The strategy selects liquid NYSE and AMEX stocks, combining momentum and investment-to-assets ratios, going long on high-momentum, low-investment stocks, short on low-momentum, high-investment stocks, and rebalancing semiannually.
ASSET CLASS: stocks | REGION: United States | FREQUENCY:
6 Months | MARKET: equities | KEYWORD: Investment, Momentum
I. STRATEGY IN A NUTSHELL
Trades NYSE and AMEX stocks above $5 with low bid-ask spreads, combining six-month momentum and investment-to-assets (I/A) ratios. Long positions are taken in high-momentum, low-investment stocks, and short positions in low-momentum, high-investment stocks, held for six months and rebalanced semiannually.
II. ECONOMIC RATIONALE
Combining momentum and investment factors exploits behavioral biases and market inefficiencies, producing stronger, more persistent returns than either factor alone, particularly in liquid stocks with low trading costs.
III. SOURCE PAPER
Investment-Momentum: A Two-Dimensional Behavioral Strategy [Click to Open PDF]
Xu, Fangming; Zhao, Huainan; Zheng, Liyi — University of Bristol; Loughborough University – School of Business and Economics; University of Bristol.
<Abstract>
We propose an investment-momentum strategy of buying past winners with low investment and selling past losers with high investment, which exploits simultaneously two dimensions of market inefficiencies. The new strategy generates twice the monthly returns earned by either the price momentum or investment strategy (1.44% vs. 0.75% or 0.61%) for 1965-2015. Despite of the diminishing anomalies in recent decades, the investment-momentum stays persistent. The mispricing-based strategy performs better in periods of high investor sentiment or for stocks with high limits-to-arbitrage, which is consistent with our expectation. Overall, we show that, in addition to “fundamentals” enhanced momentum strategies, one can simultaneously condition on multi-dimension of inefficiencies to attain superior performance.
IV. BACKTEST PERFORMANCE
| Annualised Return | 8.99% |
| Volatility | 11.66% |
| Beta | -0.121 |
| Sharpe Ratio | 0.77 |
| Sortino Ratio | 0.059 |
| Maximum Drawdown | N/A |
| Win Rate | 49% |
V. FULL PYTHON CODE
from AlgorithmImports import *
from pandas.core.frame import dataframe
from numpy import isnan
class InvestmentMomentumStrategy(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
self.SetSecurityInitializer(lambda x: x.SetMarketPrice(self.GetLastKnownPrice(x)))
market:Symbol = self.AddEquity("SPY", Resolution.Daily).Symbol
self.long:List[Symbol] = []
self.short:List[Symbol] = []
self.data:Dict[Symbol, SymbolData] = {}
self.period:int = 6 * 21
self.leverage:int = 5
self.quantile:int = 5
self.fundamental_count:int = 500
self.fundamental_sorting_key = lambda x: x.DollarVolume
self.months:int = 0
self.selection_flag = True
self.UniverseSettings.Resolution = Resolution.Daily
self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
self.AddUniverse(self.FundamentalSelectionFunction)
self.Schedule.On(self.DateRules.MonthEnd(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]:
# Update the rolling window every day.
for stock in fundamental:
symbol:Symbol = stock.Symbol
# Store monthly price.
if symbol in self.data:
self.data[symbol].update_price(stock.AdjustedPrice)
if not self.selection_flag:
return Universe.Unchanged
selected:List[Fundamental] = [x for x in fundamental if x.HasFundamentalData and x.Market == 'usa' and \
not isnan(x.FinancialStatements.BalanceSheet.GrossPPE.TwelveMonths) and x.FinancialStatements.BalanceSheet.GrossPPE.TwelveMonths != 0 and \
not isnan(x.FinancialStatements.BalanceSheet.Inventory.TwelveMonths) and x.FinancialStatements.BalanceSheet.Inventory.TwelveMonths != 0 and \
not isnan(x.FinancialStatements.BalanceSheet.TangibleBookValue.ThreeMonths) and x.FinancialStatements.BalanceSheet.TangibleBookValue.ThreeMonths != 0
]
if len(selected) > self.fundamental_count:
selected = [x for x in sorted(selected, key=self.fundamental_sorting_key, reverse=True)[:self.fundamental_count]]
selected_symbols:List[Symbol] = [x.Symbol for x in selected]
momentum:Dict[Symbol, float] = {}
ia_ratio:Dict[Symbol, float] = {}
# Warmup price rolling windows.
for stock in selected:
symbol:Symbol = stock.Symbol
if symbol not in self.data:
self.data[symbol] = SymbolData(self.period)
history:dataframe = self.History(symbol, self.period, Resolution.Daily)
if history.empty:
self.Log(f"Not enough data for {symbol} yet.")
continue
closes:pd.Series = history.loc[symbol].close
for time, close in closes.items():
self.data[symbol].update_price(close)
if self.data[symbol].is_ready():
momentum[symbol] = self.data[symbol].performance()
ppe:float = stock.FinancialStatements.BalanceSheet.GrossPPE.TwelveMonths
inv:float = stock.FinancialStatements.BalanceSheet.Inventory.TwelveMonths
book_value:float = stock.FinancialStatements.BalanceSheet.TangibleBookValue.ThreeMonths
if self.data[symbol]._inventory == 0 or self.data[symbol]._PPE == 0 or self.data[symbol]._book_value == 0:
self.data[symbol].update_data(ppe, inv, book_value)
continue
ppe_change:float = ppe - self.data[symbol]._PPE
inv_change:float = inv - self.data[symbol]._inventory
# IA calc
ia_ratio[symbol] = (ppe_change + inv_change) / book_value
self.data[symbol].update_data(ppe, inv, book_value)
# Reset not updated symbols.
for symbol in self.data:
if symbol not in selected_symbols:
self.data[symbol].update_data(0,0,0)
if len(momentum) >= self.quantile:
# Momentum sorting
sorted_by_mom:List[Symbol] = sorted(momentum, key = momentum.get, reverse = True)
quantile:int = int(len(sorted_by_mom) / self.quantile)
high_by_mom:List[Symbol] = sorted_by_mom[:quantile]
low_by_mom:List[Symbol] = sorted_by_mom[-quantile:]
# IA sorting
sorted_by_ia:List[Symbol] = sorted(ia_ratio, key = ia_ratio.get, reverse = True)
quantile = int(len(sorted_by_ia) / self.quantile)
high_by_ia:List[Symbol] = sorted_by_ia[:quantile]
low_by_ia:List[Symbol] = sorted_by_ia[-quantile:]
self.long = [x for x in high_by_mom if x in low_by_ia]
self.short = [x for x in low_by_mom if x in high_by_ia]
return self.long + self.short
def OnData(self, data: Slice) -> None:
if not self.selection_flag:
return
self.selection_flag = False
# order execution
targets:List[PortfolioTarget] = []
for i, portfolio in enumerate([self.long, self.short]):
for symbol in portfolio:
if symbol in data and data[symbol]:
targets.append(PortfolioTarget(symbol, ((-1) ** i) / len(portfolio)))
self.SetHoldings(targets, True)
self.long.clear()
self.short.clear()
def Selection(self) -> None:
if self.months == 0 or self.months == 5:
self.selection_flag = True
self.months += 1
if self.months == 6:
self.months = 0
class SymbolData():
def __init__(self, period:int):
self._price:RollingWindow = RollingWindow[float](period)
self._PPE:float = 0.
self._inventory:float = 0.
self._book_value:float = 0.
def update_data(self, ppe:float, inv:float, book_value:float) -> None:
self._PPE = ppe
self._inventory = inv
self._book_value = book_value
def update_price(self, price:float) -> None:
self._price.Add(price)
def is_ready(self) -> bool:
return self._price.IsReady
def performance(self, values_to_skip = 0) -> float:
return self._price[values_to_skip] / self._price[self._price.Count - 1] - 1
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))VI. Backtest Performance
