# Is it possible to generate yield by using pair-trading on bonds with the cointegration method?

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In Finance, derivatives and arbitrage positions are two possible recourses for investors looking to increase their profit. The pair-trading is an alternative asset management method consisting on generating arbitrage opportunity between two assets having a similar evolution.

For a given asset A and asset B, having a correlated price movement, the Pair-Trading strategy consists on selling the asset A once it reaches its peak value and buying the asset B once it reaches its minimum value. Specifically, pair-trading matches a long and a short position of two different correlated assets. It allows a simple hedging strategy to benefit from arbitrage opportunity in both bullish (increase) or bearish (decrease) market. Numerous pair-trading strategies are available. For instance, we can analyze the moving average dissimilarity or the correlation evolution. In this study, we will focus on Bond Pair-Trading method using the cointegration method, introduced by Engle & Granger, and stress on the possible spread cointegrations on bonds.

The cointegration verifies the long-term relationship between two time series. The method consists, for two time series X𝑡and Y𝑡, to conduct an ordinary least-squares regression is made in order to determine the parameters α and β of the following equation:

We then test the residue stationarity with the Augmented Dickey-Fuller (ADF). If it is the case, we consider a cointegration between two time series spread and can profit from a short run divergence between two assets.

After simulating a pair-trade strategy on the bond market using the cointegration method regarding different scenarios and respecting given conditions (concerning the regression, the cointegration and the error level to determine the opportune moment to get into position) we notice that a 2-year difference in duration generates, in average, 3 more pair-trades compared to an increase of 50 bps the spread difference. We add 3 to 4 pair-trades with a duration difference of 2.5 years and 5 additional pair-trades for a 3-year duration while having an additional 5 bps for the spread difference. We conclude that increasing the spread difference or the duration difference poorly affects the number of pair-trades engendered.

By studying the performance of pair-trades after 1 month, 3 months and 6 months of investment, we find that 50% of pair-trades generate negative returns over the whole time covered. However, 45% of pair-trades generate performance after 1 month, 35% after 3 months and 30% after 6 months. We can terminate on the necessity to not hold a position for a long term.

By reckoning the maximum performance, we note that all pair-trades generate performance. Based on the different terms, between 55% and 70% of pair-trades generate a maximum return of 1%. The portion of pair-trades generating between 1% and 2% of return are steady: around 17% to 20%. However, from 1 month to 6 months, the portion of pair-trades generating over 2% of return goes from 30% to 45%. We can conclude that the most performing pair-trades require more time whereas the least performing pair-trades generate return swiftly. The pair-trade performances are represented by a curve with a J form.

When we consider transaction costs (at least 1%) it is impossible to outperform the bond market due to peer-trade yields. The bond market is an efficient market.