Original paper
Abstract
We investigate empirically the dependence of the size effect on the top performing stocks in a cross-section of risky assets separated by industry. We propose a test for a lottery-style factor payoff based on a stochastic utility model for an under-diversified investor. The associated conditional logit model is used to rank different investment portfolios based on size and we assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. Our results show that the size effect has a lottery-style payoff and is spurious for most industries once we remove the single best returning stock in an industry from the sample each month. Analysis in an asset pricing framework shows that standard asset pricing models fail to correctly specify the size premium on risky assets when industry winners are excluded from the construction of the size factor. Our findings have implications for stock picking, investment management and risk factor analysis.
Keywords:Â size effect, lottery, asset pricing, industry momentum, monotonicity tests, risk factors, ranked sorted portfolios
Trading rules
- Target assets: Stocks from the NYSE, AMEX, and NASDAQ.
- Organize stocks into five groups determined by their market value.
- Choose the group with the smallest market capitalization.
- Hold for one year.
- Rebalance portfolio annually.
Python code
Backtrader
import backtrader as bt
import datetime
class MarketCapStrategy(bt.Strategy):
params = (
('quintile', 5),
('rebalance_days', 252),
)
def __init__(self):
self.counter = 0
def next(self):
self.counter += 1
if self.counter % self.params.rebalance_days == 0:
self.rebalance_portfolio()
def rebalance_portfolio(self):
market_caps = []
for data in self.datas:
market_cap = data.close[0] * data.volume[0]
market_caps.append((data, market_cap))
sorted_data = sorted(market_caps, key=lambda x: x[1])
quintile_size = len(sorted_data) // self.params.quintile
lowest_quintile = sorted_data[:quintile_size]
# Calculate total market cap for lowest quintile
total_market_cap = sum([x[1] for x in lowest_quintile])
# Sell all current holdings
for data in self.datas:
self.order_target_percent(data, target=0)
# Buy stocks in lowest quintile
for data, market_cap in lowest_quintile:
target_weight = market_cap / total_market_cap
self.order_target_percent(data, target=target_weight)
if __name__ == '__main__':
cerebro = bt.Cerebro()
# Add investment universe
for ticker in ['NYSE_ticker1', 'NYSE_ticker2', 'AMEX_ticker1', 'NASDAQ_ticker1']:
data = bt.feeds.YahooFinanceData(
dataname=ticker,
fromdate=datetime.datetime(2015, 1, 1),
todate=datetime.datetime(2021, 9, 30),
adjclose=True,
plot=False,
)
cerebro.adddata(data)
cerebro.addstrategy(MarketCapStrategy)
cerebro.broker.setcash(100000.0)
cerebro.broker.setcommission(commission=0.001)
print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue())
cerebro.run()
print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue())