Original paper

SSRN-id3220825.pdf1021.9KB

Abstract

Size and value premia comove strongly with one another at low frequencies, but they are both negatively related to long-run movements in the equity premium. We explain these patterns in an investment-based asset pricing model featuring persistent micro and macro uncertainty. Micro uncertainty generates size and value premia waves, while macroeconomic uncertainty produces equity premium waves. The negative correlation between micro and macro uncertainty at low frequencies explains why the equity premium is a long-term hedge for size and value premia. Persistent micro uncertainty is also a source of instability for size and value factors in short samples.

Keywords: Production-based asset pricing, Neoclassical Investment, Long-run risks, Cross-section of returns, Micro uncertainty, TFP

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())

Micro Uncertainty and Asset Prices

Original paper

Abstract

Trading rules

Python code

Backtrader