## An Impact of Correlation and Volatility on a Pairs Trading Strategy

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

#12 – Pairs Trading with Stocks

**Authors: **Riedinger

**Title: **Idiosyncratic Risk, Costly Arbitrage and Asymmetry: Evidence from Pairs Trading

**Link:** https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2833800

**Abstract:**

This paper explains the idiosyncratic risk puzzle in a novel test setting with a combination of arbitrage risk and arbitrage asymmetry as in Stambaugh/Yu/Yuan (2015). We utilize the popular investment strategy pairs trading to identify a different kind of mispricing and find a dominant negative (positive) relationship among overpriced (underpriced) stocks between idiosyncratic volatility and returns in the US stock market between 1990 and 2014. The return rises for higher idiosyncratic risk levels, however not monotonically contrary to related papers. We clarify this issue with a profound analysis of the pairs trading’s algorithm and demonstrate how the technical drivers, volatility and correlation, influence returns. Our findings reveal why pairs trading’s profitability varies across markets, industries, over time, and firm characteristics, and how to improve the trading strategy. Double-sorted portfolios on volatility and correlation earn significant risk-adjusted monthly returns of up to 76bp, which is 43bp more than the traditional portfolio earns.

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

"Our first research proposition claims that higher IVOL increases the total return, similar to findings for other investment strategies8. In terms of IVOL, pairs trading is basically a long-short strategy, which profits from the positive IVOL effect among underpriced stocks, but also from the negative IVOL effect among overpriced stocks. We compute the monthly pairs trading return for different volatility levels. To decide whether bearing IVOL is compensated, we must also consider whether our pairs trading portfolio is diversified. A portfolio, which includes a short and a long position of two highly correlated stocks, is for instance almost perfectly diversified. We therefore not only control for different levels of volatility, but we also control for different levels of pair correlation in the following analyzes. We challenge the traditional selection procedure and form twenty-five double sorted portfolios out of five pair volatility9 (σAB = σA2 + σB2) quintiles and five pair correlation ρAB quintiles. Afterwards, we apply the traditional trading procedure for twenty pairs out of each portfolio and compute monthly returns. Analysis compares the monthly development of a 1$ investment in the traditionally selected portfolio with the performance of two alternatively formed portfolios in January 2011. Both alternative portfolios include highly correlated pairs, however one includes highly volatile pairs whereas the other one includes pairs with low volatility. Both alternative portfolios clearly outperform the traditional portfolio. The cumulative return of the portfolio with highly volatile correlated stocks earns four times more than the traditional SSD portfolio and two times more than a portfolio with less volatile pairs. Overall, we find that twenty out of twenty-five portfolios (risk-adjusted return of 39bp – 209bp) outperform the traditional SSD selected portfolio (37bp). The monthly pairs trading returns are higher for higher levels of volatility. However, it comes as a surprise that not the most volatile stocks earn the highest return, but stocks with a medium to high volatility. The return increase with IVOL is not monotonically in contrast to previous studies, which represents a puzzle that we address in the second part of the paper.

Our second research proposition conjectures that the IVOL effect of overpriced securities dominates. We calculate the short leg return (overpriced stocks) and the long leg return (un-derpriced stocks) for each trade and determine the percentage contribution of the long leg to the total trade return for each volatility level. Consistent with arbitrage asymmetry, our short leg contributes 29% on average more to the total trade return than the long leg among pairs with high IVOL. In contrast, both legs’ contribution is on average equal among low IVOL stocks, which confirms the our research proposition.

We derive three further research propositions from financial and stochastic literature, which we confirm empirically: Firstly, up to 88% of SSD’s variation are explained by pair correla-tion (positive relationship) and pair volatility (negative relationship). Strictly speaking, the traditionally selected pairs with the lowest SSD are highly correlated with little volatility. High correlation and low volatility in turn affect the return per trade and the trading frequen-cy. Secondly, the 2σ-trading rule induces the following relationship: Highly volatile (less vol-atile) pairs and negatively (positively) correlated pairs increase (decrease) the return per trade. Thirdly, low pair volatility and high pair correlation during the identification period, coupled with higher volatility and lower correlation during the trading period, increase the number of trades. Consistent with the theory of mean-reverting volatility, pair volatility increases are more likely for pairs with currently low volatility. Likewise, correlation declines are more likely for highly correlated pairs. Combining these insights, we get the following big picture: The influence of high volatility and negative correlation is positive for the return per trade on the one hand, but at the same time negative for the trading frequency on the other hand. We expect a monotonically increasing return for higher IVOL levels based on the arbitrage risk argument. However, the negative effects of high volatility on the trading frequency and strong correlation on the return per trade reduce the returns for highly volatile and highly correlated stock pairs. In a perfect world, without the influence of the trading rule, we would probably see a linear IVOL effect in pairs trading."

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