ITG_PairsTradingAlgos_20130215.pdf

7/27/2019 ITG_PairsTradingAlgos_20130215.pdf

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Pas Tag Algothms Equtes Makets1

In equities markets, the concept o a pairs trade includes a variety o investmentstrategies. The investment models themselves range rom simple to complex, yet all

engage in the simultaneous purchase and sale o two securities with the goal o

generating alpha while controlling risk. The inherent sophistication o such strategies

makes order execution very challenging. A trader must not only seek liquidity or two

stocks concurrently, but the liquidity sought or one stock is entirely contingent upon

the available liquidity in the other. These challenges are addressed by many traders

through deploying algorithms as an ecient and eective way to source liquidity,

reduce transaction cost, and streamline workow.

There are generally two categories o pairs trading: spread trade and switch trade.

The ormer represents the strategies that attempt to proft rom temporary

dislocation in the relative valuation o underlying assets; the latter consists o

swapping two instruments or purposes such as rebalancing portolio holdings.These distinct investment needs result in two types o pairs algorithms with

dierent trading objectives2.

In this paper, we frst discuss the defning eatures or the spread trade and the

switch trade. Then, as cross-market pairs have become a ast-growing investment

strategy in recent years, we examine the special requirements or executing pairs

across dierent countries. We conclude with a brie discussion on some new trends

in pairs algorithms.

SPrEAd TrAdE

A spread is derived rom the price relationship between two assets; a relationship

that can be defned in various ways. Spread trade algorithms are designed to detectchanges in spread narrowing or widening and intelligently place orders when the

spread becomes attractive or particular investment goals. For example, a merger/

acquisition deal may lead to the long (short) o the target (acquirer) company shares

with the expectation that an acquirer will later raise its bid; or a statistical arbitrageur

buys and sells two co-integrated stocks so that she can proft rom temporary price

dislocation. The ollowing eatures play an integral role in the algorithmic execution o

spread trade.

1 This is a revised and extended version o a paper originally published in The Trade Asia, Issue 13, Sep-Dec 2012.2

In a sample set o 19,480 orders submitted to ITGs pairs algorithm, 76% o the pairs can be categorized as spreadtrade vs. 24% as switch trade.

AUTHOrS

d Wu

Vice President,

Algorithmic Trading

[email protected]

Key doe

Director,

Electronic Trading Desk

[email protected]

Cy Y. Yag

Quantitative Analyst,

Algorithmic Trading

[email protected]

COnTACT

Asa Pacfc

+852.2846.3500

Caaa

+1.416.874.0900

EMEA

+44.20.7670.4000

Ute States

+1.212.588.4000

[email protected]

www.itg.com


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Spea Captue

While a pairs trade oten involves complex models, well-designed algorithms should

support three basic spread types noted in Table 1: price ratio, cash spread, and

relative return. The spread should be monitored in real-time by algorithms, while

underlying market access tools execute at target price levels. I and when the spread

moves away, trading must be paused.

Considering the spread represents the desired proftability to be locked in, it is critical

that spread calculation is consistent with trading tactics. For example, i the spread

is derived rom the bid (oer) price or buy (sell) orders, a loss may occur i liquiditytaking is indeed necessary. A more conservative approach is to construct the spread

by using the bid (oer) price or sell (buy) orders. Doing so will guarantee spread

capture as long as orders are executed within the NBBO.

Oe Placemet

Trading aggressively reduces the odds o missing avorable prices. However, liquidity

taking may lead not only to adverse price impact on one leg3, but consequential

adverse spread movement or the pair itsel. Thus, algorithms must make a trade-o

between liquidity provision and removal. Moreover, this decision has to be consistent

with how spread is defned. I spread capture assumes buying (selling) at the bid

(oer), algorithms can only place passive orders. On the other hand, i the spread is

constructed as buying (selling) at the oer (bid), algorithms will have the exibility o

either providing or removing liquidity whenever appropriate.

Applying dierent tactics to dierent legs also improves execution quality. For

liquid stocks with high trading volumes, passive trading may be sucient to

access the liquidity that is needed. For illiquid stocks, a simple solution could be

to start with a passive order, then, as time passes, correct to an aggressive order

to increase fll rates.

TABLE 1:

Three Basic Spread Types

Pce rato Cash Spea relatve retu

Tag

Objectve

Relative value arbitragebased on price ratios

Risk arbitrage such astakeover and mergers

Relative value arbitragebased on the dierential o

price returns

Example Sceao: Stock X and Y are

co-integrated at a historical

price ratio (Y to X) o 0.5Pce ato spea: Y Price

dese spea: 0.5Tae: Buy 1,000 shares X,

short 1,000 shares Y whenspread 0.5

Sceao: Company A

acquires B in a merger deal

that allows B shareholders

to receive 0.5 share o A and

$0.15 in cashCash spea: 0.5A Price +

0.15 B Pricedese spea: $0.10Tae: Buy 1,000 shares B,

sell 500 shares A when

spread $0.10

Sceao: Stock C and D

usually move in tandem

within a range o 1%Bechmak: Previous close

relatve etu spea:

dese spea: 1%Trade: Buy 1,000 shares C,

short 1,000 shares D when

spread 1%

Source: ITG Inc.

X PriceD Price

DPrevClose

C Price

CPreClose

3 In pairs trading terminology, an order rom one side o a pair is oten reerred to as a leg.


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Leg rsk

Typically, the sell and the buy leg o a pair remain hedged to lower risk by

continuously reducing the net market exposure, i.e., minimizing(|SellFilledValue

HedgeRatioBuyFilledValue|). One possible solution to achieve this goal is to

execute both legs simultaneously. The downside is that when both legs are working

in tandem, market exposure itsel becomes a moving target, which is dicult and

potentially costly to maintain. Another possible solution is to place orders in

sequence; i.e., frst trade the initiating leg (oten the more dicult side o a pair) or

a certain number o shares, then hedge with the opposing leg to quickly oset the

initiated position. By trading each side o a pair sequentially, the task o minimizing

market exposure becomes more ecient and achievable.

Child orders rom both legs must be properly sized to not demand more liquidity than

the market is willing to provide. Ater all, the relationship o the pair must be

considered, not just the single leg being traded. I not done eectively, a well-

designed pair may instead become a risky, one-sided bet caused by its un-hedged

positions. For example, to counter an oversized sell position, an algorithm is orced to

buy 1,000 shares when only 600 shares are available in the market. This will orce the

algorithm to incur large impact to complete the remaining 400 shares.Figure 1 exhibits a hypothetical case o a price-ratio spread trade, in which sell and

buy orders have to be flled at 1:1 ratio and execution was only triggered when

(SellStock Price)/(BuyStock Price)0.5. The algorithm chose to execute the buy frst,

then hedge with the sell, as the buy leg is the more dicult stock in this example.

"()

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

0.4985

0.4990

0.4995

0.5000

0.5005

0.5010

0.5015

0.5020

0.5025

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15

FilledDollarValue$

PriceRatio

Time

Desired Price RatioMarket Price RatioBUY Filled $ SELL Filled $

Execution is only triggered when spread is

in-the-money (i.e., market price ratio desired

price ratio).

Execution is paused if spread becomes out-of-money

(i.e., market price ratio < desired price ratio).

Buy and sell legs are closely

hedged against each other.

Source: ITG Inc.

FIGURE 1:

Spread Trade Execution


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SWiTCH TrAdE

Instead o arbitraging mispriced assets, switch trades ocus on eciently exchanging

one position or another by contemporaneously managing leg risk. For example, a

trader may want to liquidate an out-o-avor stock and replace it with another that is

expected to perorm well in the uture; or a portolio rebalancing transaction sells an

overweight holding and buys an underweight position. All o these investmentstrategies can beneft rom algorithms that enhance perormance while preserving

market neutrality. There are two unique eatures that contribute to the outcome o a

switch trade: execution plan and liquidity sourcing.

Executo Pla

Unlike a spread trade, a switch trade has no notion o capturing spread. Instead, the

implementation requires a base plan that intelligently breaks large orders into

smaller slices over a target time horizon. This plan ocuses on the more dicult leg,

which sets the overall pace o execution and typically weighs most heavily on the

total transaction cost. The primary objective o the base plan is to reduce slippage

against particular benchmarks by employing various approaches, such as schedule-

based or implementation-shortall-based strategies.Additionally, to remain market neutral, a separate plan is applied to the second leg,

which is designed to mitigate leg risk through minimizing the net market exposure o

a pair. This can be achieved by leveraging ast market access tactics that allow

positions to be continually oset. Moreover, the progress o the hedging plan has to

be synchronized with the base plan to preserve a balanced two-sided execution.

Soucg Lquty

Speed is less o a concern or a switch trade, because chasing transitory price

ineciency is not its main objective. Thus, it can aord to more patiently discover

liquidity rom a wider range o venues including lit markets and dark pools, which

inherently improves execution quality. For example, algorithms can leverage a

lit-market trading strategy to make necessary progress; and overlay it with anopportunistic dark-pool aggregation strategy, which subsequently leads to more

midpoint crossing, lower market impact, and less inormation leakage4.

Depending on the urgency levels that traders choose, algorithms must be able to

dynamically shit the degree o dark exposure. Under high urgency, priority should be

given to executing in lit markets aggressively to reduce the opportunity cost o

unflled shares. Conversely, low urgency orders can submit more shares to dark pools

and take advantage o avorable liquidity conditions. It is worth noting that dark

orders have to be careully sized to avoid liquidity shocks (e.g., large blocks are

crossed on only one leg), which oten result in undesired market exposure and

elevated leg risk.

Figure 2 shows a hypothetical example o a switch trade. An implementation-

shortall execution plan was chosen to reduce arrival price slippage. The net market

exposure at any point in time is tightly controlled: never more than 0.5% o the total

notional value o the pair.

4 Selway J. and Pearson P., Dark Liquidity Aggregation State o Play, ITG White Paper, November 2012.


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CrOSS-MArKET PAirS

Todays globalized fnancial markets create opportunities to proft rom investing in

cross-market pairs, such as a spread trade to arbitrage between an ADR and its local

listing, or a switch trade to rebalance two positions rom dierent countries to

maintain target levels o regional exposure. To successully execute pairs across the

globe, algorithms have to not only resolve market microstructure issues, but also

manage currency risk.

Among the complexities that are caused by market idiosyncrasies, the most

pertinent is the accessibility o liquidity. I one leg o a pair must stop trading due to

events like auctions, trading halts, lunch breaks, etc., the other leg must take action

immediately to mitigate leg risk. Also, regulations and rules on lots, tick sizes, and

short selling require sophisticated order placement logic. For example, i exchange A

imposes restrictions on odd lot trading but exchange B does not, an eective way to

minimize risk is to initiate a position o round lots in A and then quickly oset it with

round and odd lots in B. Finally, to cope with varying market dynamics such as

ragmentation and dark pool prolieration, algorithms should choose the appropriate

liquidity sourcing methods in each market while still keeping the execution rom both

legs synchronized.

Currency risk plays two important roles in cross-market pairs. When dierent

currencies are involved, spread calculation must account or the conversion rates.

Otherwise, algorithms will calculate incorrect spread levels, which may negatively

aect the proftability o underlying investment strategies. Another aspect o

currency risk emerges when shares have to be settled in a single currency. This

requires algorithms to simultaneously trade in the FX market and hedge currency

exposure in real time.

(1,500)

(500)

500

0

5,000

10,000

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10

NetMarketExposure($)

FilledValue($)

BUY Filled$ SELL Filled$ BUY Filled$- SELL Filled$

-8

-6-4-2

02468

bps

Time

Performance is driven by price

movements on both legs

Market neturality is

tightly maintained

Execution is continuous without any

pause over the trading horizon

Source: ITG Inc.

FIGURE 2:

Switch Trade Execution

BUY Return SELL Return Pair Execution Performance (arrival price benchmark)


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SUMMArY

The complexity o pairs trading requires sophisticated trading tools or best

execution. We introduced two types o pairs the spread and the switch and

touched on the strategies that algorithms use to implement such trades. We also

outlined some o the unique challenges when executing pairs in dierent markets.

Many traders fnd it a daunting challenge to capture spread and/or reducetransaction cost, while curtailing risk at the same time. Equipped with advanced

quantitative trading techniques, pairs algorithms oer valuable solutions to address

these issues and help asset managers accomplish their investment goals.

As fnancial markets continue to become more integrated, opportunities abound or

multiple-asset pairs in the realms o cash equities, FX, utures, options, and other

derivative instruments. Also, the demand or multiple-leg pairs has been increasing

as more complex investment models are being developed, e.g., a spin-o deal

involving three legs. These emerging trends represent the new rontier o the next-

generation pairs algorithms.

2013 Investment Technology Group, Inc. All rights reserved. Not to be reproduced or retransmitted without permission. 12213-19318

The opinions, positions, and/or predictions taken or made in this document reect the judgment o the individual author(s) and are not

necessarily those o ITG. These materials are or inormational purposes only, and are not intended to be used or trading or investment

purposes or as an oer to sell or the solicitation o an oer to buy any security or fnancial product. The inormation contained herein has

been taken rom trade and statistical services and other sources we deem reliable but we do not represent that such inormation is accurate

or complete and it should not be relied upon as such. No guarantee or warranty is made as to the reasonableness o the assumptions or the

accuracy o the models or market data used by ITG or the actual results that may be achieved. These materials do not provide any orm o

advice (investment, tax or legal). ITG Inc. is not a registered investment adviser and does not provide investment advice or recommendations

to buy or sell securities, to hire any investment adviser or to pursue any investment or trading strategy.

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Investor Protection Fund (CIPF) and Investment Industry Regulatory Organization o Canada (IIROC); in Europe, Investment Technology

Group Limited, registered in Ireland No. 283940 (ITGL) and/or Investment Technology Group Europe Limited, registered in Ireland No. 283939

(ITGEL) (the registered oce o ITGL and ITGEL is First Floor, Block A, Georges Quay, Dublin 2, Ireland and ITGL is a member o the London

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