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# Statistical arbitrage

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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.

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### Statistical arbitrage

1. 1. 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.
3. 3. The Market Neutral ElementMany 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
4. 4. The Market Neutral ElementShare 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
5. 5. Market Falls 20%, Stock A OutperformsStock 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
6. 6. The Trading ProcessModel or Screening Tool Technical Analysis Market Element Neutral Element Arbitrage Fundamental / Technical Overlays Element Additional Statistical Filters PAIRS PORTFOLIO
7. 7. 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
8. 8. How Pairs Trading Works (a) go short75 go long go long go short go short go long70 go short65 go long
9. 9. How Pairs Trading Works (b) liq,goshort +50075 -200 +7300 liq,golong liq +7100 goshort liq,goshort liq,golong +800 +0 liq,golong70 +700 +500 +500 liq,goshort -6700 -300 -6500 +500 liq65 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.
10. 10. 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
11. 11. 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
12. 12. 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
13. 13. The next four slides are for illustration purpose onlyThese are not stock recommendations Examples of pair trade
14. 14. 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
15. 15. 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
16. 16. 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
17. 17. Applying Pairs Techniques to Futures TradingAnalyzing Similar Commodity Types:Futures with similar characteristics Futures on Stock Indices Energy Complex Agricultural commodities Interest Rate Futures Precious Metals CurrenciesFutures with inverse relationships Gold and the U.S. Dollar Stock Index Futures and Interest Rate Future in Certain Economic Environments Some Currencies
18. 18. The Euro Currency Analyzing Similar Commodity Types Swiss Franc
19. 19. Analyzing Similar Commodity Types Ratio of the Euro divided by the Swiss Franc
20. 20. Crude Oil Futures Analyzing Similar Commodity Types Heating Oil Futures
21. 21. Analyzing Similar Commodity Types Ratio of Crude Oil divided by Heating Oil
22. 22. Thanks