Backtest Period
1950-2010
Markets Traded
Equities
Maximum Drawdown
-83%
Period of Rebalancing
Yearly
Return (Annual)
12.4%
Sharpe Ratio
0.28
Standard Deviation (Annual)
20%
Original paper
SSRN-id2477293.pdf274.1KB
Abstract
The active shares of traditional value style indices are dominated by industry bets. They also capture less than the entire value premium because, weighting constituents on the basis of capitalization, they tend to hold large positions in overpriced stocks and small positions in underpriced (i.e., value) stocks. Smart beta strategies, in comparison, are better diversified, and they systematically buy low and sell high by periodically rebalancing to non-price related target weights. In addition to exploiting mean reversion in prices, smart beta strategies profit from mean reversion in the value premium by effectively implementing a dollar cost averaging program.
Keywords: Value Index, Smart Beta, Value Strategies
Trading rules
- Focus on the largest quintile (top 20%) of firms (by market value) from NYSE, AMEX, and NASDAQ.
- Create five portfolios using the Book-to-Market ratio as a criterion.
- Highest quintile based on Book-to-Market ratio is held for a 12-month period.
- Portfolio is weighted based on market capitalization.
- Refresh the portfolio composition annually.
Python code
Backtrader
# assume universe_df has columns ['asset', 'marketcap', 'exchange', 'book_to_market']
# include necessary imports
import backtrader as bt
import pandas as pd
class Top20HighestMarketCap(bt.Algo):
def __init__(self, universe_df):
self.top20 = universe_df.sort_values('marketcap', ascending=False)[:int(len(universe_df)*0.2)]['asset']
def __call__(self, target):
if target._name in self.top20:
return True
else:
return False
class BookToMarketQuintilePortfolio(bt.Algo):
def __init__(self, universe_df):
self.quintiles = universe_df.groupby('exchange')['book_to_market'].transform(lambda x: pd.qcut(x, 5, labels=False))
def __call__(self, target):
if target.book_to_market >= 4: # highest quintile
return True
else:
return False
class MarketCapWeighted(bt.Algo):
def __init__(self, universe_df):
self.weights = universe_df['marketcap']/universe_df['marketcap'].sum()
def __call__(self, target):
return self.weights[target._name]
# assume cerebro has been created and data has already been added
universe_df = pd.DataFrame({'asset': [d._name for d in cerebro.datas],
'marketcap': [d.lines[0][-1] for d in cerebro.datas],
'exchange': [d._name.split('-')[0] for d in cerebro.datas],
'book_to_market': [d.lines[1][-1] for d in cerebro.datas]})
cerebro.addanalyzer(bt.analyzers.TimeReturn, timeframe=bt.TimeFrame.Years)
cerebro.addsizer(MarketCapWeighted(universe_df))
cerebro.addstrategy(bt.Strategy)
cerebro.broker.setcommission(commission=0.001)
cerebro.broker.setcash(100000)
# define trading rules
cerebro.addanalyzer(bt.analyzers.TimeReturn, timeframe=bt.TimeFrame.Years, _name='TimeReturn_1yr')
cerebro.addanalyzer(bt.analyzers.SharpeRatio_Annual, timeframe=bt.TimeFrame.Years, _name='SharpeRatio_1yr')
cerebro.addanalyzer(bt.analyzers.DrawDown, _name='DrawDown')
cerebro.addanalyzer(bt.analyzers.Returns, _name='Returns')
cerebro.addanalyzer(bt.analyzers.Transactions, _name='Transactions')
cerebro.addobserver(bt.observers.Value)
cerebro.addobserver(bt.observers.DrawDown)
cerebro.addanalyzer(bt.analyzers.AnnualReturn, timeframe=bt.TimeFrame.Years)
cerebro.addanalyzer(bt.analyzers.Calmar, timeframe=bt.TimeFrame.Years)
cerebro.addanalyzer(bt.analyzers.PositionsValue, _name='PositionsValue')
# define which stocks to select based on market cap
cerebro.addfi(Top20HighestMarketCap(universe_df))
# define quintile strategies
cerebro.addfi(BookToMarketQuintilePortfolio(universe_df))
# run backtest
cerebro.run()
# print out analysis results
print('Annual Return:', cerebro.analyzers.getbyname('AnnualReturn').get_analysis())
print('Drawdown:', cerebro.analyzers.getbyname('Drawdown').get_analysis())
print('Sharpe Ratio:', cerebro.analyzers.getbyname('SharpeRatio_Annual').get_analysis())
print('Calmar Ratio:', cerebro.analyzers.getbyname('Calmar').get_analysis())