Original paper
Abstract
Do past alphas predict future country and industry returns? Examination of equity indexes from 51 stock markets between 1973 and 2018 allows us to demonstrate new return patterns in the cross-section of country and industry returns. Past short-term (long-term) alphas positively (negatively) predict future returns. These phenomena can be translated into effective international equity allocation strategies, producing economically and statistically significant raw and risk-adjusted returns. The profitability is robust to many considerations, including alternative alpha models, the effect of trading costs, different holding periods, or subsample and subperiod analyses. Also, the alpha momentum and reversal subsume their return-based counterparts. Finally, the alpha-based patterns are particularly pronounced following bull markets and across the markets characterized by high arbitrage constraints, supporting the behavioral explanation of the anomalies.
Keywords:Â alpha momentum, alpha reversal, international investment, country momentum, country reversal, industry momentum, industry reversal, asset pricing, the cross-section of returns return predictability, equity anomalies
Trading rules
- Targeted investment universe: Focus on 51 country indices.
- Compute alphas: Employ the basic CAPM framework.
- Alpha score calculation: Adjust alphas by considering return variability (eg. standard deviation).
- Alpha momentum assessment (for month t): Use volatility-adjusted alpha from months t-12 to t-1.
- Index prioritization: Organize indices using the alpha score.
- Portfolio orientation: Take bullish positions on the top quintile and bearish positions on the bottom quintile.
- Investment approach: Value or equally weighted, rebalancing on a monthly cadence.
Python code
Backtrader
import backtrader as bt
class AlphaMomentum(bt.Strategy):
params = (
('lookback', 12),
)
def __init__(self):
self.alphas = {}
self.market_rets = {}
self.scores = {}
def next(self):
# Compute alphas and returns for each index
for d in self.getdatanames():
data = self.getdatabyname(d)
# Compute returns and alphas using simple CAPM model
market_ret = data.close[0] / data.close[-1] - 1
self.market_rets[d] = market_ret
alpha = market_ret - (self._owner.broker.getvalue() / self._owner.broker.startingcash - 1)
self.alphas[d] = alpha
# Calculate alpha score
alpha_vol = bt.indicators.StdDev(self.alphas[d], period=self.params.lookback)
self.scores[d] = alpha / alpha_vol
# Determine alpha momentum and rank indexes
sorted_indexes = sorted(self.scores, key=self.scores.get, reverse=True)
top_quintile = sorted_indexes[:len(sorted_indexes) // 5]
bottom_quintile = sorted_indexes[-(len(sorted_indexes) // 5):]
# Positioning: Long highest quintile, short lowest quintile
for d in self.getdatanames():
data = self.getdatabyname(d)
position_size = self.broker.getvalue() / (len(top_quintile) + len(bottom_quintile))
if d in top_quintile:
self.order_target_value(data, target=position_size)
elif d in bottom_quintile:
self.order_target_value(data, target=-position_size)
else:
self.order_target_value(data, target=0)
# Rebalance monthly
self.notify_timer(when=bt.Timer.SESSION_END)
if __name__ == '__main__':
cerebro = bt.Cerebro()
# Add investment universe
for index in range(51):
data = bt.feeds.GenericCSVData(dataname=f'index_{index}.csv')
cerebro.adddata(data, name=f'index_{index}')
# Add strategy
cerebro.addstrategy(AlphaMomentum)
# Set initial cash and run backtest
cerebro.broker.set_cash(100000)
cerebro.run()Please note that this is a simplified example of the trading rules provided, and you may need to adjust the code to fit your specific data and requirements. Additionally, the code assumes you have separate CSV files for each of the 51 country indexes.