Original paper
Abstract
This paper compares the performance of three enhanced momentum strategies proposed in the literature: constant volatility-scaled momentum, constant semi-volatility-scaled momentum, and dynamic-scaled momentum. Using data for individual stocks from the U.S. and across 48 international countries, we find that all three approaches decrease momentum crashes and lead to higher risk-adjusted returns. However, in multiple factor comparison tests, no enhanced momentum strategy emerges as consistently superior. Finally, cross-country analyses relate momentum and the two constant volatility-scaled momentum returns to market dynamics, whereas dynamic-scaled momentum is significantly less affected, suggesting a reduced sensitivity to time-varying investor overconfidence.
Keywords:Â Anomalies, Asset pricing, Momentum, International stock markets
Trading rules
- Target assets: Stocks from NYSE, AMEX, and NASDAQ that have a market capitalization surpassing the 20th percentile of NYSE stocks (considered large capitalization).
- Determine monthly return beyond the risk-free rate for every stock.
- Apply CAPM analysis for each stock utilizing a 3-year dataset (use market factor from Kenneth French's data collection as the determining variable).
- Compute idiosyncratic momentum: cumulative idiosyncratic return (residuals from regression) over 11-month period (month t-12 to month t-2).
- Organize stocks into five categories according to their individual momentum.
- Go long on the stocks in the highest category and short-sell those in the lowest category.
- Equally weighted portfolio.
- Adjust the portfolio's composition each month.
Python code
Backtrader
import backtrader as bt
import pandas as pd
import numpy as np
import statsmodels.api as sm
from scipy.stats import percentileofscore
class IdiosyncraticMomentum(bt.Strategy):
params = dict(
momentum_period=11,
rebalance_interval=21
)
def __init__(self):
self.rf_rate = 0.02 # risk-free rate (assuming 2% annual rate)
self.rebalance_days = 0
def next(self):
if self.rebalance_days % self.params.rebalance_interval == 0:
self.rebalance_portfolio()
self.rebalance_days += 1
def rebalance_portfolio(self):
market_caps = {d: d.market_cap[0] for d in self.datas}
large_cap_threshold = np.percentile(list(market_caps.values()), 80)
large_cap_stocks = [d for d, cap in market_caps.items() if cap > large_cap_threshold]
excess_returns = {}
for d in large_cap_stocks:
adj_close = d.close_adj
monthly_return = (adj_close[0] - adj_close[-21]) / adj_close[-21]
excess_return = (monthly_return - (1 + self.rf_rate) ** (1/12) + 1) - 1
excess_returns[d] = excess_return
capm_regressions = {}
for d in large_cap_stocks:
excess_returns_stock = excess_returns[d].get(size=-36) # 3 years of data
excess_returns_market = d.market_factor.get(size=-36)
excess_returns_market = sm.add_constant(excess_returns_market)
model = sm.OLS(excess_returns_stock, excess_returns_market).fit()
residuals = model.resid
capm_regressions[d] = residuals
idiosyncratic_momentum = {}
for d in large_cap_stocks:
cum_idiosyncratic_return = np.sum(capm_regressions[d][-11])
idiosyncratic_momentum[d] = cum_idiosyncratic_return
sorted_stocks = sorted(large_cap_stocks, key=lambda x: idiosyncratic_momentum[x], reverse=True)
long_stocks = sorted_stocks[:len(sorted_stocks) // 5]
short_stocks = sorted_stocks[-len(sorted_stocks) // 5:]
for d in self.datas:
if d in long_stocks:
target_value = self.broker.getvalue() / len(long_stocks)
size = target_value / d.close[0]
self.order_target_size(target=d, size=size)
elif d in short_stocks:
target_value = -self.broker.getvalue() / len(short_stocks)
size = target_value / d.close[0]
self.order_target_size(target=d, size=size)
else:
self.order_target_size(target=d, size=0)
if __name__ == '__main__':
cerebro = bt.Cerebro()
cerebro.addstrategy(IdiosyncraticMomentum)
cerebro.broker.setcash(100000.0)
cerebro.run()