Momentum Trading with theℓ₁‐Filter: Are the Markets Efficient?*

Abstract

This paper explores the possibility of generating consistent momentum profits by trading on nine major indices across the globe using the ℓ 1-filter. This methodology penalizes slope reversion of the filtered trend and identifies piecewise linear trends in the asset prices. We find the buy strategy to offer considerably higher momentum returns compared to the sell strategy. Our strategy beats the buy-and-hold (BH) strategy on all fronts and, thus, highlights the inefficiencies in financial markets in recent years (2000-2016). Comparing the momentum profits across a set of advanced economies (AEs) and emerging market economies (EMEs), we find that the developed and efficient financial markets of the AEs provide lower opportunities for momentum profits. The momentum profits are more than double in the EMEs as compared to the AEs. Highlighting the instability of the momentum strategy in different market states by using the global financial crisis (GFC) as a turning point, we further find that considerable opportunity exists for momentum strategies in the bullish runs that precede the crisis, as happened before the GFC. However, the momentum profits reduce significantly as the crisis sets in, increasing the degree of market uncertainty, fear, and riskaversiveness.

$$\ell _{1}$$ Common Trend Filtering

“…1 Figure 1 illustrates a continuous piecewise linear trend. The filter and its variants have been subsequently applied in various fields, including astronomy (Politsch et al 2020), climatology (Khodadadi and McDonald 2019), economics (Yamada and Jin 2013;Yamada and Yoon 2014;Winkelried 2016;Yamada 2017;Klein 2018), electronics (Suo et al 2019), environmental science (Brantley et al 2019), finance (Mitra and Rohit 2018), and geophysics (Wu et al 2018).…”