# Strategy Library

## Momentum Effect in Stocks in Small Portfolios

### Introduction

The main reason for the momentum anomaly is the behavioral biases of the investor like underreaction and confirmation bias. Momentum strategy usually uses portfolios filled by thousands of stocks to compute the momentum factor return. This is not possible for small retail investors with small portfolios. They are constrained compared to big hedge funds and cannot diversify so well. In this tutorial, we'll construct a small portfolio consisting of up to 50 stocks to check the effect of momentum.

### Method

The investment universe consists of all US listed companies. Stocks which have no fundamental data are ruled out from the universe.

def CoarseSelectionFunction(self, coarse): if self.yearly_rebalance: # drop stocks which have no fundamental data self.filtered_coarse = [x.Symbol for x in coarse if (x.HasFundamentalData)] return self.filtered_coarse else: return []

In `FineSelectionFunction`

, stocks with the lowest market capitalization (25% of the universe) are excluded due to low liquidity.
The momentum is defined as the stock market return over the previous 12 months. Momentum profits are calculated by ranking companies on the basis of yearly return.
The ranking period is one year.

def FineSelectionFunction(self, fine): if self.yearly_rebalance: # Calculate the yearly return and market cap for i in fine: i.MarketCap = float(i.EarningReports.BasicAverageShares.ThreeMonths * (i.EarningReports.BasicEPS.TwelveMonths*i.ValuationRatios.PERatio)) top_market_cap = sorted(fine, key = lambda x:x.MarketCap, reverse=True)[:int(len(fine)*0.75)] has_return = [] for i in top_market_cap: history = self.History([i.Symbol], timedelta(days=365), Resolution.Daily) if not history.empty: close = history.loc[str(i.Symbol)]['close'] i.returns = (close[0]-close[-1])/close[-1] has_return.append(i) sorted_by_return = sorted(has_return, key = lambda x: x.returns) self.long = [i.Symbol for i in sorted_by_return[-10:]] self.short = [i.Symbol for i in sorted_by_return[:10]] return self.long+self.short else: return []

The investor goes long in the ten stocks with the highest performance and goes short in the ten stocks with the lowest performance. The portfolio is equally weighted and rebalanced yearly.

def OnData(self, data): if not self.yearly_rebalance: return if self.long and self.short: stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested] # liquidate stocks not in the trading list for i in stocks_invested: if i not in self.long+self.short: self.Liquidate(i) for i in self.short: self.SetHoldings(i, -0.5/len(self.short)) for i in self.long: self.SetHoldings(i, 0.5/len(self.long)) self.long = None self.short = None self.yearly_rebalance = False

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