Low-Price Effect
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Strategy in a nutshell
Investment universe: NYSE-listed stocks with above-median market capitalization.
Data sources: CRSP (monthly return data) and Compustat (accounting data).
Portfolio formation:
Each month, stocks are sorted into deciles by split-adjusted price.
The portfolio is long the lowest-price decile and short the highest-price decile.
Positions are value-weighted by market capitalization.
Rebalancing: Monthly, based on updated stock prices.
Economic rationale
A stock’s price equals its expected returns multiplied by a discount factor, implying a link between expected returns and price.
Since realized returns are positively correlated with expected returns, lower split-adjusted prices should correspond to higher future realized returns.
Therefore, buying low-priced stocks and shorting high-priced stocks exploits the negative relationship between price level and future returns, producing the low-price anomaly effect.
Backtest performance
Full Python code
from AlgorithmImports import *
class LowPriceEffect(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
market:Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
self.weight:Dict[Symbol, float] = {}
self.fundamental_count:int = 500
self.fundamental_sorting_key = lambda x: x.DollarVolume
self.quantile:int = 10
self.leverage:int = 5
self.selection_flag:bool = False
self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse(self.FundamentalSelectionFunction)
self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
self.Schedule.On(self.DateRules.MonthStart(market), self.TimeRules.AfterMarketOpen(market), self.Selection)
self.settings.daily_precise_end_time = False
def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
for security in changes.AddedSecurities:
security.SetFeeModel(CustomFeeModel())
security.SetLeverage(self.leverage)
def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
if not self.selection_flag:
return Universe.Unchanged
selected:List[Fundamental] = [x for x in fundamental if x.HasFundamentalData and x.Market == 'usa' and x.SecurityReference.ExchangeId == "NYS" and x.MarketCap != 0]
if len(selected) > self.fundamental_count:
selected = [x for x in sorted(selected, key=self.fundamental_sorting_key, reverse=True)[:self.fundamental_count]]
long:List[Fundamental] = []
short:List[Fundamental] = []
# Store stock adjusted price.
price:Dict[Fundamental, float] = { x : x.AdjustedPrice for x in selected }
if len(price) >= self.quantile:
sorted_by_price:List[Fundamental] = sorted(price, key = price.get, reverse = True)
quantile:int = int(len(sorted_by_price) / self.quantile)
long = sorted_by_price[-quantile:]
short = sorted_by_price[:quantile]
# Market cap weighting.
for i, portfolio in enumerate([long, short]):
mc_sum:float = sum(map(lambda x: x.MarketCap, portfolio))
for stock in portfolio:
self.weight[stock.Symbol] = ((-1) ** i) * stock.MarketCap / mc_sum
return list(self.weight.keys())
def OnData(self, data: Slice) -> None:
if not self.selection_flag:
return
self.selection_flag = False
# Trade execution.
portfolio:List[PortfolioTarget] = [PortfolioTarget(symbol, w) for symbol, w in self.weight.items() if symbol in data and data[symbol]]
self.SetHoldings(portfolio, True)
self.weight.clear()
def Selection(self) -> None:
self.selection_flag = True
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))