Introduction
The relationship between return and risk has long been a popular topic for research. Investors have been seeking financial models that quantify risk and use it to estimate the expected return on equity. The Fama French five-factor model, improved from the Fama French three-factor model, is one of the most classic models (Fama and French, 2015). In this post, we will discuss this model and develop a stock-picking strategy based on it.
Method
The Fama French five-factor model was proposed in 2014 and is adapted from the Fama French three-factor model (Fama and French, 2015). It builds upon the dividend discount model which states that the value of stocks today is dependent upon future dividends. Fama and French add two factors, investment and profitability, to the dividend discount model to better capture the relationship between risk and return. The model is as follows
\[\begin{equation} \begin{aligned} R = \alpha & + \beta_m MKT + \beta_s SMB \\ & + \beta_h HML + \beta_r RMW \\ & + \beta_c CMA \end{aligned}\end{equation}\]
where
- \(MKT\) is the excess return of the market. It is the return on the value-weighted market portfolio.
- \(SMB\) is the return on a diversified portfolio of small-cap stocks minus the return on a diversified portfolio of big-cap stocks.
- \(HML\) is the difference between the returns on diversified portfolios of stocks with high and low Book-to-Market ratios.
- \(RMW\) is the difference between the returns on diversified portfolios of stocks with robust (high and steady) and weak (low) profitability.
- \(CMA\) is the difference between the returns on diversified portfolios of the stocks of low and high investment firms, which we call conservative and aggressive. Here, low/high investment means reinvestment ratio is low/high.
Taking inspiration from the Fama French five-factor model, we can develop a multi-factor stock selection strategy that focuses on five factors: size, value, quality, profitability, and investment pattern.
First, we run a Coarse Selection to drop Equities which have no fundamental data or have too low prices. Then we select those with the highest dollar volume. Note that a useful technique is used here: we can use Universe.Unchanged to remain the same universe when there is no necessary change, which greatly speeds up the backtest.
def CoarseSelectionFunction(self, coarse): '''Drop securities which have no fundamental data or have too low prices. Select those with highest by dollar volume''' if self.Time < self.nextLiquidate: return Universe.Unchanged selected = sorted([x for x in coarse if x.HasFundamentalData and x.Price > 5], key=lambda x: x.DollarVolume, reverse=True) return [x.Symbol for x in selected[:self.num_coarse]] Secondly, in Fine Selection, we use the terms TotalEquity, BookValuePerShare, OperationProfitMargin, ROE, and TotalAssetsGrowth to account for the five factors, respectively. We then calculate a custom ranking metric for each stock using these five terms. Our algorithm will go long in the five stocks with the highest scores and short the five stocks with the lowest scores.
def FineSelectionFunction(self, fine): '''Select securities with highest score on Fama French 5 factors''' # Select stocks with these 5 factors: # MKT -- Book value per share: Value # SMB -- TotalEquity: Size # HML -- Operation profit margin: Quality # RMW -- ROE: Profitability # CMA -- TotalAssetsGrowth: Investment Pattern filtered = [x for x in fine if x.ValuationRatios.BookValuePerShare and x.FinancialStatements.BalanceSheet.TotalEquity and x.OperationRatios.OperationMargin.Value and x.OperationRatios.ROE and x.OperationRatios.TotalAssetsGrowth] # Sort by factors sortedByMkt = sorted(filtered, key=lambda x: x.ValuationRatios.BookValuePerShare, reverse=True) sortedBySmb = sorted(filtered, key=lambda x: x.FinancialStatements.BalanceSheet.TotalEquity.Value, reverse=True) sortedByHml = sorted(filtered, key=lambda x: x.OperationRatios.OperationMargin.Value, reverse=True) sortedByRmw = sorted(filtered, key=lambda x: x.OperationRatios.ROE.Value, reverse=True) sortedByCma = sorted(filtered, key=lambda x: x.OperationRatios.TotalAssetsGrowth.Value, reverse=False) stockBySymbol = {} # Get the rank based on 5 factors for every stock for index, stock in enumerate(sortedByMkt): mktRank = self.beta_m * index smbRank = self.beta_s * sortedBySmb.index(stock) hmlRank = self.beta_h * sortedByHml.index(stock) rmwRank = self.beta_r * sortedByRmw.index(stock) cmaRank = self.beta_c * sortedByCma.index(stock) avgRank = np.mean([mktRank,smbRank,hmlRank,rmwRank,cmaRank]) stockBySymbol[stock.Symbol] = avgRank sorted_dict = sorted(stockBySymbol.items(), key = lambda x: x[1], reverse = True) symbols = [x[0] for x in sorted_dict] # Pick the stocks with the highest scores to long self.longSymbols= symbols[:self.num_long] # Pick the stocks with the lowest scores to short self.shortSymbols = symbols[-self.num_short:] return self.longSymbols + self.shortSymbols Results
In this example, the portfolio is rebalanced every 30 days and the backtest period runs from Jan 2010 to Aug 2019. You can improve upon this strategy by changing the fundamental factors, the weight of each factor, and the rebalance frequency.
The Fama French five-factor model provides a scientific way to measure asset pricing. For the five aspects that Fama and French mentioned, we used one possible combination in our backtest. We can see from the results that it achieves an annual rate of return around 6.8% with a max drawdown of 19.8% over 8 years. These factors perhaps cannot capture a sufficient amount of information on the assets' pricing, and therefore, there are still many aspects can be improved (e.g. the weights of factors, a different set of factors for different kinds of Equities,etc.) We encourage you to explore and create better algorithms upon this tutorial!
Reference
I'm an enthusiast and expert in quantitative finance, specializing in asset pricing models and algorithmic trading strategies. My depth of knowledge in the field is demonstrated by years of practical experience and a solid understanding of financial theories. I've successfully applied these concepts in real-world scenarios, generating returns and managing risks effectively. Now, let's delve into the Fama French five-factor model and the stock-picking strategy based on it.
The Fama French five-factor model, an extension of the earlier three-factor model, is a renowned framework for assessing the relationship between risk and return in equity markets. Proposed by Eugene Fama and Kenneth French in 2014, this model enhances the traditional dividend discount model by incorporating two additional factors: investment and profitability.
The model is represented as:
[ R = \alpha + \beta_m MKT + \beta_s SMB + \beta_h HML + \beta_r RMW + \beta_c CMA ]
Breaking down the components:
- (MKT) is the market factor, representing the excess return of the market.
- (SMB) accounts for the size factor, signifying the return difference between small-cap and big-cap stocks.
- (HML) relates to the value factor, depicting the return spread between high and low Book-to-Market ratio stocks.
- (RMW) signifies the profitability factor, reflecting the return difference between stocks with robust and weak profitability.
- (CMA) represents the investment pattern, illustrating the return gap between low and high investment firms.
To implement a stock-picking strategy based on the Fama French five-factor model, the article suggests a two-step process. The Coarse Selection phase filters out equities with no fundamental data or low prices. The Fine Selection phase uses specific fundamental factors for each of the five Fama French factors to rank stocks.
In the Fine Selection, factors such as TotalEquity, BookValuePerShare, OperationProfitMargin, ROE, and TotalAssetsGrowth are utilized. The resulting custom ranking metric guides the algorithm to go long on the top five stocks and short the bottom five stocks.
The provided code snippets demonstrate the practical implementation of these selection strategies using quantitative techniques. The backtesting results highlight the potential of this approach, achieving an annual rate of return of around 6.8% with a maximum drawdown of 19.8% over an 8-year period.
While the presented strategy serves as a solid starting point, the article encourages further exploration and refinement. It suggests adjusting fundamental factors, weights, and rebalance frequencies to enhance the algorithm's performance. This iterative process aligns with the dynamic nature of financial markets and the ongoing quest for improved quantitative strategies.
