## Zero-Crossing Variant of Pairs Trading Strategy Friday, 14 October, 2016

**A related paper has been added to:**

#12 - Pairs Trading with Stocks

**Authors: **Donninger

**Title: **Is Daily Pairs Trading of ETF-Stocks Profitable?

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2816288

**Abstract:**

Pairs trading is a venerable trading strategy. There is agreement that it worked fine in the far past. But it is less clear if it still profitable today. In this working paper the universe of eligible pairs is defined by the holdings of a given ETF. It is shown that the stocks must be from ETFs which select high-quality, low-volatility stocks. The usual closeness measure presented in the literature performs poor. The paper presents a simple and clearly superior alternative based on zero-crossings. The strategy performs with the correct universe and the improved pairs selection rule before trading costs quite fine. It depends on the assumed trading costs if this is also in real-trading life the case.

**Notable quotations from the academic research paper:**

"The seminal paper on pairs trading is Gatev et. al. [1]. They authors did not invent the strategy. It was in common use since the 1980s. The pairs are formed from a universe of stocks. There is a one year formation period. Each stock is normalized to 1 at the beginning of this period. One selects for each stock the closest neighbor. The distance measure is the summed up squared daily difference of the normalized prices.

The initial results with the distance method were rather disappointing. Pairs trading is based on mean-reversion. The distance measures if the stocks stick together. But sticking together and mean-reversion are two different concepts. Vidyamurthy proposes zero-crossings as an alternative. One counts the number of times the spread moved above or below the mean-spread. But this measure is also not satisfactory. It is known from the theory of Brownian-motions that zero-crossings are much more likely in the first few steps of the motion. If one starts at zero a small up- followed by a larger down-move is a zero crossing. The path moves in the following away from zero and a crossing gets very unlikely. The situation is somewhat different for a mean-reverting process but the general behavior is still the same. A zero (or mean) crossing does also not create a profit. The interesting case is a crossing which started initially outside the two-sigma band. This is the main distance function. A larger number of crossings is of course better than a lower one. For two pairs with the same number of crossing the distance is used as a secondary measure. But a pair with 5 crossings is always closer than a pair with only 4. The strategy defines also a minimum number of crossings (usually 4). A pair with less crossings is never traded.

The strategy does not use overlapping formation periods. The set of tradeable pairs is determined each month (every 21 trading days). The formation window is like in most studies a year (252 trading days). But an open position is not automatically closed at the end of the trading period. An open position is – if mean reversion does not happen before – closed after 30 trading days. There are usually pairs from the previous formation period open. It makes no sense to close a position which was entered at day 20 of the trading period just because a new formation calculation is performed. The strategy does not reset the spread to zero at the end of the formation phase. It uses the mean and the standard deviation from the formation period also in the trading phase. A position is only opened, if the spread is between 2 and 4 standard deviations. It is unlikely that the spread is by chance larger than 4 deviations. A very large spread is a sign that the pair is in divorce. As an additional stop-loss an already open position is closed if the spread gets larger than 8 standard deviations. This stop-loss is only triggered a few times but it avoids some

really disastrous losses.

As already noted simulated trading is done from 2011-01-01 till 2016-07-26. The strategy has an overall profit of 144.4%, a monthly Sharpe ratio of 1.16 and a max. relative drawdown of 8.2%."

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