Tag: statistical arbitrage

IBS and Relative Value Mean Reversion

I’m writing a paper on the IBS effect, but it’s taking a bit longer than expected so I thought I’d share some of the results in a blog post. The starting point is a paper by Levy & Lieberman: Overreaction of Country ETFs to US Market Returns, in which the authors find that country ETFs over-react to US returns during non-overlapping trading hours, which gives rise to abnormal returns as the country ETFs revert back the next day. In terms of the IBS effect, this suggests that a high SPY IBS would lead to over-reaction in the country ETFs and thus lower returns the next day, and vice versa.

To quickly recap, Internal Bar Strength (or IBS) is an indicator with impressive (mean reversion) predictive ability for equity indices. It is calculated as follows:


Using a selection of 32 equity index ETFs, let’s take a look at next-day returns after IBS extremes (top and bottom 20%), split up by SPY’s IBS (top and bottom half):

 returns by SPY IBS

The results were the exact opposite of what I was expecting. Instead of over-reacting to a high SPY IBS, the ETFs instead under-react to it. A high SPY IBS is followed by higher returns for the ETFs, while a low SPY IBS is followed by lower returns. These results suggest a pair approach using SPY as the first leg of the pair, and ETFs at IBS extremes as the other. For a dollar-neutral strategy, the rules are the following:

  • If SPY IBS <= 50% and ETF IBS > 80%, go long SPY and short the other ETF, in equal dollar amounts.
  • If SPY IBS > 50% and ETF IBS < 20%, go short SPY and long the other ETF, in equal dollar amounts.

The results1:

pair strat returns

The numbers are excellent: high returns and relatively few trades with a high win rate. Let’s take a look at the alphas and betas from a regression of the excess returns to the pair strategy, using the Carhart 4 factor model:

four factor regression

Values in bold are statistically significantly different from zero at the 1% level.

On average, this strategy generates a daily alpha of 0.037%, or 9.28% annually, with essentially zero exposure to any of the factors. Transaction costs would certainly eat into this, but given the reasonable amount of trades (about 23 trades per year per pair on average) there should be a lot left over. The fact that over 90% of days consist of zero excess returns obscures the features of the actual returns to the strategy. Repeating the regression using only the days in which the strategy is in the market yields the following results:

four factor regression trade days only

Values in bold are statistically significantly different from zero at the 1% level.

Unfortunately, these results are pretty much a historical curiosity at this point. Most of the opportunity has been arbitraged away: during the last 4 years the average return per trade has fallen to 0.150%, less than half the average over the entire sample. The parameters haven’t been optimized, so there may be more profitable opportunities still left by filtering only for more extreme values, but it’s clear that there is relatively little juice left in the approach.

In fact if we take a closer look at the differences between the returns before and after 2008, the over-reaction hypothesis seems to be borne out by the data (another factor that may be at play here are the heightened correlations we’ve seen in the last years): low SPY IBS leads to higher next-day returns for the ETFs, and vice versa.

pre and post 2008 results

The lesson to take away from these numbers is that cross-market effects can be very significant, especially when global markets are in a state of high correlation. Accounting for the state of US markets in your models can add significant information (and returns) to your IBS approach.

  1. As with any dollar-neutral approach, calculating returns is a tricky matter; in this case I have calculated the returns as a % of the capital allocated to one of the legs[]

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