*5.2. Sub-Period Analysis*

Motivated by the time-varying returns of Liu et al. (2017) and Stübinger and Knoll (2018), we analyzed the stability and potential of the strategies over time. Figure 4, therefore, presents the development of an investment of USD 1 after transaction costs for FTS, GVS, RVS, JDS (first column), and the S&P 500 buy-and-hold strategy BHS (second column) over three partial periods. Table A2 provides a detailed overview of the corresponding annualized risk-return ratios for sub-periods of three years.

The first sub-period ran from 1998–2006 and described the bursting of the Internet bubble and the start of the Iraq war, as well as the subsequent bull market. We observed meaningful differences in performance between the mean-reverting and non-mean-reverting strategies: the average annual returns after transaction costs of up to 73.76 percent for RVS and up to 64.08 percent for JDS were well above those of BHS (7.87 percent), FTS (27.31 percent), and GVS (42.26 percent). As a typical feature in the financial context, the baseline methods were nevertheless successful in this period due to market inefficiencies and a lack of transparency.

The second sub-period ranged from 2007–2009 and was characterized by the global financial crisis and its consequences. In the course of the sub-prime crisis, the overall market showed strong fluctuations and substantial declines. In contrast, the other strategies generated positive returns, ranging from 27.35 percent for FTS to 315.02 percent for JDS. This strong performance was not astonishing as Avellaneda and Lee (2010) and Rad et al. (2016) demonstrated that statistical arbitrage trading strategies achieved abnormal returns during bear markets.

The third sub-period extends from 2010–2015 and covered a period of comebacks and restarts. The benchmarks FTS and GVS showed declining trends compared to the overall market, caused by the increasing public availability of these methods. RVS achieved an almost constant cumulative return of one, i.e., this strategy generated exactly the costs that were incurred. For JDS, we observed that 1 USD invested in January 2010 grew to 5 USD after transaction costs; performance did not decline across time and seemed to be robust against drawdowns.
