Pairs Trading (ETFs)

First of all thanks for your patience, and from now on I’ll be posting again on a more frequent basis.

And furthermore I’d like to advise those interested in quantitative research of a new blog I just came across: Engineering Returns by Frank Hassler.

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Due to the fact that I’m a big fan of statistical arbitrage (and trading it for a living), I thought it would be interesting to check if – and to what extend – there are pairs of ETFs (Exchange Traded Funds) which – as always based on historical data, statistical anomalies, regularities and irregularities, … – would provide a favorable and tradable edge maintaining a market neutral position.

I personally prefer ETFs to individual stocks due to the fact that the latter are much more sensitive to unforeseeable events and/or outcomes like earnings, fundamentals, crew changes (CEO, CFO, …), rate disputes, strikes, take-overs, force majeure (casualties, disasters, …). And I speak from my own experience …

In conjunction with pairs trading, you’ll probably hear about two (quite different) concepts: correlation and cointegration.

Correlation states the degree to which the (daily, weekly, monthly …) returns of two series of prices (e.g. the S&P 500 and the Nasdaq 100) will move in the same direction most days/weeks/month over a period of time (but  probably drifting farther and farther away from each other due to deviations in the magnitude of daily returns), while a pair (being long one and short the other series of prices in the right proportion) is called cointegrated if it has a consistent mean and standard deviation, both prices series never indefinitely wandering off in opposite directions and never drifting farther and farther away from its mean without eventually returning to the initial ratio or mean (mean-reversion).

But – unfortunately – the so-called half-life (the expected time to revert half of its deviation from the mean) concerning a cointegrated pair of price series will regularly be measured in weeks or month (see stats below), and I’m more a high-frequency trader looking for opportunities on a day-by-day basis.

The following are the ETF’s I’ve been utilizing for my investigations, meeting the necessary requirements like adequate liquidity (daily trading volume), as low as possible transaction costs (narrow bid/ask spreads), adequate volatility (in order to justify the arising high transaction costs), among others:

• SPY: S&P 500
• QQQQ: Nasdaq 100
• IWM: Russel 2000
• SMH: Semiconductor
• RTH: Retail

Other ETFs may be subject to a follow-up posting.

To test for cointegration, the primarily method used is called the augmented Dickey-Fuller test. If two price series are cointegrated (with a probability of better than 90%), the Dickey-Fuller test would’ve to come up with a t-statistic exceeding the 90% critical value of -3.038 (in absolute terms), otherwise the hypothesis that those two price series are conintegrated would be rejected. The following table provides the respective t-statistics based on the augmented Dickey-Fuller test for the time frame between 01/01/2002 and 08/06/2010 (price series are adjusted for dividend and cash payments).

Interestingly there are only two pairs – IWM vs. RTH (gt. 90%) and SMH vs. RTH (gt. than 95%) – which are cointegrated with a probability of better than 90%, while the SPY (as a proxy for the S&P 500) and the QQQQ (as a proxy for the Nasdaq 100) show the least probability for being cointegrated. IWM vs. RTH shows a half-life of 194 sessions, and SMH vs. RTH a half-life of 92 sessions. Both pairs seem to be good candidates for a (longer-term) mean-reversion strategy.

A second interesting observation is that even in conjunction with SPY and IWM, the RTH (Retail HOLDRS) seems to be a favorable candidate for a potential mean-reversion strategy.

But fortunately cointegration is not mandatory in order to find a profitable mean-reversion strategy, and on a day-by-day basis even non-cointegrated pairs (like the SPY vs. QQQQ) may provide favorable short-term mean-reversion opportunities (better fitting my style of trading). So my next step was to check for the pair’s performance based on the easiest mean-reversion strategy:

Buy (on close) the pair in the event the ratio of ETF X and ETF Y closed lower (means ETF A under-performed ETF B on the respective session), and sell short (on close) in the event the ratio of ETF X and ETF Y closed up (means ETF A out-performed ETF B on the respective session). Due to the RTH‘s inception date in 2001 start date is always Jan. 1, 2002.

“Buy” means buy ETF A and sell short ETF B (and vice versa), the number of respective shares specified by the ratio of closing prices (e.g. if the ratio of ETF A’s and ETF B’s closing prices is 3, one would sell short 3 shares of ETF B for every share bought of ETF A). A marginable account would be mandatory, especially due to the fact that it is assumed that one would invest 100% of the then current net liquidation value on both sides of the market (means 100% on the buy and 100% on the short side).

(FAQs and a glossary concerning the stats can be found at the FAQ/GLOSSARY page)

Here is the link to the stats in a ‘readable’ size: Statistics 1

Interestingly it is again the RTH in conjunction with every other ETF which delivers the best results, always exceeding the 200% mark for compounded returns (gross profits before applying commissions, slippage and fees). Unfortunately commissions, slippage and fees would regularly eat up a major part of the compounded return, due to the fact that one would always have a position in the market, with an exposure of 200% (100% on the buy and 100% on the short side), and reversing one’s position (switching from the long to the short side of the pair and vice versa) would quadruple the respective transaction costs in comparison to somone who simply closes a long or short position with an 100% exposure.

In a second step I utilized a little bit more sophisticated concept (Bollinger Bands %B with 4-days EMA and 1 standard deviation):

Buy (on close) the pair in the event the Bollinger Bands %B closed below 0.35, and sell short (on close) in the event the Bollinger Bands %B closed above 0.65. For a detailed explanation of the Bollinger Bands %B concept see Stockcharts.com. In other words: Buy the pair in the event the ratio closed almost (< 0.35) one standard deviation below its 4-day exponential moving average (ETF A is short-term ‘oversold’ in comparison to ETF B), and sell short the pair in the event the ratio closed almost (> 0.65) one standard deviation above its 4-day exponential moving average (ETF A is short-term ‘overbought’ in comparison to ETF B). A classical mean reversion concept.

Here is the link to the stats in a ‘readable’ size: Statistics 2

Things are (partly) significantly improving: Compounded returns, t-score (vs. chance and benchmark) are increasing while transaction costs, maximum drawdowns are decreasing (now Time in Market is less than 100%, with a smaller frequency of closing or reverting one’s position), and especially the SPY vs. RTH and IWM vs. RTH pairs show promising results to be worth some further investigations.

More to come in a follow-up post (at time of writing it’s almost midnight in Germany) …

to be continued …

Successful trading,
Frank

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Disclaimer: No position in the securities mentioned in this post at time of writing.

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