*5.1. Risk-Return Characteristics*

Table 3 shows the daily return characteristics and risk metrics before and after transaction costs for the top 10 stocks per strategy from January 1998–December 2015. We observed statistically-significant returns for FTS, GVS, RVS, and JDS with Newey–West (NW) *t*-statistics above 15 prior to transaction costs. From an economical point of view, daily returns ranged between 0.17 percent for FTS and 0.36 percent for JDS. If we considered transaction costs, only the mean-reverting strategies RVS and JDS produced positively significant daily returns of 0.13 percent (RVS) and 0.17 percent (JDS). As

expected, BHS generated statistically non-significant returns of 0.02 percent per day (see Endres and Stübinger (2019b)). The range, i.e., the difference of the maximum and minimum, was vastly different for JDS (approximately 0.30 percentage points), compared to BHS, FTS, GVS, and RVS (approximately 0.15 percentage points); this dissimilarity is potentially driven by the jump-diffusion term. The same argumen<sup>t</sup> explains the increased standard deviation of JDS. All individual strategy variants depicted favorable characteristics for any potential investor due to the fact that the underlying returns showed right skewness and followed a leptokurtic distribution (Cont 2001). We found that the maximum drawdown was quite different for FTS (87.84 percent) and GVS (89.47 percent), in contrast to RVS (55.91 percent), BHS (64.33 percent), and JDS (68.17 percent); the difference between non-reverting and reverting top stocks is clearly pointed out. The hit rate of JDS, i.e., the percentage of days with non-negative returns, outperformed with 58.41 percent after transactions costs, compared to the benchmarks, ranging between 41.79 percent for FTS and 55.92 percent for RVS.

**Table 3.** Daily return characteristics and risk metrics for BHS, FTS, GVS, RVS, and JDS from January 1998–December 2015. NW denotes Newey–West standard errors with 1-lag correction and CVaR the conditional value at risk.


In Table 4, we depict annualized risk-return measures before transaction costs (left side) and after transaction costs (right side). After transaction costs, JDS produced returns of 51.47 percent p.a., compared to 38.85 percent for RVS, −4.07 percent for GVS, and −6.59 percent for FTS. Thus, the first two strategies achieved meaningfully better results than the naive buy-and-hold strategy (BHS) with an average return of 1.81 percent p.a. Across all strategies, the mean excess return was similar to the mean return because the risk-free rate was very close to zero, especially in the last years. Our jump-based strategy JDS generated approximately the standard deviation of the market, resulting in a Sharpe ratio of 2.38 after transaction costs. This value confirmed the results of the high-frequency studies of Knoll et al. (2018) and Stübinger (2018). The lower partial moment risk of JDS led to a Sortino ratio of 4.76, compared to the benchmarks ranging between −1.03 (FTS) and 4.67 (RVS). We summarized that JDS outperformed the classic approaches in a large number of comparisons; complexity pays off. Our task was still to evaluate the performance over time, as well as the robustness of the strategies.


**Table 4.** Annualized risk-return measures for BHS, FTS, GVS, RVS, and JDS from January 1998–December 2015.
