2.3 Short Selling

Before defining the pair trading sjstem, we review the practice of short selling. To effectively execute spreads, the trader must become adept at short selting. A short sale isfhe reverse ofalongposition: sell first and buy back later. Since short selling is a transaction where a security is first borrowed, the trader must check the brokers short hst to ensure that either ofthe stocks in the pair can be borrowed before legngiiuo the trade.

The ease of shon selling depends upon the liquidity ofthe stock. Shorting Nasdaq stocks with penny spreads makes execution smoother for the pair trader. Ifthe trader decides to leg into the long entrj first, then executing the short side should be no problem with the hquid stock. Because ofthe uptick rule, however, the short leg should alwajs be executed first. Shorting hquid NYSE stocks is just as easj, but ifthe stock is dropping fast, then the trader is not going to get an uptick; however, this problem can be solved through the practice of hedging (see Section 2.4J.

2.3.1 NYSE Rules

Stocks on the NYSE can be sold short only on apliis tick or zero-p/iis tick. A plus tickis atrade price that is higherthanthe previous trade price. Azero-plus tickis a trade price equal to the previous trade price, but the previous trade price must have occurred on aplus tick. Table 2.1 is an example of anNYSE trade sequence, showing whether each trade occurre d on a plus tick or minus tick.

Table 2.1. NYSE Short Sales Example

2.3.2 Nasdaq Rules

The Nasdaq uptick rule is different than the NYSE rule-it is based on the best bid price, not on the trade price. On the Nasdaq, one can sell short only on an up bid (denoted by an up arrow in a Level II window) and not on a down bid (de-ncrtedbyadownmrow).Table2.2slTowsanexan3leof\vhenaNasdaqstod::can be shorted and when it cannot.

Table 2.2.

Short Sales Exanple

2.4 Hedging

Ahedgeis two positions where along position and a short position in the same security offset each other. The hedge can be composed of various instruments, e.g., a long stock positron and a short options position. Inthe good old dajs circa 1995, ahedge could be created using two linked accounts. By establishing along position in Accoimt 1 and a short position in Accoimt 2, a stock could be effectively sold short byjust selhng the long position in Accoimt 1 and then bujing n back to reestablish the hedge, thereby circumventing the short sale rule in the process. The traderwas able to short a stock without an up bid or plus tick, as illustrated m Table 2.3.

Shortly thereafter, a rule was instituted that elimmated this loophole. The modern style of hedging is to combine a stock position with an option position to cieate a ccen-ersion [19]. Aconversion is along stockposition combined with asynthetic short position (long p ut and short call). Thus, by sehing the long po-sition,the trader can go net short and then buy buck the stock later to return to a hedged position. A conversion is a relatively conpticated series oftrades, but fortunately professional firms allow a trader to purchase a single day conversion onthespot,commonlyreferredto as a bullet.

2 Pair Trading

2.5 Pair Trading System (Acme P)

The introduction of single-stock futures presents another hedging altemative. A trader can simply short the stock futures contract, estabhsh a long position simultaneously, and then execute sell-buy trade sequences to short the stock.

Table 2.3. Old-Style Hedging

Account 1 BuyCSCO

SellCSCO BuyCSCO BuyCSCO SellCSCO SellCSCO

Account 2

Sell Short CSCO

Establish the hedge

Establish the hedge

Short CSCO withoutup bid

Cover CSCO (close short)

Go long CSCO

Close long position

Go short again

2.5 Pair Trading System (Acme P)

The Acme P system is a mechanical trading system for trading stockpairs. First, we calculate the volatility measures, and then define the entry and exit rules for each pair combination. We recommend using either a five-minute chart or even a three-minute chart for timely signals since the pair trades are entered on the close ofthe 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 VolatttityConstant. This constant can be multiphed by any number of days to adjust the Spread Bands to the properwidth.

Calculations

1. Set the Standard Deviations (SD), defauh value is 2.0.

2. Obtain the 30-day Volatility of Stock A ( ).

3. Obtain the 30-day Volatility of Stock (HVb).

4. Calculate the 30-day Correlation of Stock A and Stock (Rab)-

5. Calculate the Spread Band (SB).

6. Calculate the Spread (S).

2.5.1 Long A-Short Rules

Entry Rules

1. S crosses above -SB

2. Sell Short Stock 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 on Close.

Exit Rules: Stop Loss

1. S<(SD*-SB)

2. Sell Stock A on Close.

3. Cover Stock 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 back above the SB. As an altemative, the aggressive trader may choose to let the 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 signal occurs at the open, then the trader may choose to execute the trade immediately, and maintain a stop loss of two times the SB, the standard stop in the Acme P System.

25.2 Short A-Long Rules

Entry Rules

1. S crosses below SB.

2. Sell Short Stock A on Close.

3. Buy Stock on Close.

ir Trading

25 Pair Tratfing Sj-stem (Acme P)

Exit Rules: Profit Target

1. S crosses below 0

2. Sell StockB on Close.

3. Cover Stock A on Cbse.

Exit Rules: Stop Loss

1. S-(SD*SB)

2. SeU StockB on Cbse.

3. Cover Stock A on Close.

Inthe Acme P Sjstem shown m Example 2.1, the mmiber of shares N is calculated from the daHy data of Stock A, in this case Data3. Because each stock in the pair uses the Percent Volatilitj Model for position size, the pair is voliilitj-hedged. If a stock hiding at 40 has an ATR oftwo and anotiier stock at 20 has an ATR oftwo, then the position size for both stocks will be exactiy the same. For this reason, gaps are an important part ofpair trading. In this example, if both stocks gapped up one pcdnt, then the stock at 41 becomes imder%alued relative to the stock at 21, and there is potential for a quick pairtrade.

After position sizing, the HVs of both Stock A and Stock are calculated from Data3 and Data4, respectively. The two stocks are then correlated, and the sjstem can calculate the SpreadBands forthe stock pair. First, the band for one standard deviation is calculated. Then, the sjstem multiplies this band value by the mmiber of standard deviations to obtain the SpreadBand figure.

The upper Spread Band is the positive SB figure, and the lower Spread Band is the negative figure. Finally, the spread is calculated, and any crossover condition will trier a pair signal.

As an alternative to the exit rules implemented in the code, the trader may wish for the Spread to traverse from one band aU of the way to the other band instead ofthe crossing point at zero. In this case, the stop loss rule can be modified to allow for greater volatility in the Spread. Increase the Staiidai-dDeviations parameter for wider latitude.

The following code in Example 2.1 is an EasyLanguage rendition ofthe pan-trading sjstem The sjstem uses the mmiber of standard deviations to determine the stop loss; however, a trader may wish to implement a separate stop for the system instead of depending on the number of standard deviations. The trader is also free to change the reference prices P/-ice/and Price2 for computing the spread. For example, Pricel and Price2 could refrence the open oftod versus the close of yesterday.

Example 2.1. Acme p System

Acme P System: Pair Trading

Datai:Stock l Intraday Data2:Stock 2 Intraday Dataa: Stock 1 Daily (hidden) Data4: Stock 2 DaUy (hidden)

Inputs;

Pricei(Close of Data3), Price2(Close of Data4), StandardDeviations(l.5), Length(30),

{Position Sizing Parameters}

Equity(100000),

RiskModel(3),

RiskPercent(2.0),

RiskATR(1.0),

{Trade Logging}

LogTrades(False},

LogFlle("Orders.txt");

Variables: N(O), HVl(O.O), HV2(0.0), CV(O.O),

VolatUityBand(o.o), VolatUityConstant (0.0523 ), UpperBand(O.O), LoMeiBand(o.o), Spread(0.0);

If Date <> Date[l] Then Begin

N = AcmeCetShares(Equity, RiskModel, RiskPercent, RiskATR) of Data3;

HVl = AcmeVolatility(Length) of Data3; HV2 = AcmeVolatUity(Length) of Data4; CV = Correlation(Pricel, Price2, Length); VobtilityBand - VolatUityConstant * (HVl + HV2) * (l - CV); UpperBand = StandardDeviations * VolatilityBand; LowerBand StandardDeviations * (-VolatilityBand); End;

Spread (Close of Dotal / Pricel) - (Close of Data2 / Prlce2);

I I..-..-:

If SpriMd I

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