Original paper

SSRN-id3177539.pdf817.9KB

Abstract

In the earliest days of empirical work in academic finance, the size effect was the first market anomaly to challenge the standard asset pricing model and prompt debates about market efficiency. The notion that small stocks have higher average returns than large stocks, even after risk-adjustment, was a pathbreaking discovery, one that for decades has been taken as an unwavering fact of financial markets. In practice, the discovery of the size effect fueled a crowd of small cap indices and active funds to a point where the investment landscape is now segmented into large and small stock universes. Despite its long and illustrious history in academia and its commonplace acceptance in practice, there is still confusion and debate about the size effect. We examine many claims about the size effect and aim to clarify some of the misunderstanding surrounding it by performing simple tests using publicly available data.

Keywords: Size, Size effect, Size anomaly, Small Cap, Microcap, Market efficiency, Illiquidity, January effect

Trading rules

Scope of investment: Stocks from NYSE, AMEX, and NASDAQ.
Segment portfolios into five groups by market size.
Select the bottom 20%, considering market capitalization.
Hold for a 12-month period.
Adjust the portfolio once every year.

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())

Fact, Fiction, and the Size Effect

Original paper

Abstract

Trading rules

Python code

Backtrader