8 Matroduction CoverTurgett, Cover Target2)
{Log Trades for Spreadsheet Export)
‘Condtiont = Acmel ogTrades(LogTrades, LogFie, SysteriD);
Figure 14 shows an example ofthe profit target and stop Joss levels using the function AemeEeitTargets This function draws horizontal price levels on the ‘hurt to display He stop loss and profil targets The stop los is denoted by LX ~ ‘and the muli-bar profit tarzet is denoted by LX + The muli-bar profit taret is Similar to Darvass box theory [7] where stock prices move upwards in a series ‘ofstacked boxes with defined ranges
Figure 14 Trade Exit
‘The trader may wish to change the Trade Manager to implement different stop Toss and profit target strategies, eg, ext along trade on the close ifthe close is below the open By changing the Trade Manager, each of the Acme strategies Can be tested with various trade exit techniques One suggestion for changing the Trade Manager isto use different profit factors for the single-bar target and the multi-bar target For example, the trader may want 2 L2-ATR move in one day and a 20-ATR move in to days,
Holding Period
In the Trade Manager, the trailer has the option ofturning offprofit targets to ‘depend only on the holding period When selecting @ holding period, the trader wants to maximize the deployment of capital before the Law of diminishing re- tums takes hold, i.e, how fast can the trades be turned over without sacificing
14 A Trading Model ”
‘rofl factor The trader may wish to optimize the HoldBars parameter over a ertflio ofstoe!s to determine the eptimum holding period
‘Many swing-trading techniques have holding periods of three to five days ‘Taylor defined a gee ofthree days with each day representing a Buying Day, 8 Selling Day, and a Short Sell day [33] The eyeles vary according to sector, technology stocks hive short cycles oftwo to three days, while eylical stocks Ihave eyeles lasting up to thinty days An example of @ 30-day gle isthe retail sector, where same-store sales data ae released the fit week ofevery month,
143 The Trading System
So far, we have Dut an infrastructure for Ue core ofthe Trading Model Now, ‘we want to focus on the trading system ilsele As an analogy, Chink ofthe Trad ‘ng Model as the car and the Trading System(s) as the engine Ifthe engine is broken, then the car is not going to move Unless the systems have an edge, the Pontfoli is poing to stay in Park, ‘Trading system design is difficult because a trader has to overcome reliance ‘on canned technical analysisrome software packages make it too easy to pli
‘inamoving average crossover system or a channel breakout system By tweaking
‘parameters, a trader res to get resus thai hệ o she wants, a dangerous form of Inuman optimization The main issue is that any system can appear profitable in 2 nargowly defined time frame or on 8 sarrowly defined portfolio The key to any trading system is to look for consistent profitability across a wide range of stocks and maukets over long periods oftime Thejob ofback testing is essential to-good system design [30] “The first question trader mst ask sbou! a known trading system is “Ifthe system is so good, then why is it published?” The answer is tht the system may ‘be a decent trading system, Dut certainly no ene in his or her sight mind would sive away a great trading system Obvioualy,agrea! system has to be traded, not sold This question even applies to the trading systems in this book Each ofthe ‘Acme systems has a historical edze and a decent profit factor, but Me best trad ing systems are in the hands ofthe people making money with them We have enhanced the Acme systems as @ departure point for systems with better profit factors, Iatrader designs a system with aprofit factor of2.0, then he orshe will be motivated to make the system even beer through a process ofiteratien
So how does one design atrading system? Without hesitation, we claim that {he best systems result from a combination ofmarket observation and total im mersion in technical analysis, The wisdom acquired through reading, studying, analyzing, and observing leads to an explosion of eeativity-simple concepts are combined to create a great trading system or technique A trader soon discovers that thebesbystems ae vất pm
Trang 2” 1 tntroduction
“The professional trader experiences breakthrough moments when all ofthe dis parate technical elements that have ben flcating around in one's mind for years syushesize to preduce inspired, original techniques Some traders get there faster than others, but one day the trader realizes that money can be pulled out ‘ofthe market consistently Once the trader gets to that point, all ofthe external noise is eliminated He or she stops going to chat rooms, tums offthe television and cancels all subscriptions Ultimately, the pursuits just pure trading
Design
‘The design of successful trading system is based on a discovery that yields a Satistical edge We find an edge through number erunehing, net ftom desiga- ing around technical indicators The objective is to find recurring patterns in daily, weekly, or even intraday data, The process is iterative and painstaking, a cognitive panning for go ‘The best systems alternate winning streaks with relatively fat periods of drawdown Look for consistency across parameter sets and across time frames, ‘and exploit as much historical data as possible Experiment with combinations ofprofittagets and stop loses [30], For example, ifthe profit target is 15 times the ATR and the stop loss is 10 times the ATR, determine the winging per- ‘centage and then chart the trade distribution like a probability eurve as shown in Figme 1 Plot the number oftrades on the Y-axis and the percentage retum fon the Nasis, Repeal this exercise for rsk/reward ratios of 11, 12, and 13 ‘The wade distribution plot should resemble a normal curve that is shifted to the right with a peak in profitable trades to the sight ofzero Prof Frequencies 3S589388888 Fiygue BS Dial
LAA Trading Model a
As discussed, Average Te Range (ATR) isthe standard for ll Acme trading systems Entry and exit points are percentages of the ATR Consequently, profit tayets and stop losses must be adjusted to the appropriate time frame
For esample, ifthe ATR of stock is two points, then the profit target for 8 Uee-day holding period may be twice the ATR The multiplier ofthe ATR for ‘a profit target is a constant that is adjusted to the holding period,
‘Simitady, the muliplier ofthe ATR for a stop los is also a constant For the day trader using 2 five-minute chart and a holding period of several! hours the profit multiplier may be 05 times the ATR and the stop muiplier may be 0.3 times the ATR Day trading and systems trading are net mutually eschusive, as ‘one might be led to believe
‘Over time, the professional realizes that trading is ä game of statistics and probability (12), Traditionally, most trading books have focused on entry and exit points, eg, a one-point Stop loss or a 2% stop lees When designing a trading system, stat with the goat of finding a strategy that is profitable 50% ‘ofthe time, but the ratio ofthe average win to the average los is 21 ‘The winning percentage changes as the risk/reward parameters are adjusted In general, the lower the risk he lower the winning percentage wil be Tight- ening a stop reduces the number ofwinners but reduces risk as wel In contast, Toosening a stop increases the number ofwinners but increases risk Trading is ‘an equation-all parameters must be balanced to find the optinnl stap loss set- tings and profit targets The trader must adjust the parameters to fit his or her risk profile A higher winning percentage may feel more comfortable, but the trader may be sacrificing profit or corvfoft
ures
Afiera system has been designed, the entry and sit ries must be defined Each ‘Acme trading system conforms to 2 standard formst with rules for beth long ‘and shot positions, as shown in Table 16
“Table 1.6 System Rules
Rule Desription
Lone Beng | Define buy setup conditions and buy der Lang ait | Define sll emaiions and sll rer
Shot Kitry_ | Deine star sale setup contin aa sll short onder Ma
đúng: and
Trang 32 1 Introduction AA Trade Fitters
‘The trader ing upen the design ofthe system, cettain filters are meve relevant than ethers now has the decision of applying trade filters to the system Depent- For example, one ofthe swing trading systems, Acme N, isthe oaly one using the ADX Since Nisa pullback ten, the performance i dredly proportional to the minimum price, historical vlsility, and! ADX The higher these values ‘atest, te better the seslls vil be [4] In contrast, the Acme R system is based ‘on the rectangle, a conscldaton pattern where ahigher ADK does net inyove ver performance ‘Table 1.7 shows the filters foreach trading ystem ‘The Acme P system is the only system that docs not use ade filers, Dut a vlailiy filter could be applied toi Each system was usted on all of the trade flte-he ones tht improved testing resus were kept, while the hors were discarded however, there may be other filters that could further improve performance
‘Table1.7 Acme Trade Filters ‘Sym [are [Ma [mp [Hv [wR [2px [pML F ZÌ” “ u | “ N ⁄ZÌ”|z|z|“ P Pa v “ “ ATR AvengeTroeRemee Ai - Moving Average MP Mini Pace FE Hiểndel VdNiNg NR Narrow Range
AEX Average Dieedieml Index TA, Dhedlonl MoweMer Undex
‘The most interesting comparison oftradefilterswas the difference between the ‘Moving Average filter and the Directional Movement Index filter Some swing traders use the DMI to determine whether a stock isin an up trend or a down- wend Overall, the performance of the moving average- filter (above or below the sverage) war etter tion the DMI filter (postive or negative DMI ratio} The
a
LAA Trading Model a
‘Acme N system uses the moving average filler a8 an alternative to the DML A combination ofthe MA and DMI fillers would further improve performance Dut reduce the number ofsignals
‘The trade filters are grouped into two categories: price filters and technieal filers The ATR, MP, and NR filters ace price filters desived from a stock's trang price and range for the current bar The MA, HV, ADX and DMI fil- ters are technical filters tased on historical price calculations The trader is free ‘tomodifythe code to add other filters "Note that the FillersOn parameter is an input parameter to each ofthe Acme systems By tuming this parameter on or off, the trader can vompare the per-
formance ofthe ra system versus the filtered one Average True Range (4 TR)
Trang 4a4 troduction
Avorge Tre Range is a measure of volatility One might assume that a higher
ATR implies a more volatile sock but while ATR is @ pod sil volatty screen, abiter aren isto divide the ATR into the dock pce So, if Sock A has an ATR oftivo and a pice of 50, and Sock B has an ATR oftwo price of 4, than Sock Aas @ Voltity Percentage (WP) of2 (` 30~ A, ad and a Steck has aVPof2 | 405% Consequety, Seek ismere volatile Fostuatly even alter stock prices converted from fractional to decimal in 200), many stocks conime to have large daly ranges In 1995, the ATR ofthe epi companies to trade (Sun Miereeystems, 3Com, and Applied Meters) ranged in the vieimkyofthre to four points In 199, many Nastaq stocks al doublet ATR, some cfwhich are shown here
~ Redback Networks (RBAK:Nasdaq): 16 = Yahoo (YHOO:Nasdagy: 11
= eBay (EBAY:Nasdag): 1
~ Copper Mountain (CMTN:Nasdaqy: 9 = EMGL Ine (CMGI:Nasdaq): 8
(Only theve years later, we sill find it difficult to believe that stocks were having daily ten-point swings Since the heady days of 1999, the ATR ofthe typical ‘momentum stock has declined to two of three points again as ofthis waiting in carly 2002,
Moving Average (MA)
‘Much oftechnical analysis is salffuliling The professional traders job is to atch what other traders are watching Because the 50-day moviag average (MASO)is so closely monitored, signals that occur here should be more profit- able percentage wise’ The general principle is thal a tock in an up tend tends to pull back to the MASO as a suppert level (Figure 1.7) In contrast a stock in a <downtrend will pullup to the MASOas a resistance level (Figure 18)
‘The Aeme E, N, and V systems use the SO-day moving average as a trade filer The rules are simple trade filtenng is on, then a Jong entry is allowed ifthe stocks trading above its MASO, Similarly, a short entry is allowed only if the stocks below its MASO Because ofits importance, the moving average is @ pattern qualifier forthe Acme M System It alerts the trader to a stock neat its average by placing the letter "A" above and talow the bar
‘Technicians use the 50-day MA to take positions on either side ofthe Line, Ifa stock in a long uptrend breaks down below the average, then a trader goes short Ifa stock in a long devintrend breaks above the average, alien the trader goes long As with any strategy in the market, hoviever, nothing is ever that
y
tre hate tc esa ee
4A Trading Model
simple TheMASOgets penetrated often in either direction and the prevailing
Jong-temn trend usually wins out
Migurel.7.LongEntryat 50-day Moving Average
Trang 526 1 Hateodution
lim Pree (IP)
‘The conventional wisdom is that the professionals ignore stocks that trade for Jess than $20 per share The problem is that a minimum price sereen fillers out ‘many volaile stocks, while less volatile high-priced stocks pass the minimum price screen, For esample, if Stock A is trading a! $60 and has an ATR of 15, ‘and Stock Bis trading at $10 with an ATR of 12 ascreen based on aminimum ATR of 15 eliminates the more volatile Sock B To compare the volatility of| the two slocks we divide the ATR by the stock price to calculate the Volaility Perventage For Stock A, the VP is 15 / 60 = 2.5% In contrast, the VP for ‘Stock B is 12 / 10 = 120Ps, A volatility measure is better trade filter than
‘Minimum Price, adhongh using both is an even better trade filter,
Forlow-priced stocks, screen for both volaility and liquidity At the time of the chart in Figure 19, Ariba had a 20-day Volatility® of over 15 and traded ‘under $10 per share Further, the stock traded an average of several million shaves per day As a result, the stock passed the filtering process and had to ‘trades during this period with gains ofappresaimtely 20°6, For the trader start- ing ovt with a smaller stake, these voll, low-priced stocks are a logical chcice, Jets Avent Ho Hae 14 A Trading Model 2
A trader wants the three V's volatility, volume, and a small vig? [21] Volatility
‘rates the opportunity to go eng or go shot, volume provides the liquidity to
get in and out ofthe peiton and the small ig ims the amt ofmeney that lands inthe pocket ofthe mavket maker oc specialist,
‘Historical Volatity (HV)
Each sock has Historical Volatility (HV) It is an ansalized percentage that ‘measures the standard deviation ofa stock's price changes over a period oftime, eg, the percentage change of todays close compared to yesterdays close for the last thitty days The historical volatility calculation assumes that stock prices fall in a lognormal distribution and is desived according to the Black-Scholes ‘options model [5] Example LA Function AemeValatily _= 1466494319: xeerreilatm Acaevolatility: Glaulate the, Length Wuneric}; Variables: Daystnveax(365), Daystrorth(30), Dayslmleck(7), “iZefactor(o.0); ‘Aenevolatiity « 0;
IF Close > 0 and Close[1] > 0 Then Begin I Datacospression >= 2 and DataCorpression < 5 Then Begin IF DataCanpression = 2 Then (Day) ‘TineFactor ~ D3ysIYear
Else TẾ DataCorpression = 3 Then (Weekly) ‘TineFactor = DaysinYear / Daysirbleek Klse TẾ DataConpression = 4 Then (Northty) Tinefactor ¬ DayslnVer / Dayslrfonth;
“#⁄ac\olaUiLty = StoDev(log(Close / Close}, Length) * Squsrekoot(TineFactor);,
Trang 6
z 1 Inrodhetion
‘The EasyLanguage code for calculating HV is shown in Example 14 The HV ‘can be calculated for daily, weekly, or monthly charts Depending en the cha ime frame, the function calculates a multiplier to determine the annualized HY The HV calculation uses a sample bar range based on the input parameter Lengih to extrapolate the anmialized voit from the closing price changes for the sample petiod The steps for calculating the HV areas follows:
‘a Calculate the TimeFactor based on the chatt petiodiity
‘8 Compate the standard deviation ofthe sample basod on the natural logerithm ofthe closing price percentages using the lat Length tars 2 Muliply the standard deviation by the TimeFactor to determine the anmalized HY, Fora daily chart the TimeFactoris simply the number of ays inthe year For a ‘weekly chart, itis the number ofdays in the year divided by the number of days in a week Historical volatilities are measured over various periods oftime, but the 30-day HV (HV30) is common in many options models TheHV30 gives the trader an estimate ofa stock’ travel range For ©xamnple, a stock trading st $20 ‘with an 1V30 of 20% will have traded 20 X 0.2 = 4 points above ad below the current price approsimataly 68%!” of te time during this period, based on 2 normal distribution [29], The HVạy ofthe stock in Figure 110 is 136, or 136% hich is estremely high lướt TH Hy Figure wal Vol Apa seeneay HN 4A Trading Medel ”
In general, we require @ minimum HV reading of 5 to filter out non-volatile stocks; however, higher readings are desirable ‘The umder should experiment with vicious HV values to seepe his or her universe of stocks The IVelatlty Web site at hitp/"wiw ivelaility com has the 30-day HV readings as well as Implied Vokaty IV readings
[Narrow Range (NR)
Trang 7” Introduction
‘fa trading system places a stop aor around the previous bar's high orlow, then the range ofthe bar dictates the size ofthe loss Thus, an NR bar improves the tisk/reward ratio ofthe trade because the loss is inherently ited to the nazrow range Further, 2 narrow range day implies a greater-then-even probability that wide range (WR) day with a range greater than the ATR will occur the next day A cluster of NR days means that the macket is aticipating a major news even, such as a Fed mecting on interest rates or key economic number ‘Average Directional Index (ADX)
“The ADX is simply ameasure ofthe strength ofa trend and has been covered in depth by other authors [3, 4] As a genera rule ifthe ADX is rising then @ stocks trending strongly-cither up or down The ADX is used in combination ‘with the DMI for momentum trading systems Although most systems use a absolute value of ADS to assess a strong trend (eg, a minimum of 25 or 30), the ADN for a strong stock in a pulllxek will fall as low as 15 Thus, when screening for trading candidates, consider the ADX five or ten days ago along ‘with the current reading
‘A characteristic ofthe ADN is that a rising value indicates a strengshening tend This is true but @ stock develops a strong trend well before the ADX re- flects the movement ofthe stock Geometric breakouts from along or shot base rigger signals much eatier The stock in Figure L12 had a 30% move before the [4-day ADX even reached 30 in late September
"—¬-
14.ATradingMMcdel 31
‘Each technical indicator has its niche, however As shown in Figure 1.12, high ‘ADX teadiags are useful for pullbacks (denoted by P) in very strong tends A retracerent of two or more bars is usually intemupted by a resumption ofthe ‘prevailing long-term trend Returning tothe example, a strong reversal begins in ealy October, and the ‘AX does not resume rising unfil well imo the reversal Thus, reat the ADS as 2 lagging indicator-tho trader will benefit from shortening the study length from 14 to 7, expecially for shot sales
Diectionel Movernent index (OM)
Trang 82 1 Introduction 3.5Performance
‘This section establishes some guidelines on evaluating trading system perform ance using the TradeStation Performance Report For a thorough evaluation of trading system, referto Stridsman's book Trading Sestems That Work [30) As te trader will discover, the key to any trading system is to analyze ts drown interms oflesing streaks and the size ofthe average losing trade Based on these ‘data, we can calculate the appropriate amount of capital to risk per trade
‘Table 18 shows a sample performance report The Taal Net Profit and Percent profitable numbers are alluring but the important mumber is the Profit Factor: the number of dollars gained for each one lest In this example, dividing the Gross Profit of $H7,001.50 by the Gross Loss of $174,787.00 yields a profit factor of 56 Reviewing, some other ratios, the ratio ofthe average win to the average less is $4,217.00 divided by $2361.99 equals 179 The holding period ratio is the average number ofbars in the winners (30) divided by the average number of ‘bars in the losers (16), approximately 188
‘Table 18 TradeStation Strategy Peformance Repert— A Stam QQQ- 10min “Tel Net Pro 82722145) OpenpesitionP/L $0.00
GrossProfit SH7.001.50 Gross Loss (61478700)
‘Tota Hofwrades 180 Perenrofisble — S880 Numberwinningtrades 106 Largestwinningtrade — SI26800 — [aedtleangtmde — (5528000) Averaeewiminetrsde - S421700 — Awengelodnetsde ($2,361.99) Raiemnewdưaygles 1.79 Numberlosiagtiades 74 ‘Avotrade Win les) $1,512.30
Maxconsee Winners 7 Masconser.losers 5
AvgHbarsinwiness 30 Avetibarsinlosers 16
Masintraday drawdown ($21,993.00)
Profit Factor 256 Masticontractsheld 9500
‘To assess the impact of drawdown, multiply the largest losing trade (85,280.00) bythe maximum consecutive losers (5) to get $26,400.00 The actual maximum Arwvidovin (not shown in the table) vas $19,720.00, The maximum intraday <rawdowen of $21,993.00 eccurred when the system was short Defore a surprise
tee ut sowearefortunatetohavetispriceshoekinthereslt
1s Pesformance 3
We look for month-to-month consistency with any trading system, as shown in ‘Table 19 Day waders should espe consistent weekly profitability swing trader should expect occasional sing, weeks because the combination of time frame and losing streak makes it almost impossible to avid a losing week For cecample, ifthe trader makes five trades a week and the maximum consecutive losers is four, then the odds of a losing week ae highly probable Compare the actual monthly performance with the expected monthly income in Table 13 to ‘et reasonable profit goals,
‘Table 1.9 Monthly Analysis Poriad | NetProft_SGuin Profit Factor # Trade: Profile January [1453200 904% 221 H350 48:15% February | 3899425 400% 172 1250 5600 March | 819,95275 9286 710 800 75006 Apdl — | s1946750 010% 221 1900 5789 May - |Ø43800 153 30% 1700 64715 June | $18,02050 766% 340 - 1300 - 7698 July [82230450 880% 679 1600 6875% August |Ø7/9900 105% 388 1600 - 685% September] $5841.00 199% 159 1000 #000 Ocrober |$1059200 349% 157 I3 4615 November | $9,00100 765% 168 U50 - 6083 December | 2050850 12.79% 327 1550 2% As displayed in Figure 1.14, the Equity Curve (EC) isa graph ofthe cunmlative profit of set oftrading systems The vertical distance belween cach point on the chart represents the profit orloss ofan individual trade The EC isjust lke price chatt-it has trend and it has pulltacks (the distance from peak to trough is the dravdown) Technical indicators such as the moving average and ADN can be calculated forthe curve to asess the strength ‘Analyze the Equity Curve from a three-month perspective because trader of atrading system, should expect flat periods lasting up to titty ot sixty dbys fer a system The EC in Figure 1.14 has roughly the same net profit for cach three-month period Plot the EC every month to detemine whether or not the system perfomance is Adeteriorating,e-g., it advances half 2s much ever consecutive periods
Trang 9
“ 1 Invodhetien
gure L14 Equity Curve
Finally, measure the distance (in terms of number oftrades) between suecessive ‘equity peaks and troughs to approximate the eycle ofthe system This eyee is a
function ofthe number of winning and losing, streaks made by the system,
151 ATale ofTwo Stocks Ciena ene Cigna
We finish the introduction with the tale oftwo stocks: Cigna and Ciena Just fone letter apart, the two stocks could not have been more opposite in personal- ity, one a staid insurance company and the other a volatile optical stock Since Cigna was listed on the New York Stock Exchange and Ciena on the Nasdaq bitter rivalry developed, so the two stocks requested a performance review from the Acme trading systems
‘The performance reponts in Tables 110 and LL evaluate the unfiltered performance ofthe trading systems for both ofthe stocks Cleatly, any system that generates profit factor of 0.65 is useless for trading but instructive, For ‘Cigna the systems fared poely, with enly five out of eighteen winning trades In contrast, Ciena performance results were just the epposite-a profit factor ‘of 449 with only three losing trades
“The whole point ofthis exercise is to demonstrate thal a system orsystems canaot be blindly applied to a universe of stocks First, we neod to identify the characteristics that differentiate these stecks through # learning process known ete nee, 1S Peefermance 4s “Table 1.10 TradeStation Strategy Pecfoance Repor~ Acre All Seraepes C-Daily
‘Tora Net Profit, ($6,644.60) Openposiion P/L $0.00
Gross Profit 81237840 GiosLo (19,023.00)
Tora #oftades " escent profitable 2778 Nomberswianingtndes 5 Largestwinning trade $4,995.00 Averagewinningtiade $2475.68 Ratioavgwinengloss 1.69 Maxconsee Winnes 1 Nomberlosingmades 13 Largestlosingtaade (82,500.00) Averagelosingtwade (81,463.81) ` Maxcoseclosen 6 Awgfbasinvimsen 3 Asgfbaninloeen 2 Maxintraday drawdown (811,528.00) Protie Factor 65 ‘Maxcflcontractsbeld 1,600 ‘Table 1.11 TradeSnition Strategy Performance Report - Asme AllSetegies CIEN-Datly ‘Tetal Net Profit S1781410 — OpenposdenD/L - $0.00
Gross Profit 8291730 GrossLoxs (8510320)
“Tenl#oftades “ Percent profitable 7.57%
Trang 1036 introduction
First, we mine the trading filers to extract the characteristics that separate the trading stocks from the non-trading stocks Then, we iterate through the char- acteristics to explain the difference in performance between two stocks Cleay, ‘we need fo re-apply the trade filters everynight to create anew stoccuriverse,
trading stock can revert to a non-trading stock and vice versa
‘The find distinguishing characteristic is volatility AS shown in Figures LIS and 116, the HV for Cigna is 0.36 and the HV_ for Ciena is 1.09 Cigna’s HIV does not meet the minimum thresheld of $ set by the indicator, although, its HIV is turning up, and it may soon become a trading candidate The choice ofa minimum threshold is a balance between disertion and automation, ie, the higher the value, the fewer the rmmber of charts to review, a lower value ‘means the trader exercises mocejudgment during the stock selection process
Trang 112 Pair Trading
We used to think that ifwe knew one, We knew two, because one and one are two
We are finding that we must learn A great deal more about ‘and
Sir Arthur Eddington
Mathematical Maxims and Minims
Pair trading is a market-neutral strategy where a long position in one stock and a short position in another stock are initiated simultaneously The profit principle
of the trade is based on mean reversion, i.¢., two stocks that normally trade in the same direction become temporarily uncorrelated and eventually will revert to the mean; this technique is also known as statistical arbitrage
Most of the published work on pair trading pertains to positions held over several days [24] or as much as several months, ¢.g., a typical arbitrage where an acquiring company's stock is shorted and the target stock is bought However, recent changes in margin requirements circa 2001 give the day trader access to as much as 4:1 intraday buying power, perfectly suited for intraday pair trading
This chapter presents a complete strategy for trading stock pairs intraday, although the technique can be extended to positions of several days or more First, a definition for the spread is presented along with a visual TradeStation indicator Then, the spread bands are calculated to determine when a pair trade is initiated; a trade triggers only in the area outside the upper and lower bands Finally, the complete entry and exit rules for the pair trading system are defined, followed by several examples
The allure of pair trading is that it is a strategy with little risk Further, the trader does not really care about the direction ofthe market and does not have to worry about nagging issues such as the S&P futures or the reaction to economic reports However, no stock is immune to the risk of a trailing halt or an earnings warning, Before trailing begins each day, review each of the stocks for specific
Trang 1240 2 Pair Trading
downgrades Be aware that news will frequently create a spread oppertunty, but fastock with major news may demand a reverse spread strategy 2.1 The Spread
‘The Spreadis the difference Vetween two stock ratios sharing a common anchor point in time, for example, the closing price of today compared to the closing Dice ofyesterday For a stock pair AB, if Stock A closed today at 21 and yes- terday st 20, thenits clesing ratio is 21 / 20 105, Similay, ifStockB closed today al 42 and yesterday a 40, then its closing ratiois 42 / 40 = L5, Thúc the spread is 105 minus 105 equals zero Here, inthis narrow instance, the stocks _aremeovinginsynchronization, ie, they ate correlated Consider te stock pair A-B again IfStock A closed today at 20 and yester- ay ul 20, then its closing ratio is 20 / 20 = 10 IFStock B closed today at 42 ‘and yesterday al 40, then its closing ratio is 42 / 40= 10S Here, the spread is 10 minus 1.05 equals ~05, and Stock A is undervalued reatve to Steck B If the spread were a postive number, then Stack A would be overvalued relative to ‘Stock B
For a daily spread system, the anchor point could be the number of days ‘0, eg the close of today compared to the close five days ago For an intraday system, we compare the last price on an intraday chart to either the closing price ‘ofyesterday or the opening price oftoday ‘The difference is whether or not the trader wants to factor gaps into the spread calculation If'so, then the closing price ofyesterday is chosen
Spread = (Lest, + Close) - (last, + Coe) ap We calculate the Spread with Equation 2 using the variable Lastto indicate a real-time price Divide the last real-time trade price of Stock A by its closing price yesterday, and do the same for Stock B Subtract the difference to obiain the current Spread
“The spread is displayed in a separate plot below the chads ofthe stock pais: ‘As the charts update in real-time, the spread is plotted as a Tne within two channel lines known a8 spread hods In Figure 2.1, the parallel fine running, across the top ofthe bottom pane! is the upperspread tand, and the bottom line is the lower spread band The spread bands aze computed at the beginaing of ‘eachdayusingyesterday's When the spread fine touches the upper band, the stock in the top panel historical volatilities and correlation see below (Sock A) becomes overvalued relative to the stcck in the lover panel (Stock B), ‘a condition i ‘Stock A should be shorted and Stock B should be bought When tin- spread touches the lower band, Sock A becomes underval
22 Spread Bands 41
ued rdative to Stock B In this case, Stock A should be bought and Stock B should be shorted atthe same time
igure 21 The Spread
2.2 Spread Bands
A Spread Band (8B) is a standard deviation-based unit ofthe normal probability ‘une The SB factors in the combined voailty and correlation ofa stock pairto derive an estimate of where a pair trade should be initiated The trader then de- termines how many standard deviations are appropriate for any given pair For ‘example, ifone standard deviation is selected, then when the sqread hts the SB, the stock par has a 65% chance ofreverting to the mean Iftwo standard devia- tions ae selected, then the pair has 2 95% probability [29] However, practice is different than theory-these calculations presume the absence ofnews and other external factorsthat affect stockprices
First, we review the factors in the SB caleulstion The Histerical Veltility (ITV) was discussed in Chapter 1, sothe 30-day HV must be calculated foreach stock in the pair: HV, and HV The next factr in the Spread Band equaticn is the Cemiehon Cafe, do kuoun as Cogficrnt E- The R-value carldee the movement of ene stock price with another A correlation of +1 means that the two stocks move synehzonously, while a correlation of -1 means that the tne stocks meve in oppesite directions” Ris the second factor in the SB equation,
Trang 132 2 Pair Trading
‘The chart below (Figure 2.2) shows a daily chart oftwo correlated stocks with ø ‘currentR300f0:33, towards the low end of the established comelation range
‘The Acme P System is based on highly comeated stock pais with an R ofa least +0.3 However, itis perfectly possible to reverse the signals to trade non- ‘cerrelated pairs and use the area outside ofthe spread bands, Use an R-value of 0.3 of less for now-cortelated stock pals
For further information on equity correlations, go to the Market Topology Web ste at hitp/wwoimpactopis.com, At this ste, 2 steck symbol query will, retum ais ofstocks that are mest comreated to a reference stock The ste pro- Vides equity maps for domestic und foreign matket indices such a’ the S&P 500 showing the corelatons among all ofthe stocks composing the index
Am TC WmhÔ Ba
Elgure 22, Conebtion CocficenE
[Now we can calculate the Spread Bands fora stock pair for one trading day, 9s showin in Equation 32 The formula assumes 365 days in a yea, so the square root of | / 365 is takento get the constant 0523, represented by k The variable ‘SD represents the number ofstandacd deviations The variables 1, and Hp
arethehistericvolailtes ofStock And StockB, respectively
‘The retationship between the Spread Bands and R is an inverse relationship, ‘As the correlation R increases, the bands narrow and vice versa, Consequently, es are multiplied by the factor QF)
22 Spread Bands “
“The formula forthe Spread Band is as follows:
SH =R XSD X(MỤ + HT) X(1-R) 62
Heres an example oftwo corelated video game software stocks Our Stock Ais ‘Adtivision(ATV: Nasdaq), and Steck is THQlncorporsted (THQI-Nasdaq) ‘The 30-day voailtes and correlation ae as follows: © HV mof ATVIis 0643, © HV of THOLis 0822 © Rwis033 “The Spread Band for astendard deviation forthe ATVE-THQI Pais: (0.0523 % 1 x (0.643 + 0.822) x (1-033) = 00513
‘The final factor to consider is the mumber of standard deviations required for ‘generating a pair-trading signal We have selectedtwo standard deviations as the ‘faut value because prices have a least 295% chance ofreverting to the mean, assuming a normal probability curve Therefore, we multiply the Spread Band value (6.0513) by te number ofstandard deviations (2.0) to obtain the upper
and Jower Spread Band values, +0,1025 and-0.1025 (Figure 2),
bp
f
Trang 14“ 2Pair Trading
23 Short Selling,
Before defining te pair trading system, we review the practice of short selling To effectively execute spreads, the trader must become adept at short selling A shot sal iste reverse ofa long postion: sel first and buy back later Since short seling is a transaction where a secusity is first borzowed, the trader must check the broker's short is te ensure that either ofthe socks in the pair can be bor= rowedbefore eggingisto the trade
‘The ease of'shor selling depends upon the liguidty ofthe stock Shorting ‘Nasdaq stocks with penny spreads makes execution smoother forthe pair trade Ifthe trader decides to leg info the long entry first, then executing the sheet side should be no problem with the liquid steck Because ofthe uptick nile, however, the short leg should slways be executed firs Shorting liquid NYSE stocks is {just 2s easy, bu ifthe stock is dropping fast, then the trader isnot going to get ‘an uptick; however, this problem ean be solved through the practice ofliedging (ee Section24)
23 NYSE Rules
Stocks on the NYSE can be sold short only on aps tik or zero-plus tick, A plus tickis trade price that is higherthan the previous trade price Azero-pls tickis trade price equal to the previous trae price, but the previous trade price must have occured on aplus ick Table 21 is an example ofan NYSE trade sequence, showing whether each trade occurred on a pls tick or minus tick
‘Table 2.1 NYSE Shoat Sales Exanple
“Trade Prie | Tek Type Aion
3000 | Plus Tick Shon
2995 | Mims Tick, No Shor 30.00 | Plus Tick Short 4005 | Plas Tick Short 3005 | Zevo-Piue Tick | Short 30.00 | Minus Tick No Shore
s0.00 | Zen MimeeTiek | Na Shor wos Lit tik Stent
24Hedgine 4s
232 Nasdaq Rules
‘The Nasdaq uptick rule is different than the NYSE nulest is based on the best bid price, not onthe trade pice On the Nasdag, ene can sll shert only on an bid (dencted by an up arow in a Level IL window) and net en a down Bi (úc- notedbyado marrow) Table? 2shows anesampleofwhenaNasdagstoc-can be shorted andwhen t eannet
Table 22, Nasdag Sheet Siles Example Trade Pte [Bow Bid Tih Type Aetion 3000 | 3000 UpBid — Shor 2995 | 2995 DownBid NoShort 3000 | 2995 Down Bid NoShon 405 | 3000 UpBid — Shor 4005 | 3000 UpBid Short 3000 | 2995 DownBid NoShon 43005 2995 Down Bid _No Shor 24 Hedging
‘edge is two positions where a ong position anda shor position in the same
‘security offset each other The hedge can be composed of various instruments
S8, aleng sock postion 1985, a hedge cotld be exated using two Tinked accounts By establishing an nshrt options pesto Inthe good oé days circa a one, positon in Accouat 1 anda shoe poston in Account 2, tock could be effec= tvely sold shor by jus sling the log pesition in Aecourt 1 an then buying
‘back to reestablish the hedge, thereby circumventing the short sale rule in the process The trader was able to shor stock witout an up bid or lis ck, asl- tose in Table 2.3,
Shortly thereafter, a rule was instituted that eliminated this loophole The modern style ofhedging is to combine a stock position with an option position
tocresteacaerson [19] A conversion va longstockpostion combined wih synthetic shox position (eng putandshest call) Ths, by seine fore po- sition the trader ean go net srt and then buy bck the tock arto return to 4 holes postion A conversion is a relatively complicated series of trates, bat
Trang 1546 2 Pair Trading 2.5 Pair Trading System (Acme P) 47
The introduction of single-stock futures presents another hedging alternative A trader can simply short the stock futures contract, establish a long position simultaneously, and then execute sell-buy trade sequences to short the stock Table 2.3 Old-Style Hedging
Account I Account 2 Action
Buy CSCO Establish the hedge Sell ShortCSCO _ Establish the hedge
Sell CSCO Short CSCO without up bid BuyCSCO Cover CSCO (close short) BuyCSCO Go long CSCO
SellCSCO Close long position
Sell CSCO Go short again
2.5 Pair Trading System (Acme P)
The Acme P system is a mechanical trading system for trading stock pairs First, we calculate the volatility measures, and then define the entry and exit rules for each pair combination We recommend using either a frve-minute chart or even a three-minute chart for timely signals since the pair trades are entered on the close of the bar
Although the system is designed for intraday pair trading, the system can be adapted to position trading because it works on any time frame The system
shown here uses the one-day YolatilitvConstant This constant can be multiplied
by any number of days to adjust the Spread Bands to the proper width
2.5.1 Long A-Short B Rules
Entry Rules
1 S crosses above -SB
2 Sell Short Stock B on Close
3 Buy Stock A on Close Exit Rules: Profit Target
1 S crosses above 0 2 Sell Stock A on Close 3 Cover Stock B on Close
Exit Rules: Stop Loss
1 S <(SD*-SB)
2 Sell Stock A on Close 3 Cover Stock B on Close
Note how the entry rule waits for the Spread to cross over the lower Spread Band Ifthe spread falls below the lower SB, then the system waits for a reversal Spread fall below the SB and then execute the pair trade as soon as the Spread ticks up, at which point the Spread maybe well underneath the lower SB Ifthe
ignal occurs at the open, then the trader may choose to execute the trade imme-
diately, and maintain a stop loss of two times the SB, the standard stop in the Acme P System
Calculations
1 Set the Standard Deviations (SD), default value is 2.0 2 Obtain the 30-day Volatility of Stock A (HV 4) 3 Obtain the 30-day Volatility of Stock B (HV3:)
4 Calculate the 30-day Correlation of Stock A and Stock B (Rag)- 5 Calculate the Spread Band (SB)
6 Calculate the Spread (S)
2.9.2 Short A-Long B Rules
Entry Rules
1 S crosses below SB
2 Sell Short Stock A on Close
Trang 16+“ 2 Pair Trading Est Rules: Profit Target
1 8 crosses below 0 2 Sdl Stock B on Close
3 Cover Stock A on Close Exit Rules: Stop Lose
1 $= @D*SB)
2 Sal Stock B on Close 3 Cover Stock A on Close
In the Acme P System shown in Example 2.1, the number ofshares N is esleu- led from the daily daca of Stock A, i this case Data3 Because each stockin the pair uses the Percent Volailty Model for position size, the pair is volatility edged Ifa stock trading at 40 has an ATR oftwo and another sock af 20 has an ATR oftwo, then the position size for both stocks will be exactly the same For this reason, gaps are an important pant ofpair trading In this example, ifboth stocks gapped up one point, then thẻ đoka 41 becomes undervalued relative to the stockat 21, and there is potential fora quick pairtrade
Alter position sizing, the HVs ofboth Stock A and Stock B are calculated from Data8 and Datat, respectively The two stocks are then correlated, and the system can calculate the Spread Bands for the stock pair Fis, the band for one ‘standard deviation is calculated, Then, the system muliplie this band value by the mumber ofstandard deviations to cbtain the Spread Band figure ‘The upper Spread Band is the pasitive SB figure, and the lower Spread ‘Band is the negative figure Finally, Ue spread is calculated and any erossover ‘condition wil trigger pair signal
‘As an alterative to the exit miles implemented in the code, the trader may ‘wish for the Spread to traverse from one band all of the way to the other band instead ofthe erossing point at zero Inthis case, the stop Joss rule can be modi- fied to allow for greater volatility inthe Spread Increase the StondardDeviations parameter for wider latitude, ‘The following code in Example 2.1 is an EasyLanguage rendition ofthe pair trading system The system uses the number of standard deviations to detet= ‘mine the stop less, however, a trader may wish to implement aseparate stop for the stem instead of depending on the number of standard deviations The traders also free to change the reference prices Price and Price? for computing, the spread For example, Price} and Price? could reffence the open of today versus the close of yesterday
25 Pair Trading System (Acme P) Example 21 Acme P System
Kae’ Systent Pair Tadig ™
Dataa: Stock 4 Intraday iden) Datag: Stock 2 Daily ., Pricea(Close of Data3), Price2(Close of Uatas), StandaxeDeviatiers(4-5}, Length(30), {Fosition Sizing Paransters) Equity(s00000), Risioocel (3), RiskPercent(.0), RiskATE(2.0), {Trade Logging) Wikigendo.o, Nelatiityentat(.32), ppereardo.0), Uinerterd(e-0), Spread(0.0; TF Date «> Datel] Then Begin N= AcnecetShares(tquity, Riskodel, RiskPercent, RisKATR) nh
Wr = AcneVolatidity(Length) of Dates; = AceVolatility{ Length) of Dataas
(WV - Correlation(Pricel, Pricez, Length): Volatilitysand = Volotilityconstant © (Ina + v2) * (1 - CV); pperöard ` Standardbeviatione * yfand;
LowerBird = StandardDevéations * (-Volatilatyéond); End
Spread < (Close of Datat / Pricet) - (Close of Data2 / Price2);, AF Spread crosses show Hemera th TH be IL) Shae tle
AE gue cts ae
Trang 1750 2 Pair Trading, EsitLeng(*Acee P UX 4") This Gar on Close
Else TF Spread <= StandardDeviations ® Loverband Then xdtong( "Acne P LX `") Thds Oar on Closes If Spread crosses below UpperBand Then Seli(*Aene P SE") N shares This Bar on Close; IF Spread crosses below 0 Then Etshort( Acne P 5% +") This Bar on Close
Else If Spread >» Standardeviations * Upperlard Then Đátghort(fAene P SK -") This Bar on Clese; (Log Trades for Spreadsheet Export)
Conitiont = Aenelogtrades(Logtrades, Logfile, “P”);
‘To see both legs ofthe pair trade executing simultaneously, the TradeStation ‘workspace must be set up to luve two chatting windows stacked horizontally, ‘one window configured as shown in Table 24 and the ether configured as shown inTable2.5 “Table2.4.Pair Configuration for Chast Window I StockA Intraday ——— ‘Stock A, Daily Stock Daity ‘Acme Spread Indicator “Table25 Pair Configuration for Chart Window 2
Daal Stock B Intraday Daa? Stock A Tntradgy Dulas Stock B Daily Dưa SkA — Dạ
ates Acmefprsae Iudiedler
‘With the windows configured inthis manner, the trader will receve the long and sheet signals of the pair simultaneously Fer a Long A-Sheet B pair, the long signal will trip in Chart Window 1, and the short signal will fire in Chart Win- ow 2 Por a Short A Long B pair, the short signal will be displayed in Chart ‘Window 1, snd the long signal will appear in Chart Window 2,
26 Examples 3
26 Examples
“The following, examples illustrate how to tre the Acme P System Fach exam ple uses an Equity value of $100,000, a Percent Volatility Model with 2 risk value ‘0f2%, and the number of Standard Deviations is two Because each leg wes the Percent Volatility Mode, the number ofshares is adjusted to each stock's ATR 264 Activsion-THQ Incorporated