments lie at the heart of hedging and risk-management strategies. In this section we shall explore only a few preliminary concepts relative to securities, deposits, and FX positions. The necessary extensions of the analysis will be covered later in this book.

  Long and Short Securities Positions

  The definition of a long securities position is quite straightforward. You are long a security when you own it. Accordingly, if you are long, you gain if the security price goes up and you lose if it goes down. This connection (long r gain, if the price increases) holds for all financial instruments, including derivatives (in fact, the quotation system of derivative instruments, such as futures, has been designed in such a way as to preserve this relationship). Owning a security does not necessarily imply possession and control but only that you have contracted to buy it at a predetermined price. In other words, the buyer is long the securities beginning with trade date, or time-0, irrespective of the settlement date.
  You have a short securities position when you have a commitment to deliver a security and you do not own it. In most cases, being short a security means that you have borrowed the security to sell it to a third party. The sale of a borrowed security is indicated as a short sale. Generally, securities are sold short in the belief that the price will decline and that it will be possible to make a profit buying back the security at a lower price to return it to the lender.

  Example: If on 3 July 1996 you had shorted the World Bank global bond (6 3 ¤8 % mty 21 July 2005) at 95.80, you could have bought it back on 8 July 1996 at a price of 94.25, thereby realizing a profit of 1.55% on the face value of the bond. (This profit figure is calculated assuming a frictionless financial system- no bid-ask spread; the bond is bought/ sold at the mid-price- and zero borrowing costs.) The drop in price was due to the announcement on Friday, 5 July 1996, by the U. S. Labor Department that employment was booming (239,000 jobs had been created in June) and that wages were rising at a record-setting rate. The potential overheating of the economy made a rate increase by the Federal Reserve Board likely. Bond traders dumped inventory, sending the price of the benchmark 30yr Treasury bond plunging and driving the yield to 7.15%, up from 6.93% on Wednesday.

  Usually, short sales are made when the short seller has already borrowed the securities or is reasonably certain that the securities can be borrowed in time for regular settlement (if it turns out that the short seller cannot borrow the shorted securities, this will result in a fail to deliver). A securities dealer can, however, be temporarily short a certain quantity of a given security if she has sold it without having it in her inventory and has not yet bought it to cover the short. Given the stringent settlement rules, this temporary short can be kept for only a very limited time without seriously risking a fail to deliver.
  In theory, you could short a security without having to borrow it by contracting a forward sale. In practice, this is not common. An exception to this rule is when U. S. Treasuries trade on a when-issued basis (wi) after the announcement of the auction and must be delivered on issue date (see Section 1-7).

  Long and Short Positions in Money-Market Deposits

  You are long a deposit when you have borrowed funds for a certain time, at a given interest rate; in money-market jargon, you have bought a deposit. You are short a deposit

  when you are the lender (you have sold the deposit). The price of a time deposit is its contract rate (say LIBOR plus 10 basis points). Therefore, when the rate goes up, the longs gain and the shorts lose. Conversely, when the rate goes down, the longs lose and the shorts gain.
  You gain (lose) if you have secured borrowing at a rate that is lower (higher) than the current market rate. This gain (loss) can, therefore, be measured by the amount of interest saved (lost). This entails that the term of the deposit is quite important. The longer the term, the larger the gain (loss) given a market rate movement.
  Note that this is only a first approximation. Interest is paid at maturity and there-fore should be discounted back to obtain a really accurate measure. Exhibit 1-10 shows that (due to the importance of term to maturity) a long and a short position do not necessarily compensate each other. If a bank funded itself buying a 90-day deposit to fund a 270-day loan, it would register a profit if rates decrease and a loss if they increase. This is a very simple example of the duration issue and of its importance in hedging.

  Long and Short FX Positions

  Determining net FX exposure is easier than doing so for interest rate securities. A nearly one-to-one relationship exists between FX rate movement and exposure. If a U. S. firm is long ¥ 124 million (equivalent to $1 million, at 0.8065$/ 100 ¥), it will gain or lose in direct proportion to the $ value of the ¥; see Exhibit 1-11. If you have a series of long and short positions in a currency, you can easily prepare a currency balance sheet just by taking their algebraic sum.
  In computing its FX position, a firm (nonfinancial corporation, asset manager, bank, broker/ dealer) will, as a rule, utilize its home currency as a base. A ¥ asset (e. g., a loan to a customer) will entail an FX exposure for a U. S. firm. Conversely, a $ asset will represent an FX exposure for a Japanese corporation.

  Short Selling Securities

  In most cases, securities are not sold for forward delivery. A short position is therefore implemented by a regular sale of borrowed securities. As a general rule, which does admit some exceptions, when you borrow securities you must post collateral to mitigate the credit risk for the lender of the securities. This collateral is always higher than the market value of the borrowed securities to provide a cushion against their appreciation. The market value includes accrued interest in the case of coupon bonds or notes. In a frictionless economy where you can borrow or lend at the same riskless rate without posting collateral, a short sale generates cash for the short seller (the revenue of the sale). In the real world, a short sale usually absorbs cash or other collateral.
  The over collateralization margin is dependent on the volatility of the securities borrowed. It will be very small for U. S. T-bills and quite high for long-term bonds or stocks. The borrowing agreement usually provides for an increase of the collateral when the market price of the securities increases (margin call) and a release of collateral when the price declines. Most short sales are organized through a securities dealer, as visualized in the flow chart (Exhibit 1-12).
  The lender of the securities is compensated with a fee that will depend on market demand and supply. When a security is in short supply relative to the demand for borrowing it, it is known as a special and commands a higher lending fee. The lender is also entitled to receive the dividends or coupon payments that accrue during the lending period. This means that the short seller will have to make equivalent payments to the lender because the real dividends or coupons are paid to the holder of record.
  Note that the securities lender may well be subject to an unfavorable tax treatment on, say, dividend payments. In this case, lending stock to a borrower who enjoys a lighter tax burden could generate a tax advantage, the so-called coupon/ dividend washing tax loophole.
  The practice of short selling securities is often regulated and restricted. The best-known example of this regulation is the U. S. stock market, where the Securities and Exchange Commission has established the following:

  • Every short sale (and reversal of short sale) must be declared as such on the trade ticket. Market transparency is therefore enhanced by the availability of data on short interest, that is, the outstanding amount of stock of each corporation that is borrowed for short selling.
  • Short sales cannot be executed when the price of the stock is declining. A short sale can therefore take place only on an up-tick (when the price has increased at least one tick) or on a zero-plus-tick, that is, at the price of the last trade( s), but at least one tick higher than the last price that was not equal to the price of the short sale. The uptick rule is based on the assumption that short sellers could exacerbate the situation for a declining stock, causing panic to manipulate the market. Most finance experts, however, believe that this rule is not very useful, especially in a sophisticated market such as the U. S. stock market; see Sharpe (1995).

  1-4 ARBITRAGE-FREE PRICING AND THE LAW OF ONE PRICE

  Arbitrage is usually defined as the possibility of locking in a riskless profit by simultaneously buying and selling in different markets. Arbitrage-free pricing implies that a

  set of prices that allows arbitrage will not last long because financial intermediaries and sophisticated investors will spot arbitrage opportunities and trade to exploit them. This in turn will quickly eliminate the arbitrage windows by:

  • Increasing demand in the relatively cheap market( s); this will drive up prices, making it more expensive
  • Increasing supply in the more expensive market( s), exerting a downward pressure on prices and making it less expensive.
  A security (or a portfolio of securities, derivatives, or both) will provide a set of future payments, identified by the times at which the payments are due and the states of the world on which they are contingent (time-state claims). This is known as the time-state paradigm, and its initial development is associated with Kenneth Arrow and Gerard Debreu, two Nobel laureates in economics. Within this framework one can say that an arbitrage provides a positive net payoff in at least one time and state and no negative net payoff in any time and state.
  Another well-known way of referring to arbitrage-free pricing is the law of one price. With reference to the Arrow-Debreu time-state paradigm, we can say that two securities (or two portfolios) that are characterized by the same time-state claims must have the same price. This leads naturally to the concept of replicating portfolio, defined as a portfolio that replicates the time-state claims of the security or derivative that we want to price.
  The arbitrage-free approach is extremely important in pricing securities and derivatives (pricing based on the law of one price and on replicating portfolios). Arbitrage pricing theory is also one of the building blocks of mainstream modern investment theory. The arbitrage theory of capital asset pricing was pioneered by S. Ross (1976). The general concept of arbitrage is relatively straightforward-some would say downright obvious. Its applications can be rather complex, however. A number of examples of arbitrage-free pricing will be analyzed throughout this book, with reference to specific contexts. In this section we shall examine only some very general concepts, to help build a clearer insight into this fundamental tool of modern finance.

  Transaction Costs and Arbitrage-Free Prices

  When observing live quotations on trading screens (Reuters, Bloomberg, etc.), we can often detect small deviations from arbitrage-free prices. However, if we tried to take advantage of these small price misalignments, transaction costs would offset the risk-less profit. The markets are therefore said to be trading within transaction costs or trans-action costs close. To simplify the analysis, most arbitrage-free pricing equations are expressed assuming that there are no transaction costs and that securities and other financial instruments can be bought/ sold at the midpoint between bid and ask prices.
  You will often find references to arbitrageurs as a specific group of market participants. Remember, however, that most arbitrage trades are done by dealers that are in a very favorable position to lock in arbitrage profits. They have the necessary human and computational resources to spot price misalignments as soon as they appear. They also incur much smaller transaction costs because most often they do not have to pay the full bid-ask spread on their trades. Moreover, since different market makers may have different transaction costs, it may be possible for some, but not all, to exploit arbitrage opportunities.
  Bid-ask market-making spreads cannot be considered as riskless arbitrage profits; if they were, then the bid-ask spread would collapse to zero. The spread is both fee revenue, for providing a service to clients, and compensation to market makers for the risks they incur in holding inventory. In the case of credit-risk-sensitive products (money-market deposits, forward FX transactions, swaps, etc.), the spread must also compensate for the credit risk incurred by the financial intermediary.
  Market prices are therefore nearer to arbitrage-free prices whenever the implementation of an arbitrage strategy implies relatively low transaction costs. The U. S. Treasury bonds market is a good example of this state of affairs. Coupon bonds can be broken down into a series of zero coupon bonds (also known as Treasury STRIPS or T-STRIPS), and an appropriate series of T STRIPS may be reconstituted to form a coupon bond or note. Stripping and reconstituting involve negligible transaction costs, no credit risk is involved, and there are no capital adequacy requirements. This insures that the pricing of Treasury coupons and T-STRIPS is very close to arbitrage-free.

  Arbitrage and Capital Adequacy Ratios

  Exploiting certain arbitrage possibilities can well imply a regulatory capital absorption that may not be sufficiently compensated by the arbitrage profit. A number of arbitrage possibilities relate forward prices to spot prices. The riskless profit can often take the form of a borrowing rate lower than the current market rate, or a yield rate on a riskless asset that is higher than the riskless rate. These arbitrage opportunities can imply setting up a complex position (replicating portfolio) and keeping it on your books for some amount of time; this is where capital adequacy ratios come into play.

  Full Arbitrage and Path Arbitrage

  Full arbitrage involves setting up a trade (either spot or with forward components) with the purpose of locking in a profit, net of transaction costs. Path arbitrage occurs when a firm has, say, two or more different ways of carrying out the same financial transaction and chooses between the alternatives depending on current market prices. A typical example occurs in FX transactions.
  Example: A U. S. firm needs to have the availability of ¥ 1 billion, in 3 months' time, to make a payment to a supplier. The firm has the necessary $ amount currently available, and it wants to lock in the forward $/¥ exchange rate to avoid FX risk. The firm has two options:

  • Buy forward the ¥ and invest for 3 months the necessary $ amount.
  • Buy spot ¥ and invest them for 3 months at the current ¥ rate.
  Choosing between the two possibilities does not represent a full arbitrage. Path arbitrage does not incur in extra bid-ask spreads and therefore is available to non-market makers.

  Necessity of a Market-Clearing Mechanism

  The law of one price requires the presence of an adequate market mechanism that will allow arbitrage to take place. If there is no such market mechanism, we can have apparent violations of the law of one price. In Chapter 12 we shall examine one of these possible violations in the context of the put-call parity for options. There are, however, many other interesting examples, some of which we shall now succinctly survey.
  A closed-end mutual fund can trade at a discount to its book value, that is, at a price that is lower than the aggregate value of its investment portfolio. This obviously means that the market does not have a high opinion of the fund managers, who in fact are considered as a shadow liability. There is an apparent violation of the law of one price because the fund is valued at less than its assets, contradicting the principle of value additivity. An obvious arbitrage would be to buy the fund and liquidate it, thereby unlocking the value represented by the difference between the fund's market capitalization and its net asset value (NAV). This arbitrage, however, is costly, time-consuming, and conditional on a variety of legal requirements. This is why the financial pages are graced by a number of below-NAV quotations for closed-end funds.
  The concept of management as a liability can apply to conglomerates that have a stock-exchange capitalization that appears to be lower than the value that would be fetched by the different firms included in the conglomerate if they were self-standing entities. This is known as conglomerate discount. The arbitrage strategy is quite complex, time-consuming, and expensive. It often involves a hostile takeover bid on the conglomerate to spin off its assets. The bestseller Barbarians at the Gate: the Fall of RJR Nabisco by Burrough and Helyar (1990) provides a gripping description of the takeover of RJR Nabisco by the leveraged-buyout firm of Kohlberg, Kravis, and Roberts.
  One last interesting example of apparent violation of the law of one price was provided, on a macro scale, by the FX market. The ECU was defined as a fixed basket of currencies after the Maastricht treaty of 1992. The composition of the ECU is shown in Exhibit 1-13. The value of the ECU against a non-ECU currency, such as the US$, should therefore have always been equal to the value of the underlying basket (again, for the principle of value additivity). However, the two values did diverge (the spread was in the order of 3% in Q1-1996) because there was no mechanism for breaking down the ECU into its constituent currencies or for creating an ECU with the appropriate currency basket.

  1-5 EUROMARKET TIME DEPOSITS AND LIBOR REFERENCE RATE

  The explosive growth of international finance centers around a well-organized global OTC market for interbank time deposits, denominated in all the main freely convertible currencies. The growth of this market is of course connected to that of the foreign exchange market. This global market continues to be called the Euromarket because of its London origin in the 1960s. It now spans a number of financial centers (New York and Tokyo being the most important after London, which has managed to keep its leading role). The defining characteristic of this international market is that deposits are not subject to reserve requirements and that interest is usually paid without being subject to withholding tax.
  Euromarket rates can change freely in time and are continuously broadcasted, with real-time updates, by the large information providers such as REUTERS and Bloomberg. The liquidity of this global OTC multicurrency market is also enhanced by foreign exchange and money-market brokers such as Cantor Fitzgerald, Tullet and Tokyo and others.
  The importance of this free market has grown to the point that most domestic rates track the Euromarket rates, after the necessary adjustments for reserve requirements and taxation. Euromarket rates also serve as a pricing reference for a number of important and widespread financial products and derivatives (e. g., floating-rate notes and bonds, floating-rate loans, FRAs, swaps, futures, options). With reference to the London-quoted rates, the following terminology is now well established:

  • LIBOR 4 London interbank offered (ask) rate
  • LIBID 4 London interbank bid rate.
  • LIMEAN 4 Average between LIBOR and LIBID (midpoint rate)

  Reference rates fixed in other financial centers are designated with names that refer to the city where they are quoted, for example, PIBOR 4 Paris, FIBOR 4 Frankfurt, and TIBOR 4 Tokyo.
  Banks operating in the main centers of the global market quote interbank bid-ask rates for wholesale deposits (minimum amount $1 million or equivalent) for different currencies and different maturities, usually from 1 day to 1 year (see Exhibit 1-14). For maturities of up to 1 year, interest is assumed to be paid at maturity. For the most important currencies, banks quote rates for multiyear periods; in this case, interest is paid annually, in arrears (in accordance with the Euromarket standards, where fixed-rate bonds usually carry annual coupons).

  • Banks will make interbank deposits only to those banks with which they have an open credit line. The whole business of extending and reviewing money-market credit lines is a complex area of international bank management (money-market lines are also used for foreign exchange transactions and for money-market derivatives).
  • Bid-ask rates are not cast in bronze. Banks that enjoy a very high creditworthiness are able to fund themselves at a cheaper rate. Conversely, banks that are not perceived to be solid may have to pay a premium over the offered rate. An interesting example is represented by the so-called Japan premium, which Japanese banks had to pay for a few months (Q3 of 1996) when a series of bad news about their credit losses made the markets less eager to fund them. Japan premium reemerged in 1997± 1998 due to the bad news about the Japanese financial system and to the Asian financial crisis.
  • x Highly rated nonbanks can get rates that are similar to interbank rates. A role is played, however, by capital-adequacy ratios, which favor banks over nonbanks.

  LIBOR Reference Rate

  A number of forward-looking financial instruments are anchored to the future value( s) of some well defined interest rate( s) (see Exhibit 1-15). Due to the established role of both the Euromarkets and of London, a number of those instruments are based on LIBOR. But LIBOR is a continuously changing rate; furthermore, different banks can quote, at any time, different bid-ask rates.
  To have a reliable yardstick on which to base financial commitments, most con-tracts adopt the British Bankers Association (BBA) daily LIBOR reference rate. BBA-LIBOR is determined as the average offered rate, quoted at 11:00 A. M. London time, by the most active banks for the currency in question. The procedure calls for an ideal number of 16 banks; the 4 highest and the 4 lowest rates are excluded, and LIBOR is defined as the arithmetic average of the remaining 8 rates. BBA-LIBOR rates are officially disseminated by Dow-Jones Telerate at page 3740 for the main currencies (see Exhibit 1-16) and at page 3750 for other currencies.

  1-6 SHORT-TERM DISCOUNT SECURITIES

  US T-bills are the most important short-term securities in the international financial markets. They are backed by the full faith and credit of the United States Treasury and are considered virtually exempt from credit risk. Their outstanding volume is substantial, and they are widely held by non-U. S. residents, including central banks that utilize them as a liquid investment for their $-denominated reserves.
  Their importance lies also in the fact that they are one of the instruments of the Federal Reserve's intervention in the money markets to control the level of interest rates. The T-bill market is very liquid and the bid-ask spreads are quite narrow. The bid-ask spread for T-bills is expressed in basis points of discount rate and can appear to be rather large for bills maturing in a short time. In fact, when the bid-ask spreads are translated into $ prices, they are quite small.
  T-bills are issued in book-entry form; the bills are not paper certificates but are represented by records in the computers of the Federal Reserve (in accounts held by banks that are members of the Federal Reserve System). In secondary-market transactions, T-bills settle regular way on the business day following the trade date (T ` 1) (see Exhibits 1-17 and 1-18). T-bills are issued through auction, where primary dealers (recognized as such by the Treasury) submit their competitive bids, expressed in terms of discount rate (see Section 1-7). On any given date, there will be T-bills maturing every week for the following 6 months and every 4 weeks for a further 6 months.

  • Thirteen-week and 26-week T-bills are auctioned every week, normally on a Monday, and issued on the following Thursday. Maturity is usually on a Thursday. When Thursday is not a business day, the issuing or maturity date will be the first business day after Thursday (such as Friday, 5 July in Exhibit 1-18). This means that the supply of 3M bills is increased by 6M initial maturity bills with 13 weeks to maturity. The amounts to be auctioned are ordinarily announced late in the afternoon on the Tuesday preceding the auction.
  • One-year (52-week) T-bills are issued every 4 weeks. The auction takes place on a Friday and the bills are issued on the Thursday of the following week. Every 4 weeks, the supply of 13-week T-bills is increased by an old 1yr bill with 13 weeks to maturity. The amounts to be auctioned are ordinarily announced late in the afternoon on the Tuesday preceding the auction.
  • Cash-management bills are issued at irregular intervals with maturities ranging from a few days to almost 9 months. Typically, they are issued to fund government spending peaks, and they usually mature shortly after one of the major midmonth tax-receipt dates (March, April, June, September, and December). Most of the time, cash-management bills mature on a Thursday so that they become interchangeable with normal bills. There are exceptions however; see Exhibit 1-18, where the T-bill maturing on Tuesday, 18 June 1996, is a cash-management bill.

    U. S. Commercial Paper

    U. S. commercial paper (USCP) is short-term unsecured debt issued by domestic and foreign corporations in the U. S. market. The maximum maturity is 270 days (beyond 270 days, the securities would have to be filed with the Securities and Exchange Com-mission [SEC]). De facto, maturities tend to be a lot shorter, such as 30 days, and commercial paper is utilized mainly for short-term liquidity management by both the issuers and the buyers.
    Commercial paper is also considered an exempt security, that is, freely tradable by U. S. banks, which were severely limited in their ability to underwrite corporate debt and equity by the Glass-Steagall legislation. Some very large issuers have their own sales force that places the corporate commercial paper with wholesale investors (directly placed commercial paper). Most issuers, however, find it expedient to utilize the professional services of banks and broker/ dealers that specialize in commercial paper placement (dealer-placed commercial paper) (see Exhibit 1-19). Financial companies now account for over 80% of the market. These issuers include special-purpose companies established by large industrial corporations that produce consumer durables to provide consumer financing to their customers (such as General Motors Acceptance Corporation [GMAC]). Non-U. S. issuers also tap the USCP market and represent over 20% of the dealer-placed market. The USCP market is very liquid and provides issuers with a large degree of flexibility. Well-known and highly rated issuers can tap the market for large amounts on a very short timetable. Corporations have issued in the USCP market to bridge-fund mergers and acquisitions. Three interesting examples are:

    • American Home Products raised $8.4 billion in 1 day in November 1994 to bridge-fund the acquisition of American Cyanamid.
    • In March 1996, Walt Disney raised $8 billion for its acquisition of Capital Cites/ABC and Lockheed Martin raised nearly $7 billion to acquire Loral.

    Euro Commercial Paper

    Euro commercial paper (ECP) first appeared in the 1970s, much later than USCP, which dates back to the last century. It is a relevant component of the Euromarkets but has never achieved the size or degree of liquidity comparable to those of the USCP market. One of the reasons for this lack of importance resides in the fact that other financial instruments (such as Euronotes) are more flexible and are not limited by regulatory constraints (the USCP market growth is attributable in part to regulatory issues such as the exemption of commercial paper from SEC registration and Glass-Steagall limitations). An interesting feature of ECP is the possibility of issuing it in several currencies, as shown in Exhibit 1-20.

    1-7 AUCTIONS

    Many fixed-income instruments are created and issued through bilateral OTC negotiation (term deposits, commercial paper, FX spot and forward transactions, repos, forward rate agreements, and swaps). This issuing flexibility is greatly facilitated by the existence of standardized master agreements that define the legal profile of the transactions. Securities issues tend to be somewhat more formalized and can take place through well-regulated auctions or through syndicated placements.
    Auctions tend to be utilized by governments to issue treasury securities, whereas syndicated placements are adopted by corporations and other issuers. Both auctions and syndicated placements can take many different shapes in accordance with market practice and regulatory framework. The theory of auctions is also a budding field of economic research. The involvement of economists in designing optimal auction procedures hit the news when radio bandwidth was auctioned in the United States in the 1990s.
    An in-depth analysis of auctions and syndicated placements is clearly beyond the scope of this book. We shall therefore provide an extremely concise description of the auction of treasury securities in the United States. Not only is the U. S. treasuries market the largest homogeneous fixed-income market in the world, but its issuing mechanisms are considered to be at the cutting edge of market practice and increasingly are being adopted by other countries. If you are interested in learning more about U. S. treasury auctions, you are advised to read the relevant chapter in Sundaresan (1997).
    The description of U. S. treasuries auctions is based on a circular of the Department of the Treasury entitled "Sale and Issue of Marketable Book-Entry Treasury Bills, Notes and Bonds" (published 5 January 1993, effective 1 March 1993). Book-entry security means a security the issue and maintenance of which are represented by accounting entries or electronic records and not by a paper certificate. This circular reflects some changes in the terms and conditions governing treasuries auctions, which were proposed by the Department of the Treasury in 1992, partly in response to the problems that emerged in 1991, when Salomon Brothers was caught violating the auction rules (this was considered a serious breach and led to the resignation of Salomon's chairman, president, and other senior managing directors).

    Auction Calendar for U. S. Treasuries

    Treasuries are divided into the following three classes:

    1. Bills, which are short-term discount securities with maturities of up to 1 year
    2. Notes, which are coupon-bearing securities (semiannual coupon) with original maturities up to 10 years. Notes are issued with terms of 2, 3, 5, or 10 years.
    3. Bonds, with initial maturities of up to 30 years (semiannual coupon). As a rule, bonds are issued only with a 30-year maturity.

    Treasury securities are auctioned according to a well-defined calendar, which helps in maintaining an orderly and liquid market (see Exhibit 1-21). Note that for bonds and notes, the auction announcement does not fix the coupon rate. The coupon will be determined by the Treasury on the basis of the weighted average yield of the winning competitive bids. The coupon, fixed in increments of 1/ 8 of 1%, is usually set to be immediately smaller than the weighted yield, so that the bonds and notes are issued slightly below par.

    • Reopening means the auction of an additional amount of an existing security. In this case the auction announcement obviously indicates the coupon rate.
    • Dated date means the date from which the interest accrues. The dated date and the issue (settlement) date are the same, except when the dated date is earlier than the issue date. In the case of reopening, the dated date can be several months before the settlement date.
    • Settlement date means the date of final and complete payment for securities awarded in an auction. Settlement amount means the par value of the securities awarded, less any discount amount and plus any premium amount and accrued interest (from dated date to settlement date).

    Bids can be submitted by primary dealers (the 40 dealers who are authorized to deal directly with the Federal Reserve) on their own account or for the account of large institutional investors. Customers can submit bids through either primary dealers, who submit bids directly to a Federal Reserve Bank, or via intermediaries, who in turn route them to a submitter (see Exhibit 1-22).

    Multiple-Price (Discriminating Price) Competitive Auctions

    Each competitive bid must indicate a quantity of securities (expressed as face value) and an annual yield (or annual discount rate in the case of T-bills). Yields and discount rates must be expressed with two decimals, for example, 5.73%. After February 1995 bids on notes and bonds can be expressed with three decimals, that is, in 10ths of a basis point of yield. Note that each bidder can submit multiple competitive bids, obviously at different yields. The Treasury allots the securities that are being auctioned beginning with the lowest yield and then moves to the next best bid, continuing in this manner until all the securities are allotted.
    Within the same auction, securities can be sold at different prices to different bidders, and also to the same bidder if that party has submitted multiple bids, some of which turn out to be winning. Multiple-price auction means an auction where each successful bidder pays the price equivalent to the yield rate that it bid.
    When bids at the highest accepted yield (or discount rate for T-bills) exceed the available amount, bids are prorated by the Department of the Treasury. Depository institutions and dealers, whether submitters or intermediaries, are responsible for pro-rating awards for their customers at the same percentage announced by the Treasury.
    Noncompetitive bids are also allowed, and they are allotted the full amount of the bidded securities. They are bids to purchase securities at the weighted average yield or discount rate of awards to competitive bidders. There are certain restrictions on noncompetitive bids, to make sure that most securities are in fact awarded to competitive bidders.

    • A bidder bidding competitively for his own account may not bid non-competitively for his own account in the same auction.
    • A bidder may not bid noncompetitively for more than $1 million in a bill auction or for more than $5 million in a note or bond auction.

    The success of an auction can be measured, albeit imprecisely, by its bid/ cover ratio, which is the ratio of the bids received to the amount awarded. The level of uncertainty about the auction outcome is usually measured by:

    • The yield spread of winning bids (highest yield minus lowest accepted bid)
    • The tail of the auction, which is the difference between the weighted average yield or discount rate of the auction (applicable to noncompetitive bidders) and the lowest accepted bid

    Uniform-Price Auctions

    With uniform-price auctions, all the winning bids pay the price corresponding to the highest winning yield (lowest winning price). This seems to entail that the proceeds from the auction will be lower than with the discriminating-price mechanism because a number of winning bidders will get securities at a price that is lower than what they were willing to pay. Things are in fact less simple. Multiple-price auctions can in fact produce lower bids than uniform-price auctions because of the so-called winner's course, that is, placing a winning bid at a price materially higher than that offered by other winning competitors. Therefore, we have a complex situation. The uniform price auction will give back part of the bids, that is, the difference between all winning bids and the lowest winning bid price. However, the bids could prove to be higher, there-fore more than offsetting the give-back effect.

    When-Issued Trading

    A well-known characteristic of the treasury market is when-issued trading (wi), which starts when the issue is announced and continues until the securities are issued (all wi trades settle on the issue date). In the case of new treasury coupons, wi trades are done on a yield basis until the coupon is announced by the Department of the Treasury and on a price basis after the coupon announcement (there is obviously no wi trading in the case of reopening).

Table of Contents

Partial table of contents:

SHORT-TERM MONEY MARKET INSTRUMENTS.

Background and Terminology.

Interest, Discount, Compounded Yield.

Foreign-Exchange Transactions.

LONG-TERM SECURITIES, FUTURES, AND SWAPS.

Zero-Coupon Bonds.

Fixed- Interest Coupon Bonds.

Futures on Bonds and Notes.

OPTIONS.

An Introduction to Options.

Fixed-Income Options, Bonds with Optionlike Features.

Modeling the Yield Curve.

Selected Bibliography.

Index.