Original paper

SSRN-id3275366.pdf1041.3KB

Abstract

In this paper, I will review the size effect, potential reasons why one observes the size effect, and correct common misconceptions and address criticisms of the Size Premia (SP). Throughout this paper, I will show that using a pure market factor as the sole risk factor in estimating the expected return provide an incomplete estimate. For the last four decades, research have shown that adjustments to the CAPM are required. I will address some of the criticism to the theoretical basis of the SP and to the application adopted through the CRSP Decile Size Premia and Risk Premium Report - Size Study. Specifically, I demonstrate that the size premium critique by Clifford Ang is not warranted and that the alternative methodology proposed by that author is misleading and cannot be considered as an alternative to the Duff & Phelps’ SP. The methodology the author is proposing picks up statistical errors that he was set to avoid by proposing a variation of Duff and Phelps’ methodology. Finally, I will provide some practical guidance on efficiently and correctly applying SP.

Keywords: size effect, CAPM, cost of capital

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())

The Size Effect Continues to be Relevant When Estimating the Cost of Capital

Original paper

Abstract

Trading rules

Python code

Backtrader