Strategy assessment

Rasmus Bruun Jørgensen, AEF Empirical results

for the SMB, HML and the momentum factors. Only the momentum factor could pro-vide some epro-vidence on the distance method. The lack of explanatory power, in general, of these factors, indicates that there must exist a number of other factors that can explain the alpha values generated. However, it must be taken into consideration that the sample period examined in the paper consists of periods of fundamental different market conditions, for which it can be difficult to obtain a linear relationship between a factor and our returns.

Even though it is not measurable to the same extent as the factor models, the VIX index and the subsequent leverage effect provide some explanation for our findings about profiting from anomalies throughout the paper. The leverage effect could also explain the statistically significant correlation with the market for some triggers; when the market drops, the leverage effect is set in play, thus increasing the volatility. This generally produces more inefficiencies in the market, which is the foundation for re-turns of the pairs trading strategy applied. As such, it might not necessarily be the direct relationship to the return of the market or the market volatility that explains the returns of this paper, but rather the interconnection between these market factors which explain the underlying mechanisms of profiting from anomalies in the market.

the reason to be the pairs composition of the distance method that favour ETFs track-ing the same index.

A consequence of the reliance on pairs comprising ETFs tracking the same index is that the pairs require a larger divergence in order to generate a positive net profit. To this, the above analysis shows that 38% of all traded spots do not generate a gross profit large enough to withstand the costs of trading with a convergence equivalent to 3x standard deviations. This implies that the fundamental trading attributes of the distance method, when applied with ETFs, are not robust to the cost of trading. Fur-ther, we find that the period 2007-2010 creates all the profit and that the subsequent years unambiguously have imposed losses for the distance method. The problematic trading attributes mentioned above also come to light in the batting and slugging ra-tios, where the average “winning” percentage is below 30% for all triggers despite the positive results of the overall period. The high slugging ratio for the entire period is solely derived from the results of the first subperiod. The distance method generates a profit over the full period, but the robustness of this profit is not persistent. The fact that the profit of the method is generated in a short period of time, rather than over the course of the entire period makes it hard to rely on the method as a general trading strategy.

The lack of robustness is also present in the application of the factor models. Here, we find the distance method to generate a statistically significant alpha for all triggers before transaction costs but none after accounting for these. The factor models further reveal that the method has a statistically significant relation to the movements in the market, but no significant alpha. All in all, we cannot conclude that applying the dis-tance method would yield any better results than applying the market portfolio.

The cointegration method | The cointegration method is the more complex method of the two, as it seeks to identify pairs exhibiting a statistically founded relationship during the formation period. Here, it is required that at least one of the ETFs explains the development of the other with the inclusion of a cointegration coefficient. By se-lecting the 20 traded pairs in this way, it is possible to identify more nuanced combi-nations of ETFs as the selection is based on an established long-run relationship. Nat-urally, two ETFs tracking the same index will thus also be selected under the

Rasmus Bruun Jørgensen, AEF Empirical results

cointegration method, but the reliance of these ETFs is much lower for this method than the distance method. The cointegration method's ability to identify more nuanced combinations of ETFs is expressed by its pair composition where only 46% of the traded pairs comprise ETFs both tracking a US-based large-cap indices, and no more than 35% tracks the same index. The consequences of the pairs composition is a much more robust and persistent method that performs well after transaction costs. The batting ratios of the triggers in the cointegration method throughout the subperiods remain high except for the last subperiod. This generates a high batting ratio across the full period. The persistent characteristics of the cointegration method is also revealed by the gross profit for the traded pairs to a great extent are robust to the costs of trading with a convergence equivalent to 3x standard deviations. It is however noticed that the associated gross profit of a convergence equivalent to 3x standard deviation has expe-rienced some variation in the second half of the overall sample period.

All in all, the cointegration method yields positive returns after transaction costs that both outperform the existing literature and the market portfolio for two out of six trig-ger settings. Despite 2009 and the last subperiod, the cointegration method has shown a strong performance. With this, the selected pairs of the cointegration approach have generally exhibited a high degree of cointegration and robustness to transaction costs.

This robustness of the return is also evident in by statistically significant alphas after transaction costs for all triggers except trigger 2/0.5. Besides the significant alpha, we find a statistically significant explanatory variable in the beta term for 2/0.5, 2.5/0 and 2.5/0.5 after transaction costs. By this, we do not find any explanation of the return generated for the cointegration method in the more classic factor variables. When re-gressing the returns of the cointegration method on the VIX index, we find a statisti-cally significant relation with a correlation of 20% for the 2 and 2.5 opening trigger and a lower correlation for the opening trigger of 3. This does not necessarily imply a causal relation, but there is a connection to the leverage effect that emerges from declining market prices.

We can thus conclude from the backtest of the two methods and triggers that the coin-tegration method exhibits superior performance to the distance method when applying pairs trading on ETFs throughout the sample period from 2007-2020. However, the

negative profit generated in the recent subperiod is worth keeping an eye on not be-coming a new normal for the cointegration method.