Original paper
Abstract
We provide a new methodology to empirically investigate the respective roles of systematic and idiosyncratic skewness in explaining expected stock returns. Using a large number of predictors, we forecast the cross-sectional ranks of systematic and idiosyncratic skewness which are easier to predict than their actual values. Compared to other measures of ex ante systematic skewness, our forecasts create a significant spread in ex post systematic skewness. A predicted systematic skewness risk factor carries a significant risk premium that ranges from 6% to 12% per year and is robust to the inclusion of downside beta, size, value, momentum, profitability, and investment factors. In contrast to systematic skewness, the role of idiosyncratic skewness in pricing stocks is less robust. Finally, we document how the determinants of systematic and idiosyncratic skewness differ.
Keywords:Â Systematic skewness, coskewness, idiosyncratic skewness, large panel regression, forecasting
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.