Original paper
Abstract
A five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than the three-factor model of Fama and French (FF 1993). The five-factor model’s main problem is its failure to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. The model’s performance is not sensitive to the way its factors are defined. With the addition of profitability and investment factors, the value factor of the FF three-factor model becomes redundant for describing average returns in the sample we examine.
Trading rules
- Eligible Stocks: Stocks listed on NYSE, Amex, and NASDAQ.
- Stock categorization:
- Sort stocks into five groups based on Size (from Small to Big) utilizing NYSE market capitalization markers as of each year-end June.
- Independently sort stocks into five Investment (Inv) categories (ranging from Low to High) according to NYSE criteria.
- Form 25 distinct portfolios by intersecting the Size and Inv categories.
- Investment metric:
- For portfolios set in June of year t, determine Inv by assessing the rise in total assets from the fiscal year closing in t-1 against the total assets at the culmination of t-1.
- Positions to adopt:
- Long: Opt for the portfolio characterized by the largest Size but the most modest Investment.
- Short: Target the portfolio marked by the largest Size and the most significant Investment.
- Portfolio distribution strategy:
- Adopt a value-weighted approach for portfolios.
Python code
Backtrader
import backtrader as bt
class SizeInvStrategy(bt.Strategy):
def __init__(self):
self.market_caps = {}
self.total_assets = {}
self.investments = {}
def next(self):
# Check if June
if self.datetime.date().month != 6:
return
# Allocate stocks to Size and Investment groups
self.market_caps.clear()
self.total_assets.clear()
self.investments.clear()
for data in self.datas:
symbol = data._name
self.market_caps[symbol] = data.market_cap[0]
self.total_assets[symbol] = data.total_assets[0]
self.investments[symbol] = (data.total_assets[0] - data.total_assets[-252]) / data.total_assets[-252]
size_sorted = sorted(self.market_caps.items(), key=lambda x: x[1])
inv_sorted = sorted(self.investments.items(), key=lambda x: x[1])
size_groups = [size_sorted[i::5] for i in range(5)]
inv_groups = [inv_sorted[i::5] for i in range(5)]
# Find long and short positions
long_position = size_groups[-1][0]
short_position = size_groups[-1][-1]
# Close existing positions
for data in self.datas:
if self.getposition(data).size > 0:
self.sell(data)
elif self.getposition(data).size < 0:
self.buy(data)
# Open new long and short positions
self.buy(data=self.getdatabyname(long_position), target=0.5)
self.sell(data=self.getdatabyname(short_position), target=0.5)
# Load data, set up cerebro, and run the strategy
cerebro = bt.Cerebro()
# Add your data feed here using the 'cerebro.adddata()' method
cerebro.addstrategy(SizeInvStrategy)
results = cerebro.run()Please note that this code assumes the availability of custom data fields like market_cap and total_assets in the data feed. You would need to create a custom data feed class in Backtrader that includes these fields for the code to work correctly.