## New related paper to #12 - Pairs Trading with Stocks Wednesday, 8 April, 2015

**#12 - Pairs Trading with Stocks**

Authors: **Xie, Liew, Wu, Zou**

Title: **Pairs Trading with Copulas**

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2383185

Abstract:

Pairs trading is a well-acknowledged speculative investment strategy that is widely used in the financial markets, and distance method is the most commonly implemented pairs trading strategy by traders and hedge funds. However, this approach, which can be seen as a standard linear correlation analysis, is only able to fully describe the dependency structure between stocks under the assumption of multivariate normal returns. To overcome this limitation, we propose a new pairs trading strategy using copula modeling technique. Copula allows separate estimation of the marginal distributions of stock returns as well as their joint dependency structure. Thus, the proposed new strategy, which is based on the estimated optimal dependency structure and marginal distributions, can identify relative undervalued or overvalued positions with more accuracy and confidence. Hence, it is deemed to generate more trading opportunities and profits. A simple one-pair-one-cycle example is used to illustrate the advantages of the proposed method. Besides, a large sample analysis using the utility industry data is provided as well. The overall empirical results have verified that the proposed strategy can generate higher profits compared with the conventional distance method. We argue that the proposed trading strategy can be considered as a generalization of the conventional pairs trading strategy.

Notable quotations from the paper:

...

" Subsequently, Do and Faff (2010) tested the profitability of pairs trading using a more recent sample period from 1962 to 2009, and found a decreasing trend in the profitability of this simple trading strategy (0.33% mean excess return per month for 2003-09 versus 1.24% mean excess return per month for 1962-88). They identified two possible explanations for the decrease in profitability, which are the market efficient hypothesis and arbitrage risk hypothesis. This simple pairs trading strategy has been publicly known for decades and its implementation procedure is easy. Hence, the market efficient hypothesis infers that the market has become sufficiently efficient that it can no longer produce any excess returns."

"The pairs trading strategy adopted by the two papers mentioned earlier is also one of the most commonly applied methods, known as the distance method. This simple relative-value strategy has the advantage of ease in implementation, and its effectiveness during different time periods and different markets has been constantly documented (Andrada et al., 2005; Perlin, 2009; Pizzutilo, 2013). Normally, distance method is recognized as a model-free approach as it does not have explicit assumption about the distribution of stock returns. However, in this paper, we argue that the intrinsic set-up of this simple strategy may not be valid without assumption of multivariate normal returns, and this rigid assumption may not be aligned with current consensus.

As we know, modern portfolio theory is largely built on the assumption of multivariate normal returns. The popularity of multivariate normal assumption comes from two main aspects. Firstly, assuming a joint normal distribution implies that the individual margins as well as their linear combinations are all normally distributed. Secondly, it requires only one correlation measurement to fully describe the association between any two variables and this fact largely simplifies the models applied in risk management, portfolio diversification and hedging.

Although the multivariate normal nature is not clearly stated in the assumption of distance method, it does enjoy the simplicities which multivariate normal assumptions brings, mainly from two aspects. Firstly, it assumes symmetrical distribution of the spread between normalized prices of the two stocks within a pair. Secondly, it uses one single spread measurement, which can be seen as an alternative measurement of linear association, to describe entire associations between two stocks. These two simplicities, especially the latter one, may not be valid unless we assume stock returns are jointly normal distributed.

As such, distance method, which enjoys simplicities of multivariate normal assumption, may miss optimal trading opportunities due to loss of specifics about marginal distributions and joint dependency structure. The general concerns regarding this conventional trading strategy come from two aspects, which are exactly matched with the two simplicities it enjoys from multivariate normal assumption. Firstly, the distribution of the spread itself is less likely to be normal if the underlying joint distribution of stock returns is not bivariate normal. Then the symmetric assumption of the spread measurement implied by same trigger points at both sides may be violated. Secondly, it uses spread between the normalized prices of the two stocks as the only characteristic to measure the degree of mispricing. However, as mentioned before, this is only adequate under the assumption of multivariate normal returns. In other words, it is only such circumstance that one spread measurement is sufficient in describing the association between two stocks, as an alternative to linear association. Yet, it is a widely acknowledged fact that stock returns are rarely multivariate normal. Thus, the spread measurement in distance method may not fully capture the dependency structure between stocks, and potentially miss out crucial dependency information, especially those regarding non-linear associations, and such loss of information may result in undesirable trades. Considering the limitations present in the conventional distance method and its rigid assumptions, we believe that there can be improvements made to enhance the performance.

Note that we do recognize the abilities of the conventional strategy, and that it is still relevant for data with joint normal distributions. However, due to the rigid assumptions of the conventional strategy, there is a need for a more general and more powerful tool to accurately capture the marginal distributions as well as the dependency structure of stock pairs. In this paper, we propose to use the copula technique. "

"The main contributions of this paper are twofold. Firstly, a pairs trading strategy using copula technique that is further improved from past research is proposed. The proposed copula strategy can estimate marginal distributions of a stock pair and their joint dependency structure separately. Hence, it is able to capture more trading opportunities and profits. Distance method, which has been proved to be profitable in the literature, can be seen as a special case to the proposed approach under normal margins and normal copula. The second contribution of this paper is to provide a large sample analysis using utility industry data to verify the advantages of using copulas. This paper conducted our analysis based on Gatev et al. (2006) and followed the paper strictly in order to provide a meaningful comparison. Generally, the results have shown that our proposed method performs better than the conventional distance method. For example, the portfolio of top 5 pairs can generate up to 9.36% annualized excess return for the proposed method while the excess return is insignificant for distance method. "

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