# Differential DV2 and ETF Arbitrage

One of the more useful applications for the DV2 is for pair trading or arbitrage. This is one of the least risky and most consistent way to take advantage of mean reversion. This is because co-integrated assets mean revert more strongly and rarely trend, especially if they are near substitutes such as in the case of two ETFs that cover the financial sector. Or another example would be a leveraged ETF vs its unleveraged counterpart–ie SSO or SDS (S&P500 2x up and 2x down) vs the SPY.

Most pair strategies that have been published involve taking positions that are longer term, such as when the pair is several standard deviations above or below a moving average such as the 20day or 100 day. This methodology is not suitable for arbitrage because most of the discrepancies get closed within days at the most. Thus the DV2 is quite useful in identifying the relative discrepancy between two assets. The differential DV2 is simply a percentile ranking of the difference between the unbounded DV2 for each side of the pair or unleveraged/leveraged ETF. I calculate this a little differently for pairs which is beyond the scope of this article, but the raw unbounded DV2 is simply the average of the C/(H+L) for the last two days. I then multiply a leverage factor to normalize raw figures for each side (ie SPY and SSO) and subtract the two to create a differential. This differential is then ranked over the last 252 trading days using the “percentrank” function to create an empirical distribution so that discrepancies are in effect normalized. In this manner we can create all sorts of different trading strategies to take advantage of the low risk opportunities presented in leveraged etfs vs their underlying unleveraged counterparts.

Performance using most variations of this Differential DV2 is spectacular and can easily survive transacation costs by either waiting for extreme levels or waiting for the oscillator to reverse in the opposite direction from entry.

Normalization and long term pair behaviour seems to be a critical component to pairs trading, which makes the DV2 stronger than the RSI. Furthermore the use of a differential which is itself is normalized further enhances this advantage. In the next part we will take a look at some examples and i will provide example spreadsheets so that calculations can be replicated.

ETF arbitrage is an excellent strategy to add to your market timing arsenal because of its lack of correlation and its high absolute returns relative to risk. As a cautionary note, arbitrage spreads tend to be the most tradeable net of commisions during periods of volatility. In fact the fall of 2008 produced spectacular gains (50-150% annualized) for arbitraging certain leveraged etfs. An arbitrage portfolio of these leveraged etfs produced far higher numbers with very low volatility. Im not sure if we will see numbers like that ever again, but certainly there will be rewarding profits going forward until enough competition reduces margins in this space.