High minus low hml

What Is High Minus Low (HML)?

High Minus Low (HML) is a core component within asset pricing models, particularly the renowned Fama-French three-factor model. It quantifies the historical tendency for value stocks to outperform growth stocks. Essentially, HML represents the difference in returns between portfolios of companies with high book-to-market ratio and those with low book-to-market ratios.

This factor is often referred to as the "value premium," suggesting that investors are compensated with higher returns for holding stocks that are perceived as undervalued relative to their assets, rather than those whose prices are driven by high future growth expectations¹⁶. High Minus Low (HML) helps explain variations in stock returns that are not captured by traditional measures of market risk, such as the Capital Asset Pricing Model (CAPM)'s beta.

History and Origin

The concept of High Minus Low (HML) gained prominence through the seminal work of economists Eugene Fama and Kenneth French. In their groundbreaking 1992 paper, "The Cross-Section of Expected Stock Returns," Fama and French challenged the prevailing view that market beta alone could explain average stock returns. They empirically demonstrated that two additional company characteristics—size (measured by market capitalization) and book-to-market equity—played a significant role in explaining the cross-section of returns.

T¹⁵his research led to the development of the Fama-French three-factor model, which integrated HML as a key factor alongside the market risk premium and the size factor (Small Minus Big, or SMB). Their findings provided a robust framework for understanding and modeling stock returns beyond what CAPM could explain, solidifying HML's place in modern portfolio management and academic finance. Da¹⁴ta for the HML factor, along with other Fama-French factors, is publicly available through Kenneth French's Data Library at Dartmouth College, updated regularly to reflect ongoing market data.

#¹³# Key Takeaways

• High Minus Low (HML) measures the historical outperformance of value stocks over growth stocks.
• It is a critical component of the Fama-French three-factor model, explaining returns beyond market risk.
• A positive HML indicates that value stocks have outperformed growth stocks during a given period.
• HML is calculated based on the difference in returns between portfolios sorted by book-to-market ratio.
• The persistence of the value premium, captured by HML, is a subject of ongoing academic and practitioner debate.

Formula and Calculation

The High Minus Low (HML) factor is constructed by taking the difference in returns between portfolios of high book-to-market (value) stocks and low book-to-market (growth) stocks. The general approach involves sorting stocks into portfolios based on their book-to-market ratios.

Specifically, Kenneth French's data library, widely used in academic and professional analysis, typically constructs the HML factor as follows:

Where:

• Small Value: The average return of portfolios containing small market capitalization stocks with high book-to-market ratios.
• Big Value: The average return of portfolios containing large market capitalization stocks with high book-to-market ratios.
• Small Growth: The average return of portfolios containing small market capitalization stocks with low book-to-market ratios.
• Big Growth: The average return of portfolios containing large market capitalization stocks with low book-to-market ratios.

This calculation involves categorizing stocks annually based on their size and book-to-market equity, forming portfolios, and then calculating the value-weighted returns of these portfolios. Th¹²e book-to-market ratio itself is typically calculated as shareholders' equity (book value) from a company's balance sheet divided by its market capitalization.

#¹¹# Interpreting the HML

Interpreting the High Minus Low (HML) factor provides insight into the performance of value strategies relative to growth strategies. A positive HML value for a given period indicates that value stocks, characterized by higher book-to-market ratios, have collectively outperformed growth stocks, which have lower book-to-market ratios. Conversely, a negative HML suggests that growth stocks have delivered higher returns than value stocks during that period.

Investors and analysts use the HML factor as a proxy for exposure to the value risk premium. If a portfolio exhibits a positive beta coefficient to HML in a linear regression analysis, it implies that the portfolio's returns are positively correlated with the performance of value stocks. This suggests the portfolio benefits when value stocks outperform growth stocks. A negative HML beta, however, would indicate a tilt towards growth stocks, meaning the portfolio tends to perform better when growth stocks lead the market. Understanding this relationship helps in evaluating a portfolio's underlying characteristics and its sensitivity to different market styles.

Hypothetical Example

Consider an investor, Sarah, who is evaluating the performance of her diversified equity portfolio over the past year. She uses the Fama-French three-factor model to understand the sources of her portfolio's returns. After performing a linear regression analysis, she finds her portfolio has a positive beta coefficient of 0.35 to the High Minus Low (HML) factor for the last year.

Let's assume the HML factor return for the past year was +2.5%. This means that, on average, a diversified portfolio of value stocks outperformed a diversified portfolio of growth stocks by 2.5% over that period. Sarah's portfolio, with its HML beta of 0.35, gained an additional (0.35 * 2.5%) = 0.875% of its return specifically attributable to its exposure to the value premium. This indicates that her portfolio benefited from the outperformance of value stocks during the year. If the HML factor had been negative, say -3.0%, her portfolio would have seen a drag of (0.35 * -3.0%) = -1.05% due to its value tilt, assuming all else equal. This example illustrates how the HML factor quantifies a portfolio's sensitivity to the relative performance of value stocks versus growth stocks.

Practical Applications

High Minus Low (HML) is a vital tool with several practical applications in finance and investing, particularly within the realm of factor investing:

• Performance Attribution: HML allows investors and analysts to dissect portfolio returns and attribute them to specific factors. By regressing a portfolio's excess returns against the HML factor (among others), managers can determine how much of their performance is due to their exposure to value or growth stocks. This helps differentiate between genuine management skill (alpha) and returns explained by known risk factors.
• Portfolio Construction: Investors aiming to capture the value risk premium can intentionally tilt their portfolios towards value stocks. Understanding HML's historical behavior can inform these strategic allocations. Fund managers may design portfolios or exchange-traded funds (ETFs) that specifically target a positive HML exposure, sometimes called "value tilts".
• ¹⁰ Academic Research and Asset Pricing: HML continues to be a cornerstone in academic finance for testing asset pricing models and exploring market anomalies. Researchers use HML, often sourced from the Kenneth R. French Data Library, to study the drivers of expected returns across various markets and asset classes. Th⁹e academic community constantly evaluates and expands upon these factor models, as discussed in various academic papers and research insights.

#⁸# Limitations and Criticisms

While High Minus Low (HML) is a widely accepted factor in asset pricing and factor investing, it faces several limitations and criticisms:

• Definition of Value: The reliance on book-to-market ratio as the sole measure of "value" is a point of contention. Some critics argue that this metric may not fully capture a company's true value, especially in an increasingly intangible-asset-driven economy. Ot⁷her metrics like earnings yield, price-to-cash flow, or enterprise value-to-EBITDA are also used to define value.
• ⁶ Varying Performance: The value premium, as captured by HML, has not been consistently positive over all periods. There have been extended periods where growth stocks have significantly outperformed value stocks, leading some to question whether the value factor is "dead" or merely undergoing a prolonged drawdown. Th⁵ese periods can test an investor's discipline.
• ⁴ Data Mining Concerns: Some critics argue that the discovery of factors like HML might be a result of "data mining" historical financial data to find patterns that may not persist in the future. While academic research strives to address these concerns by testing factors across various time periods, geographies, and asset classes, it remains a persistent debate.
• Practical Implementation Challenges: For individual investors, replicating the precise construction of the HML factor can be complex due to the need for extensive data and frequent portfolio rebalancing. While factor-tilted funds exist, their efficacy and true factor exposure can vary.

HML vs. Small Minus Big (SMB)

High Minus Low (HML) and Small Minus Big (SMB) are both key factors in the Fama-French three-factor model, designed to explain stock returns beyond market risk. While both are related to portfolio characteristics, they capture different dimensions of expected returns.

The primary confusion between HML and SMB often arises because they are introduced together as part of the Fama-French model. However, they address distinct characteristics of companies and their associated risk premium. HML focuses on the valuation aspect, while SMB focuses on company size.

FAQs

What does a positive HML value indicate?

A positive HML value means that value stocks (companies with high book-to-market ratios) have outperformed growth stocks (companies with low book-to-market ratios) over a specified period. This suggests the presence of a "value premium."

How does HML relate to the Fama-French model?

HML is one of the three original factors in the Fama-French three-factor model. This model expands on the Capital Asset Pricing Model (CAPM) by adding factors for size (Small Minus Big (SMB)) and value (HML) to better explain variations in stock returns.

#³## Can HML be used for active investment strategies?

Yes, HML is often used by investors who employ factor investing strategies. By understanding a portfolio's sensitivity to HML, investors can intentionally tilt their holdings towards value stocks if they believe the value premium will persist or revert. Ho²wever, capturing factor premiums effectively requires discipline and a long-term perspective.

Is the value premium, represented by HML, still relevant today?

The relevance and persistence of the value premium are subjects of ongoing debate in financial economics. While historical data shows a long-term value premium, there have been significant periods where value stocks underperformed. Ma¹ny researchers and practitioners still believe in the underlying economic rationale for the value premium, viewing periods of underperformance as part of the normal cycle of risk premiums.