Statistical arbitrage

Statistical Arbitrage
(Pair Trading)

A pair trade is the taking of a
long position in one security together
with an equal short position in
another that is strongly correlated
with it. It is sometimes used to
refer to multiple long and short
positions that are similarly matched.

The Elements of Pairs Trading
Overview

 Pairs Trading is the synthesis of 3 basic elements:
 :-The Market Neutral Element:
Market neutrality is central to pairs trading because it drives how trades are built and analyzed, it defines

relative risk metrics & it serves as the basis for the overall trading strategy .
:- The Arbitrage Element :
Arbitrage is central to pairs trading because it provides the framework for the success or failure of a
trade, and, therefore is the basis of absolute risk management

:- The Technical Analysis Element : Technical analysis is central to pairs trading because it provides
many of the tools by which a trader may make decisions about both the quality and the timing of any
potential trade

The Market Neutral Element
Many types of neutrality must be considered:

Sector or Industry Neutrality:
A pairs trade that crosses sector or industry lines may be statistically attractive, but each leg of the trade is

acted on by different market forces that may affect the ultimate success of the trade .
Market Capitalization Neutrality:
Pairing stocks with significantly different market caps may leave a trade vulnerable to regular market
rotations.

Beta Neutrality :
Pairing stocks with significantly different betas builds a market direction bet into a trade
where it may not be wanted. While total beta neutrality is very difficult, a pairs trader must
always be aware of the betas of the two stocks he or she is pairing

The Market Neutral Element
Share Neutrality vs. Dollar Neutrality:

Share Neutrality
The classic “spread” trade
Not really market-neutral
Creates situations of proper analysis while still losing money

Dollar Neutrality
Pure “pairs” trade
Assures proper analysis leads to profits
Example
Stock A - $10 Stock B - $5
 Share Neutral Spread Dollar Neutral Pair
 Long 1000 Shares A = $10,000 Long 1000 Shares A = $10,000
Short 1000 Shares B = $5000 Short 2000 Shares B = $10,000

Market Falls 20%, Stock A Outperforms
Stock A - $8.50 Stock B - $4

 Long 1000 Shares A = $8,500 :
 Short 1000 Shares B = $4000
 Net = Loss of $500
 Long 1000 Shares A = $8,500
 Short 2000 Shares B = $8,000
 Net = Profit of $500

The Trading Process
Model or Screening Tool

Technical
Analysis Market
Element Neutral
Element

Arbitrage
Fundamental / Technical Overlays
Element

Additional Statistical Filters

PAIRS PORTFOLIO

Hedge Funds

 Hedge -- if something loses value, something else is to gain in
value, and vice versa.

 A basic hedging strategy is pairs trading. Involves matching a
long position with a short position.

 Funds use mathematics and statistics to identify pairs with good
spread reversion characteristics. Can be done with stocks,
options, commodities, currencies, etc

How Pairs Trading Works (a)
go short

75
go long

go long
go short
go short go long
70
go short

65 go long

How Pairs Trading Works (b)
liq,goshort

+500

75 -200 +7300
liq,golong liq

+7100
goshort liq,goshort liq,golong +800
+0 liq,golong
70 +700
+500 +500 liq,goshort
-6700
-300
-6500 +500
liq

65 golong +500
Based on historic observations: Mean spread 3.0 with stdev 1.6
. Go into action, say, when spread +d or -d stdevs.
Strategy can be optimised.

Product rationale
 Aim to generate returns from a portfolio in an all-seasons environment
 Reduce the “market risk (beta)” by investing in “stocks/derivatives with
pair trades”
 Pair trades will illustrate our positive and negative convictions in stock
ideas
 The fund would endeavor to attain market neutrality by means of
executing pair trades
 Pair trades can be done on stocks and indices
 Basic premise: Aims to “Generate returns” in all market conditions
 An extension of our “active fund management” skills
 Stock selection would generate the returns (alpha) of the fund

Trading & Investment strategies

 Strategy A:
 – Long stock (equity)
 – Short stock futures
 Strategy B:
 – Long stock futures
 – Short stock futures
 Strategy C:
 – Long stock (equity) / stock futures
 – Short index futures
 Strategy D:
 – Long index futures
 – Short stock / futures
 Strategy E (possible due to stock lending, recently allowed by SEBI):
 – Long stock
 – Short stock

Investment philosophy: Portfolio returns

 Situation A: Stock A – long stock futures; stock B – short stock futures
 – Post trade, price of stock A goes up and post trade, price of stock B goes down
 – This is a best case scenario, where such trades will result in profits in both the legs of the trade
 resulting in profit
 Situation B: Stock A – long stock futures; stock B – short stock futures
 – Post trade, price of stock A goes up more than stock B
 – Relative out performance of stock A compared with stock B
 Situation C: Stock A – long stock futures; stock B – short stock futures
 – Post trade, price of stock A goes down less than stock B
 – Relative out performance of stock B compared with stock A
 Situation D: Stock A – long stock futures; stock B – short stock futures
 – Post trade, price of stock A goes down while stock B goes up (worst case scenario)
 – Trade going the other way

The next four slides are for illustration purpose only
These are not stock recommendations

 Examples of pair trade

Jspl vs. tata steel
 Trade: Buy JSPL; Sell Tata Steel
 Logic: While downcycle in steel would impact both the stocks, JSPL will likely be better off due to its
 power business which has started contributing significantly to earnings and cash flows.
 Returns: Approx. 4.5% absolute returns over a period of 11 days

Trade: Buy GVK; Sell GMR
 Logic: Funds constraints faced by GMR and lack of avenues to raise funds will hamper many of their
 projects. GVK has a lower debt and not in immediate need of funds. Also, relative valuation of GVK
 better than GMR leading to expectation of relative out-performance.
 Returns: Approx. 20% absolute returns in 12 days

Trade: Buy India Bulls Real Estate; Sell DLF

 Logic: IBREL was trading close to cash on the books while DLF due to recent run up in a tough macro
 environment was relatively expensive. However, we had to close the trade when DLF stock price shot up
 on rumors of DLF having arranged funding for DAL (DLF Assets) which would have taken care of funding
 constraints.
 Returns: Approx. absolute (-) 5% returns in 5 days

Applying Pairs Techniques to Futures Trading

Analyzing Similar Commodity Types:
Futures with similar characteristics
 Futures on Stock Indices
 Energy Complex
 Agricultural commodities
 Interest Rate Futures
 Precious Metals
 Currencies
Futures with inverse relationships
 Gold and the U.S. Dollar
 Stock Index Futures and Interest Rate Future in Certain Economic Environments
 Some Currencies

The Euro Currency
Analyzing Similar Commodity Types

Swiss Franc


 Ratio of the Euro divided by the Swiss Franc

Crude Oil Futures

Heating Oil Futures


 Ratio of Crude Oil divided by Heating Oil

Statistical arbitrage

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Statistical arbitrage