What Is High Minus Low (HML)?
High Minus Low (HML) is a factor in factor investing that captures the excess returns of value stocks over growth stocks. It is a key component of the Fama-French three-factor model, a prominent example within asset pricing models. HML represents the return difference between portfolios of stocks with high book-to-market ratios (value stocks) and stocks with low book-to-market ratios (growth stocks). The underlying premise of the HML factor is that value stocks, often considered undervalued by the market due to various reasons, tend to outperform growth stocks over the long term. This phenomenon, known as the "value premium," is a central tenet explored in quantitative finance and portfolio management.
History and Origin
The High Minus Low (HML) factor was introduced by Nobel laureate Eugene Fama and Kenneth French in their seminal 1992 paper, "The Cross-Section of Expected Stock Returns." This groundbreaking research expanded upon the traditional Capital Asset Pricing Model (CAPM) by identifying additional factors beyond market risk that explain stock returns. Prior to their work, the CAPM primarily accounted for a stock's sensitivity to the overall market. However, Fama and French observed that certain characteristics, such as a company's size and its book-to-market ratio, appeared to explain variations in stock returns that the CAPM could not. Their development of the three-factor model, which includes the HML factor alongside a size factor (Small Minus Big or SMB) and the market risk premium, significantly advanced the understanding of equity pricing. The research highlighted that while the CAPM explained about 70% of diversified portfolio returns, the Fama-French three-factor model explained over 90% of such returns. The data used to construct these factors are publicly available through Kenneth French's Data Library, which provides comprehensive historical financial data for academic and research purposes.7
Key Takeaways
- High Minus Low (HML) is a factor in asset pricing models representing the return difference between value and growth stocks.
- Value stocks typically have high book-to-market ratios, while growth stocks have low ones.
- The HML factor is a core component of the Fama-French three-factor model, explaining the "value premium."
- Historically, value stocks have shown a tendency to outperform growth stocks over long periods, though this is not guaranteed.
- Understanding HML helps investors and researchers analyze the sources of investment returns beyond overall market exposure.
Formula and Calculation
The High Minus Low (HML) factor is constructed by taking the difference in returns between a portfolio of high book-to-market ratio stocks (value stocks) and a portfolio of low book-to-market ratio stocks (growth stocks). To calculate HML, stocks are typically sorted based on their book-to-market ratios, often independently of their market capitalization (size).
The general approach involves:
- Sorting Stocks: All stocks are sorted into two or more groups based on their book-to-market ratios. For example, three groups might be formed: "Value" (high B/M), "Neutral" (medium B/M), and "Growth" (low B/M).
- Forming Portfolios: Value-weighted portfolios are constructed for the "Value" and "Growth" groups.
- Calculating HML: The return of the "Value" portfolio is subtracted from the return of the "Growth" portfolio.
The formula for the Fama-French three-factor model, which incorporates HML, is:
Where:
- ( R_{it} ) = The expected return of stock i at time t
- ( R_{ft} ) = The risk-free rate of return at time t
- ( R_{it} - R_{ft} ) = The excess return of stock i over the risk-free rate
- ( \alpha_i ) = The asset's alpha, representing the excess return not explained by the model's factors
- ( R_{Mt} - R_{ft} ) = The market risk premium, or the excess return of the market portfolio over the risk-free rate at time t
- ( \text{SMB}_t ) = Small Minus Big, the size factor at time t (return of small-cap portfolio minus return of large-cap portfolio)
- ( \text{HML}_t ) = High Minus Low, the value factor at time t
- ( \beta_1, \beta_2, \beta_3 ) = The coefficients (sensitivities) of the respective factors
- ( \epsilon_{it} ) = The residual error term
The HML factor itself represents the excess return of value firms relative to growth firms.
Interpreting the HML
Interpreting the High Minus Low (HML) factor involves understanding its role in explaining asset returns and its implications for investment strategy. A positive HML coefficient (( \beta_3 )) in a regression analysis indicates that a portfolio or stock has a tilt towards value, meaning its returns tend to move in the same direction as the value premium. Conversely, a negative HML coefficient suggests a tilt towards growth.
Historically, HML has been positive, indicating that value stocks have, on average, outperformed growth stocks over extended periods. This "value premium" suggests that investors may be compensated for holding stocks that are perceived as riskier or less attractive than growth stocks, or that are temporarily undervalued by the market. Therefore, a portfolio with a significant positive exposure to HML would have benefited from this historical premium. The strength and consistency of the value premium, however, have been subjects of ongoing debate among financial academics and practitioners.
Hypothetical Example
Consider an investor, Sarah, who is analyzing the historical returns of two hypothetical mutual funds: Fund V (Value-focused) and Fund G (Growth-focused). Sarah uses the Fama-French three-factor model to understand the sources of their returns, specifically focusing on the High Minus Low (HML) factor.
Over a certain period, let's assume the following hypothetical monthly returns for the factors and the funds:
- Risk-Free Rate (( R_f )): 0.05%
- Market Excess Return (( R_M - R_f )): 0.50%
- Small Minus Big (SMB): 0.20% (indicating small-cap outperformance)
- High Minus Low (HML): 0.30% (indicating value outperformance)