Tags: almost stochastic dominance, momentum strategies, asset pricing, EGRIE
More from: Mi-Hsiu Chiang, Hsin-Yu Chiu, Rachel J Huang

In this paper, momentum returns are strategically derived. Using utility-based Almost Stochastic Dominance (ASD) rules — capable of comprising full moment conditions of the cumulative returns, we derive winner-minus-loser return differences that are less volatile and less negatively skewed relative to those of Jegadeesh and Titman (1993). This is a benefit by design to capitalize on momentum, and not by coincidence. These abnormal returns are statistically and economically significant. Most importantly, we see to the strategy’s practical applicability by resolving the computational complexity often involved in the actual implementation of these selection rules in the stochastic dominance family. The computational costs are being effectively reduced.

In doing so, we join many attempts in the literature to examine investment decision making in an expected utility paradigm, and in particular, those who exploit the ASD rules to capitalize on several well-documented stock market anomalies (Bali, Demirtas, Levy, and Wolf (2009); Bali, Brown, and Demirtas (2013)). To the best of our knowledge, our study is the first in the literature to exploit the ASD ranking relations in order to generate abnormal stock returns.

The momentum effect is critically dependent on past information. Clark and Kassimatis (2014) construct their momentum strategies based on the classic stochastic dominance (SD) rules (Hadar and Russell, 1969; Rothschild and Stiglitz, 1970; Whitmore, 1970). By adopting second-degree SD and third-degree SD to select winning and losing stocks, Clark and Kassimatis (2014) show that past SD relations indeed provide exploitable information on future returns and the positive returns are robust when tested against the modern factor models.

In spite of the positive findings of Clark and Kassimatis (2014), the SD rules are too restrictive in a way that, in order to meet all utility functions (including the pathological ones), they may fail to rank distributions when most decision makers obviously prefer one alternative to another (Leshno and Levy, 2002). The rigidity of the SD rules and the required computationally-intensive methodology may limit the strategy’s applications in practice.

Our paper refines Clark and Kassimatis (2014) in two ways. First, this study strategically applies the utility-based ASD approaches proposed by Leshno and Levy (2002) and Tzeng, Huang and Shih (2013) to select winners and losers in the construction of momentum strategies. ASD allows for violations of the SD rules by eliminating pathological agents. The ASD rules seek the consensus of almost all investors — all non-pathological, economically important agents — and can thus significantly improve the SD rules’ ability to rank. Our paper adopts both the almost first-degree SD (AFSD) rule and the almost second-degree SD (ASSD) rule as the winner-loser selection criteria to implement the momentum strategy.

Second, applying the ASD rules to capitalize on momentum involves a critical stage of sorting among assets which could give rise to a computational burden if it were to proceed with pairwise comparisons as in Clark and Kassimatis (2014). To resolve the computational issue, we propose ranking stocks according to their ASD “violation ratios” with respect to the return on a risk-free asset — the foregone opportunity cost of an investment. To be specific, for the AFSD rule, we calculate each stock’s AFSD violation ratio which denotes, roughly speaking, the area violating first-degree stochastic dominance (FSD) divided by the total differences between the cumulative density functions (CDFs) of the returns of the stock and a risk-free asset. The AFSD rule also concludes that the smaller that the violation ratio of a stock is, the more that non-pathological and non-satiable investors would prefer the evaluated stock to the risk-free asset and we would conclude that the better the stock is. Thus, we could group stocks according to the violation ratios and identify winners (losers) as the stocks with the smallest (greatest) violation ratios by avoiding pairwise comparisons.

For the ASSD rule, two parameters are adopted. The first one is the mean return and the second one is another violation ratio, which denotes, roughly speaking, the area violating second-degree stochastic dominance (SSD) divided by the total differences between two CDFs. According to ASSD, it is necessary for the dominant portfolio to have a greater mean. Thus, if the mean return of the evaluated stock is less than the risk-free rate, then this evaluated stock 4 cannot be identified as a winner even if the violation ratio is small. By comparing mean returns and the new violation ratios, stocks could be efficiently labelled as winners or losers.

Our main findings are markedly supportive of our hypothesis. For the AFSD momentum strategies, the standard deviation, skewness and maximum drawdown of arbitrage returns are all small in absolute terms, indicating a less “volatile” return distribution — as a consequence of risk reduction — than the standard momentum strategy of Jegadeesh and Titman (1993). In addition, when equipped with overlapping holding periods of longer duration, the AFSD momentum strategies deliver arbitrage returns that exhibit a higher average monthly return, smaller standard deviation, smaller maximum drawdown, and a better risk-adjusted performance — under all chosen measures of reward-to-risk — than the standard momentum strategy. This result indicates that the AFSD momentum strategy is capable of generating abnormal stock returns. For the ASSD momentum strategies, the results are even more pronounced. The ASSD momentum strategies outperform both the AFSD and the standard momentum strategies in terms of the average monthly returns and the risk-adjusted performance — with the resulting return distributions being slightly more volatile and exhibiting a higher maximum drawdown than the standard momentum strategy. Above all, we find that these AFSD and ASSD arbitrage returns cannot be explained by the Fama-French (2015) five factors, the momentum factor, the liquidity risk factor, or the short-term and long-term reversal.

The complete paper is available at:
https://www.vwrm.rw.fau.de/egrie-2018/conference-programme/.