Applying White’s Reality Check to Pairs-Trading Returns
Summary
The discussion explains how to apply White’s Reality Check or a permutation test to a pairs strategy. It represents trading decisions as a position vector, such as long, short, or flat, and randomly permutes that vector to generate simulated strategy outcomes. Returns can be measured in different ways, including log returns or daily dollars earned on a fixed-size position; the chosen measure must be used consistently for comparison.
The tests differ in their null hypotheses. A permutation test shuffles positions to assess a rule with no predictive power. White’s Reality Check instead tests zero rule return, so the return series must be adjusted to remove its average; for a dollar-return measure, the corresponding average dollar return would be subtracted. The answers do not establish one universal test setup, and they caution that testing only a selected pair may miss data-mining bias from the process used to choose the securities. A separate answer questions whether randomizing prices or spreads preserves the time structure required by pairs analysis.
Key ideas
- Represent a pairs strategy’s long, short, and neutral decisions as a position vector.
- Permutation tests shuffle positions to model a rule with no predictive power.
- White’s Reality Check requires detrending returns to test a zero-return null.
- Choose a return measure suited to the position and apply it consistently.
- Account for data-mining bias in how the pair was selected.
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Full text
# Whites Reality Check for Pair Trading # Whites Reality Check for Pair Trading I want to use the Monte Carlo Method described in Aronsons book Evidence based Technical Analysis to test if a given pairs trading strategy is useless. First step there is to randomize the returns of the underlying instrument. Second step is to calculate daily log returns of the strategy as a performence measure. For the first step: Is it sufficient to randomize the spread that is already calculated or are the underlying instruments to be randomized and hedging coefficient estimation to be repeated? For the second step: log returns for spreads are not suitable since the spread can have negative values. So may be better use differencies of spread today minus spread yesterday? ## Answer by babelproofreader (score 2) https://quant.stackexchange.com/a/34564 There are two test methods described in Aronson's book; White's Reality Check and a Permutation test. At the heart of both is the idea of a "position vector," e.g. a numerical vector of a series of 1, -1 or 0, which correspond to long, short or neutral positions. For example, a vector of ``` [ 1 1 1 1 1 0 0 0 -1 -1 -1 -1 ] ``` would represent being long for 5 days, out of the market for 3 and finally short for 4 days. This can be directly applied to a pairs trade such as long stock A, short stock B for 5 days, no position for 3 days and finally short A and long B for 3 days. The Monte Carlo aspect of the tests in question is essentially an n number of random permutations of this position vector. The difference between the two tests is how the null hypothesis sampling distribution is defined and created. For the simpler of the two, the permutation test, the null is that the "rule" has no predictive power and so the randomized position vector is multiplied with the "returns" to give a distribution of "no predictive power returns." In the book log returns are used, but any return can be used; e.g. dollars made per day on a minimum sized pairs position, the tick value of the spread curve etc. This will simply be the test statistic used for comparative purposes, and the test will be comparing apples to apples. For White's Reality Check, the null is that the "rule's return" is zero, and so the return vector must be detrended such that a continuous long or short position would give a zero return over the test period. The book subtracts the average daily log return from each daily log return to acheive this because log return is the chosen test statistic. However, if another test statistic is chosen, it too must be detrended in an appropriate way, e.g. subtract the average dollars made per day on a minimum sized pairs position from each individual daily dollar return on the same sized position. It would, therefore, seem to be quite straightforward to apply the standard tests from the book: i) create your position vector ii) create your chosen test statistic return vector (detrended if necessary) iii) apply the test However, having written all this, I think the more pertinent problem for pairs trading is data mining bias, wherein the search process for stock A and stock B should be subject to testing, rather than testing A with B in the above framework after A and B have been selected. You may find it interesting to browse my data snooping Github, which has code and various downloaded papers related to this general area. ## Answer by d0rmLife (score 1) https://quant.stackexchange.com/a/21206 I am not familiar with the book you mention, so this may not be helpful or relevant. But the phrasing of your question is very peculiar to me. A pairs trade's quantitative appeal is determined by analyzing the historical time series of the stocks. Randomizing the stock prices or the spread also randomizes the time order, which invalidates any method of analyzing a pairs trade that I know of. So I am not sure what this is supposed to demonstrate. Also, the natural logarithm of stock prices is often used in the process of evaluating pairs trades, and it would not make sense to take the logarithm of the spread.
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