Momentum Trading with the ℓ1‐Filter: Are the Markets Efficient?*

• Date: 01 December 2020
• Author: Abhishek Rohit,Subrata K. Mitra
• DOI: http://doi.org/10.1111/irfi.12245
• Published date: 01 December 2020

Momentum Trading with the ℓ

1

-

Filter: Are the Markets Efficient?*

SUBRATA K. MITRA

†

AND ABHISHEK ROHIT

‡

†

Department of Finance, Indian Institute of Management Raipur, Raipur, India and

‡

Department of Finance & Strategy, T A Pai Management Institute, Manipal, India

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 iden-

tifies 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 effi-

cient financial markets of the AEs provide lower opportunities for momen-

tum 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 turn-

ing point, we further find that considerable opportunity exists for momen-

tum 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 risk-

aversiveness.

Accepted: 17 October 2018

I. INTRODUCTION

Technical analysis strategies based on the trend in asset prices have been inves-

tigated extensively by researchers in the last two decades. The trend component

of equity indices represents the global factors or common factors that influence

a large number of stocks to co-move in a particular direction. The deviations

from the trend, that is, noise, represent the idiosyncratic component and do

not offer any meaningful information for technical analysis strategies. In accor-

dance with the efficient market hypothesis (EMH) (Fama 1965, 1970), current

* We are thankful to the managing editor, Prof. Sudipto Dasgupta and the anonymous referee for

extremely helpful comments and suggestions. The study benefitted considerably from their expert

insights and valuable feedbacks. Any unintended errors or omissions are our own doing. This

research did not receive any specific grant from funding agencies in the public, commercial, or not-

for-profit sectors.

© 2018 International Review of Finance Ltd. 2018

International Review of Finance, 20:4, 2020: pp. 827–856

DOI: 10.1111/irfi.12245

prices in the financial markets accurately reflect all of the known information

directly or indirectly related to an asset. Moreover, any adjustment to incoming

information is rapid and complete. Thus, in addition to the current and past

information, current prices are also expected to reflect future expectations. As a

consequence, only new and unknown information can affect equity prices, and

since it is unknown, the prediction of equity prices is futile. Hence, there

should be no scope to earn abnormal profits.

The EMH provides an explanation for the supposedly random walk behavior

of equity prices. Even the weak form of EMH rejects the notion of profiting via

technical analysis. However, many academic studies have empirically demon-

strated the inefficiencies existing in the financial markets using technical strate-

gies. Momentum is one of the three important anomalies discussed in the

literature, the other two being size and value. Numerous studies have

highlighted the existence of momentum anomaly in various asset classes and

have explained it using behavioral models. Persistence of momentum anomaly

can be exploited by the traders to generate cumulative positive returns. This is

done by continuing a chain of trades via buying low and selling high when the

trend is rising (long positions) and selling high and buying low when the trend

is declining (short positions).

This paper is quite closely related to the recent research work on the use

of technical trading rules in generating abnormal returns. Ample evidence

has been forwarded that highlights the profitability of such rules, (e.g., Brock

et al. 1992; Frankel and Froot 1986; Lo et al. 2002; Neftci 1991). Brock

et al. (1992) use moving average and trading range break on Dow Jones

Industrial Average (DJIA) from 1897 to 1986 and report support for technical

trading strategies. They also find strong evidence for higher returns generated

by the buy strategy in comparison to the sell strategy. Critically analyzing

their study, Hudson et al. (1996) argue that the returns generated using such

strategies fade away when they are adjusted for transaction costs. In a similar

study, Mills (1998) suggests that the effectiveness of technical trading rules,

as compared to the buy and hold (BH) strategy, has faded in recent years.

Jegadeesh and Titman (2001) (JT) present support for the profitability of the

momentum strategy based on past winners and past losers for a holding

period of 3–12 months.

The efficacy of such strategies spans a range of asset classes and is not limited

only to equity returns. Moskowitz et al. (2012) highlight significant time-series

momentum in a total of 58 instruments including equity indices, currencies,

commodities, and bond futures. According to them, the momentum effect

based on excess returns in the past 12 months persists for 1–12 months. Vari-

ous techniques have been explored to identify the momentum anomaly in the

previous studies. Most of the studies (e.g., Faber 2007; Glabadanidis 2014,

2015, 2017; Han et al. 2013; Kilgallen 2012) have primarily focused on the

moving average technique. Other techniques that have been implemented in

the empirical literature to a lesser extent include the high-frequency trading

scalping strategy (Manahov 2016), the technical pattern recognition model

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