ereturns are much more volatile than close-to-open returns. For ourpurpose, which is to trade based on the magnitude of the return, thissituation points toward a higher threshold in order to ®lter out morenoise and try to keep only the relevant moves. However, for the sakeof comparison, we consider still a 2.5 percent threshold, and Table10-9 presents the results in a format identical to the close-to-openmodel. The total accumulated P&L is here +$32.71 ($137.87 for thelong, $105.16 for the short), for 3,395 positions (1,516 long, 1,879short). Despite the positive result, the time diagram of the P&L asshown in Figure 10-13, reveals that the model is less often pro®tableon aggregate, and indeed some days it can be quite disturbing. As werecommended before, we would have to look into more details atspeci®c dates, but we probably know the answers to several questions already. The strategy is exposed to a shift in the entire marketabove the threshold, and indeed this is exactly what happens in
494COMMON ARBITRAGE SITUATIONS
Figure 10-12 GE Close-to-Close(Source: GE Compiled by author from Datastream data.)
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
495
TABLE 10-9NameJPMINTCSBCHWPPGGMCATMOIPHONWMTXOMAAAXPMSFTIBMHDDISMCDTBAKOUTXCDDGEEKMRKMMMJNJ
No. Long No. ShortTotalPositions Positions Positions727456663849665169465825456766434750435153404474592531403830
719963894764705072598237738190647463515850455880664739504542
143173119155851131361011411051406211814815610712111394109103851021541257270908372
P&LLong
P&LShort
P&LTotal
27.7523.9519.887.148.2612.472.820.5713.541.36.312.1314.181.8323.2615.124.755.345.751.153.837.065.5810.491.515.974.696.345.870.45
38.759.259.5121.5522.491.449.611.779.021.844.451.3413.611.9425.918.488.929.771.738.646.255.057.893.3312.6821.5922.8712.4213.9721.51
66.533.229.3928.6914.2313.9112.4211.24.523.141.860.790.570.112.643.364.174.437.487.4910.0812.1113.4713.8214.1915.6218.1818.7619.8421.96
September 1998, giving rise to a large loss and an offsetting gain thenext day. Similarly, in April 1999, the same type of event occurs,causing the same effects.In terms of sensibility, the picture is somewhat better, as shownin Figure 10-14. For a large range of threshold values, the systemshows pro®ts, and those are somewhat higher than for a close-toopen model, which we know is a result of a higher volatility whenconsidering close-to-close price movements. Interestingly, the abovesensibility reveals another effect that is somewhat intuitive. If thethreshold is too low, the model is not very successful because we
496
COMMON ARBITRAGE SITUATIONS
Figure 10-13 Close-to-Close P&L
Figure 10-14 Close-to-Close Sensitivity
CHAPTER 10
PAIR TRADING AND TECHNICAL TRADING
497
Figure 10-15 Close-to-Close Exposure
are essentially keeping too much ``noise'' in it. Between 2.5 and 9.5percent, the model is successful, but it turns negative again above 10percent. This is probably a result of the fact that we are then takingpositions only on moves that have a strong informational contentÐthat is, that will not correct any time soon. Typically, for example,these are the results of very good or bad news on the company. Theprice moves up or down by 10 percent or more, and it does not comeback because the market is actually really pricing new information.Finally, if we look at the exposure in Figure 10-15, we ®nd a situation somewhat expected. On average, there is always one or morestocks moving by more than 2.5 percent; therefore, we are almostalways in the market. Again the most important source of risk is amassive shift in the market whereby all stocks move by more thanthe threshold, and we see some of it happening around September1998, for example.
CONCLUSIONIt should be apparent after several examples of different nature thatthe opportunities attached to an uncertain convergence can be quiteinteresting and potentially very pro®table. The management of such
498
COMMON ARBITRAGE SITUATIONS
positions is in general centered primarily on the convergence exposure, with relatively little worry about traditional risks such as interest rates or dividends. In general, imagination and creativity are keyin coming up with new opportunities, whereas experience and discipline are more than ever valuable assets in getting risk undercontrol.
I NDEXAbsolute convergence, 11±13, 373Accrual convention, 170Accrual period, 169Acquisition strategy, 430Actual/Actual, 169Actual/360, 169Actual/365, 169ADR futures, 224±226ADRs, 45, 73, 74, 79nAmerican depository receipts (ADRs),45, 73, 74, 79nAmerican Stock Exchange, 68Analytical method (RiskMetrics), 361,363, 364Announcement day, 76Arbitragecompetitive advantage, 810de®ned, 3explicit, 22implicit, 22index, 377±422. See also Indexarbitrageoscillators, 17±21pricing, 21±27reverse, 443risk, 423±457. See also Risk arbitragespeculative. See Speculative arbitragestatistical, 460Arbitrageurs, 911Arbitration, 3nAsian crisis, 24, 27Auction markets, 91Authorized number of shares, 98Average SQ, 127Back month, 115nBack of®ce, 273nBack-of®ce valuations, 273±275
interest rate swaps, 308money market, 300stocks, 287, 288Banking institutions, minimum capitalrequirements, 320±323Barings, 11, 116n, 273Basle agreement, 320±323Benchmarking, 6, 241nBest matching, 123nBIS minimum capital guidelines,320±323Black and Scholes option model, 277Blue sky laws, 357Borrowing/lending of securities, 83±91British Telecom±MCI merger, 434±439BT-MCI merger, 434±439CAC, 237Capital allocation (different arbitragetechniques), 465Capital asset pricing model (CAPM),230Capitalization, 105Capitalization-weighted index, 231CAPM, 230Carry, 39±41Cash-driven transaction, 83, 89, 90CCI-TRV merger, 449±453Central bank, 152, 153CFTC, 356, 357Channel breakout, 464Circuit breakers, 92±94Citicorp-Travelers merger, 449±453Clientele effect, 23Close-to-close return, 493±497Close-to-open return, 487±493Closed-end funds, 47±52Commodity futures, 115
499
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500
INDEX
Commodity Futures TradingCommission (CFTC), 356, 357Common arbitrage situationsindex arbitrage, 371±422pair trading/technical trading,459±498risk arbitrage, 423±457Competitive advantage, 810Compliance risks, 356±358Compounding, 168±171Compounding factor, 169Con¯icts of interest, 10, 11Continuitystock indices, 246valuations, 270Continuous compounding, 170, 171Convergence, 4absolute, 11±13explicit, 13±15, 104hypothetical, 15, 16risk arbitrage, 433±445speculative arbitrage, 468±472, 497,498Convergence continuum, 43±45Convergence risk, 41±43, 343Convertible funds, 53±55Corporate eventsdividends. See Dividendsfactors to consider, 104±106index tradability, 249±262mergers and acquisitions, 102±104See also Mergers andacquisitionsoutstanding number of shares,98±106reverse split, 102risk analysis, 343, 344splits, 100±102, 252, 253Correlationindex arbitrage, 416±421legs matched, 341nstock indices, 262, 263Correlation risk, 342, 343Correlation risk between the portfolioand the index, 419Cost of capital, 320±325Costs and fees, 282, 317±320Covered position, 114, 115Credit risk, 154, 155, 355, 356
Cross listings, 44±46, 72±75ADRs, 45, 73, 74ECNs, 45eurofutures, 205±207futures, 132±143settlement, 74, 75Data snooping, 466DAX, 237Dealer markets, 91De®nitionsdividend, 76eurofutures, 202±204futures, 110±117interest rate swaps, 177, 178stock indices, 230±234stocks, 64±67valuations, 269Delta, 341, 342Delta hedge, 35±39Depository institutions, 156nDepository receipts, 73, 74Discipline, 469Discount rate, 153Dividends, 76±82careful dividend management, 81de®ned, 76important dates, 76risk analysis, 351, 352risk arbitrage, 447speculative arbitrage, 473stock indices, and, 251, 252taxation, 77±81valuations, 284, 285DJI pairs, 481±485DJIA, 249, 250Dollar/yen swap, 217Dow Jones Industrial Average (DJIA),249, 250Down-tick, 94nDynamic hedge (delta hedge), 31, 35±39ECN, 45EDSP, 127Effective rate, 156, 157Ef®cient market hypothesis, 21Electronic communications network(ECN), 45ELS, 147±149
INDEX
Employee stock ownership programs(ESOPs), 99End-of-month effect, 347, 353England. See United KingdomEonia, 156Equities. See StocksEquity ®nancing, 89, 90Equity indices. See Stock indicesEquity-linked swap (ELS), 147±149ESOPs, 99EURIBOR, 163, 164Euro basis, 212±214Euro strip, 215±217Eurodollar bundles, 215nEurodollar contracts, 133n, 202nEurodollar packs, 215nEurofutures, 202±217basis, 212±214cross listings, 205±207de®nitions, 202±204fed fund futures, 204interest rate exposure, 215, 216markets, 204, 205strips, 215±217swaps, and, 216, 217yield curves, 207±212Eurosterling contracts, 202nEuroyen contracts, 133n, 202n, 205n,207nEx-date, 76Ex-dividend day, 46nEx-dividends, 46, 47Exchange delivery settlement price(EDSP), 127Execution, 4corporate events, 105, 106index arbitrage, 391±398, 416±421percentage of, 394±396, 416±421risk arbitrage, 446speculative arbitrage, 472Execution risk, 29, 30, 353, 354Explanatory valuations, 279, 280, 331interest rate swaps, 305±308money market, 298±300Explicit arbitrage, 22Explicit convergence, 13±15, 104, 426,427Exponential accrual, 170
501
Fail to deliver, 70nFair value, 224Fed fund effective rates, 156, 157Fed fund futures, 204, 347, 350Fed funds market, 156Federal Open Market Committee(FOMC), 152Federal Reserve System, 152nFIBOR, 162, 167FIFO matching, 122, 123Filter, 464Financial leverage, 131Financial valuation, 27±29, 267±325continuity/time partition, 270, 271cost of capital, 320±325de®nitions, 269eurofutures, 311±314foreign exchange swaps, 314±317forwards, 294, 295FRAs, 308±312front-of®ce vs. back-of®ce valuations,273±275futures, 288±294instrument vs. portfolio valuations,280±282interest rate swaps, 301±308liquidation/cash/present value, 269,270mark-to-market vs. theoreticalvaluations, 27±29, 275, 276money market, 295±300overnight ®nancing, 271±273parametric valuations, 271partial derivatives/explanatoryvaluations, 279, 280prerequisites, 267, 268reliability/meaningfulness, 267, 268standard valuation, 271stocks, 283±288transaction costs, 282, 317±320two-staged approach, 277, 278V@R, 278, 280valuations/random variables,276±279First-order exposure, 34First-order risk, 339nFixed-quantity hedge, 31±38Float, 99Floor market, 92
502
INDEX
FOMC, 152Foreign exchange swaps, 217±221,314±317Forward contracts, 146, 147, 294, 295Forward rate agreement (FRA),194±197, 308±312Fourier analysis, 18FRA, 194±197, 308±312Franceaverage SQ, 128futures exchange, 112, 118index arbitrage, 386open interest, 405, 407settlement (futures), 118settlement (stocks), 71stock exchange, 69time basis, 170Frankfurt Stock Exchange, 68Free lunches, 3nFront month, 115nFront of®ce, 273nFront-of®ce valuations, 273±275interest rate swaps, 301±303money market, 295±297FTSE, 237Fundamentals, 82, 83Futures, 107±150, 221±227ADR, 224±226clearinghouse, 117cross listings, 132±143customer vs. exchange margin calls,125de®nitions, 110±117exposure vs. investment, 130, 131fair value, 224fed fund, 204, 347, 348FIFO vs. LIFO matching, 122, 123®nal settlements, 130general characteristics, 115±117leverage, 131major exchanges, 112, 118margin calls/deposits, 117±125naked vs. covered positions, 114, 115other functionally identicalinstruments, 146±150payoff, 221pricing, 221±224quanto, 226, 227real-time information, 144
round-the-clock trading, 133settlement, 117, 118SPAN, 126, 127special quotation (SQ) price, 127±129stock indices, and, 245, 246synthetic, 149, 150trading, 143, 144truncature problem, 129types of orders, 143, 144valuations, 288±294volume/characteristics of market,107±113zero-sum game, as, 114, 129Futures exchanges, 112, 118Gamma, 342GDRs, 73nGermanyauction reference, 128futures exchange, 112, 118index arbitrage, 382±386open interest, 405, 407settlement (futures), 118settlement (stocks), 71stock exchange, 68Glass-Steagall Act, 5nGlobal depository receipts (GDRs), 73nHamanaka, Yasuo, 396Hedge fund performance, 57±61Hedge ratios, 39, 408Hedge strategies, 31±38HIBOR, 162Historical method (V@R), 363, 364Historical performance, 57±61Historical simulation, 363, 364Holding companies, 55±57Holidays, 173HSBC-CCF merger, 453±457Implicit arbitrage, 22Index arbitrage, 371±422. See also Stockindicesabsolute convergence, 11±13, 373basics, 371±373correlation, 416±421execution, 391±398, 416±421France, 386Germany, 382±386
INDEX
hedge ratios, 408interest rates, 411±414Japan, 381, 382long-term rolls, 408, 409market basis, 374±380open interest, 402±407opportunities, 374±386percentage of execution, 394±396,416±421pro®tability, 386±391recomposition, 415, 416reference materials, 422short squeezes, 409±411short-term rolls, 398±402Sumitomo, 396±398time diagrams, 398±411United Kingdom, 382United States, 380, 381Index concentration, 234±240Index continuity, 246±262Index funds, 241nIndex trading, 244, 245Indices. See Stock indicesInformation-based interruptions, 93Initial public offering (IPO), 98Interbank money market, 153Interest rate risk, 344Interest rate swapsconventions, 182, 183de®nitions, 177, 178long-term ®nancing, 183, 184structures, 181, 182valuation, 301±308volume/characteristics of market,178±181Interest ratesaccrual, 168accrual convention, 170±173compounding, 168±171conventions, 168±174domestic vs. international, 163±168holidays, 173index arbitrage, and, 411±414LIBOR, 161±163midmarket rate, 176nomenclature, 169notations, 174risk analysis, and, 339, 340spreads, 175, 176
503
term structure, 153n, 154time basis, 169, 170Interruptions of trading, 92±94IPO, 98Japanauction reference, 128controls on excessive volatility, 96, 97domestic vs. international rates,163±167futures exchanges, 112, 118index arbitrage, 381, 382open interest, 404, 407securities loan market, 411settlement (futures), 118settlement (stocks), 71stock exchange, 69taxes, 8, 9time basis, 170Japan premium, 163n, 164Jurisdictional turf battles, 357Jusen corporations, 164Last trading day, 76Law of one price, 39Leeson, Nick, 273Legal/compliance risks, 356±358Legging, 394nLending/borrowing of securities, 83±91Leptokurtic events, 365±368Leverage, 131LIBID, 175LIBOR, 161±163, 166, 167LIFFE-Connect, 92nLIFO matching, 122, 123Liquidity squeezes, 40nLoews Corporation (LTR), 56London, 161London inter-bank offered rate(LIBOR), 161±163, 166, 167London Stock Exchange, 68Long-Term Capital Management(LTCM), 43nLong-term rolls, 408, 409LTCM, 43nM&As. See Mergers and acquisitionsMacro arbitrage, 25, 26, 82nMacro trading, 24
504
INDEX
Macroeconomic aggregates, 24Margin trades, 90Mark-to-market valuation, 27±29, 119,275, 276eurofutures, 313, 314FRAs, 308futures, 288stocks, 283Market basis, 372, 374±380Market ef®ciency, 21±23Market microstructure, 91Market-neutral hedge funds, 82nMarket rebate, 80, 81Maturity, 169Mean reversal, 18Mean reversion, 44Mergers and acquisitionsgeneral process, 102±104risk arbitrage. See Risk arbitragestock indices, and, 253±262Microsoft, 100nMiddle of®ce, 273nMidmarket rate, 176Minimum capital rule, bankinginstitutions, 320±323Modi®ed next-business-day rule, 173Money managers, 58Money market, 151±227ADR futures, 224±226central bank, 152, 153conventions, 168±174credit risk, 154, 155domestic vs. international rates,163±168euro strips, 215±217foreign exchange swaps, 217±221forward rate agreements, 194±197importance, 151interbank markets, 153interest rate swaps, 177±185interest rates. See Interest ratesLIBOR, 161±163long-term transactions, 160, 161midmarket rate, 176nonstandard maturity, 177notations, 174overnight, 155±160quanto futures, 226, 227settlement, 175
short-term interest rate futurescontract, 202±217. See alsoEurofuturesshort-term transactions, 160spread, 175, 176standard futures, 221±224swap pricing, 197±202term structure of interest rates, 153n,154valuations, 295±300zero coupons, 171±173, 184, 194Monte Carlo simulation, 363Moving average, 464Moving average crossover rule, 17nn:m split, 101Naked position, 114, 115Nasdaq, 68, 92National holidays, 173Negative market basis, 378Nervous markets, 378Netting, 122nNew shares, 105Next-business-day convention, 173NIK, 238Nikkatsu, 242, 243, 415, 416Nikkei 300 fund, 53, 54, 55nNonconvergence, 41±43Normalized deviation, 19±21NYSE, 68, 92OD, 70On-balance volume averages, 464Open interest, 402±407Open-market operations, 152Open-outcry pit, 92Opening gap. See Close-to-close return;Close-to-open returnOperation date (OD), 70Oscillators, 17±21Outstanding number of shares, 97±106.See also Corporate eventsOvernight ®nancing expenses, 272Overnight loans, 155±160Overroll, 406Pair trading, 15, 16, 459, 460. See alsoSpeculative arbitrageParametric risks, 29
INDEX
Paris Stock Exchange, 69Partial derivative, 277±280Payment date, 76Percentage of execution, 394±396,416±421Performance ®gures, 57±61PIBOR, 162, 166Policy-setting devices, 152Preferred shares, 67nPrice-weighted index, 231, 232Prime rate, 153Procter and Gamble±Bankers Trustswap, 357Proprietary traders, 58Quanto futures, 226, 227RD-SC merger, 474±480Reciprocal clearing agreements, 132ReÁglement Mensuel, 71, 72Regulatory turf battles, 357Relative value arbitrage, 465Repo rate, 86Repo transactions, 86Reserve requirement, 156nReverse arbitrage