Original paper
Abstract
Motivated by the time-series insights of Daniel and Moskowitz (2016), we investigate the link between expected skewness and momentum in the cross-section. The alpha of skewness-enhanced (-weakened) momentum is about twice (half) as large as the traditional alpha. These findings are driven by the short leg. Portfolio sorts, Fama-MacBeth regressions, and the market reaction to earnings announcements suggest that expected skewness is an important determinant of momentum. Due to the simplicity of the approach, its economic magnitude, its existence among large stocks, and the success of risk management, the results are difficult to reconcile with the efficient market hypothesis.
Keywords:Â Momentum, skewness, market efficiency, return predictability, behavioral finance
Trading rules
- Selection criteria: Stocks from NYSE/AMEX/NASDAQ valued over $5 and having a market cap higher than 50% of the NYSE.
- Measure of skewness: Highest daily gain during the previous month.
- Monthly sorting method:
- Organize stocks into five groups based on projected skewness (peak daily gain).
- Within those groups, sort stocks further into quintiles depending on their cumulative returns from the last year.
- Defining momentum: Use a year-long formation duration, hold for a month, and skip for one month.
- Procedure for monthly portfolio setup:
- For long positions: Pick from the winners with the strongest negative skew.
- For short positions: Pick from the losers with the most significant positive skew.
- Equally weighted.
- Rebalanced monthly.
Python code
Backtrader
Here is the Backtrader python code for the given trading rules:
import backtrader as bt
import pandas as pd
import numpy as np
class SkewMomentumStrategy(bt.Strategy):
params = (
('formation_period', 12),
('holding_period', 1),
('skip_period', 1),
('min_price', 5),
('capitalization_percentile', 0.5),
)
def __init__(self):
self.inds = {}
for d in self.datas:
self.inds[d] = {}
self.inds[d]['max_return'] = bt.indicators.Highest(d.close(-1) / d.close(-2), period=21)
self.inds[d]['momentum'] = d.close / d.close(-self.p.formation_period) - 1
def prenext(self):
self.next()
def next(self):
if self._count % (self.p.holding_period + self.p.skip_period) != 0:
return
stocks = self.datas
stocks = [d for d in stocks if d.close[0] > self.p.min_price]
market_caps = np.array([d.market_cap[0] for d in stocks])
threshold = np.percentile(market_caps, self.p.capitalization_percentile * 100)
stocks = [d for d, mc in zip(stocks, market_caps) if mc >= threshold]
skews = np.array([self.inds[d]['max_return'][0] for d in stocks])
momentum = np.array([self.inds[d]['momentum'][0] for d in stocks])
skew_quintiles = pd.qcut(skews, 5, labels=False)
momentum_quintiles = pd.qcut(momentum, 5, labels=False)
long_candidates = [d for d, sq, mq in zip(stocks, skew_quintiles, momentum_quintiles) if sq == 0 and mq == 4]
short_candidates = [d for d, sq, mq in zip(stocks, skew_quintiles, momentum_quintiles) if sq == 4 and mq == 0]
long_weight = 1.0 / len(long_candidates) if long_candidates else 0
short_weight = -1.0 / len(short_candidates) if short_candidates else 0
for d in long_candidates:
self.order_target_percent(d, target=long_weight)
for d in short_candidates:
self.order_target_percent(d, target=short_weight)
for d in set(self.datas) - set(long_candidates + short_candidates):
self.order_target_percent(d, target=0)This code defines a SkewMomentumStrategy class that implements the trading rules. The strategy calculates skewness proxies and past momentum for each stock, sorts them into quintiles, and constructs a long-short portfolio according to the specified criteria. The positions are equally weighted and rebalanced monthly.