The size risk premium is a core concept within factor investing, representing the empirically observed tendency for small-cap stocks to outperform large-cap stocks over extended periods. This potential for higher return from smaller companies is often considered compensation for the additional risk associated with them, such as lower liquidity and higher volatility. It is a key element that expands beyond traditional single-factor asset pricing models, like the Capital Asset Pricing Model (CAPM), which primarily accounts for market risk.
History and Origin
The concept of the size risk premium gained significant academic traction with the groundbreaking work of Rolf Banz in his 1981 paper, which first documented what he termed the "size effect" – the observation that smaller firms tend to have higher risk-adjusted returns than larger firms. This empirical finding laid foundational groundwork. Nobel laureate Eugene Fama and Kenneth French further solidified the size premium's prominence in academic and professional finance with their seminal 1992 paper, "The Cross-Section of Expected Stock Returns." Their research introduced the widely adopted Fama-French three-factor model, which includes a size factor (SMB, or "Small Minus Big") alongside market risk and value factors to explain stock returns more comprehensively. This model suggested that by tilting a portfolio towards small and value stocks, investors could potentially achieve outperformance.
8## Key Takeaways
- The size risk premium refers to the historical tendency of small-capitalization companies to generate higher returns than large-capitalization companies.
- It is considered a compensation for the added risks inherent in smaller firms, such as reduced liquidity and higher financial distress potential.
- The size premium became a recognized factor in asset pricing following the research of Fama and French, leading to its inclusion in multi-factor models.
- While historically observed, the persistence and magnitude of the size risk premium have been subject to debate and have varied over different time periods.
- Investors seeking to capture this premium often consider dedicated small-cap stocks allocations as part of their investment strategy.
Formula and Calculation
The size risk premium is not determined by a prescriptive formula like the expected return in the CAPM. Instead, it is typically measured empirically by observing the historical difference in returns between portfolios of small- market capitalization stocks and large-market capitalization stocks.
One common approach, as used in the Fama-French three-factor model, involves constructing a "Small Minus Big" (SMB) factor. This factor is calculated as:
Where:
- (R_{Small}) represents the average return of a diversified portfolio of small-cap stocks.
- (R_{Big}) represents the average return of a diversified portfolio of large-cap stocks.
To calculate (R_{Small}) and (R_{Big}), researchers typically sort all publicly traded stocks by their market capitalization and then form portfolios (e.g., top 30% large-cap, bottom 30% small-cap) to ensure distinct size groups. The returns of these size-sorted portfolios are then averaged to derive the respective (R_{Small}) and (R_{Big}) values.
Interpreting the Size Risk Premium
Interpreting the size risk premium involves understanding its implications for portfolio construction and expected return. A positive and statistically significant size premium suggests that investors who allocate capital to smaller companies may be compensated with higher returns over time, above and beyond what would be expected from their market beta alone. This is often attributed to the perceived additional risks of smaller companies, such as lower analyst coverage, reduced liquidity, and greater susceptibility to economic downturns.
For investors, a persistent size premium would imply that tilting a portfolio diversification strategy toward small-cap equities could enhance long-term returns. However, it's crucial to consider that historical outperformance does not guarantee future results. The premium's magnitude and even its existence can fluctuate over time, making consistent harvesting of this premium challenging.
Hypothetical Example
Consider an investor, Sarah, who is evaluating two hypothetical portfolios over a 20-year period: one focused on large-cap stocks and another on small-cap stocks.
- Large-Cap Portfolio (LCP): Composed of stocks with very high market capitalization, representing established, stable companies. Over the 20 years, the LCP generated an average annual return of 8.0%.
- Small-Cap Portfolio (SCP): Composed of stocks with relatively low market capitalization, representing smaller, potentially higher-growth companies. Over the same 20 years, the SCP generated an average annual return of 10.5%.
In this hypothetical scenario, the observed size risk premium would be the difference between the SCP's return and the LCP's return:
Size Risk Premium = SCP Return - LCP Return
Size Risk Premium = 10.5% - 8.0% = 2.5%
This 2.5% represents the additional average annual return that an investor hypothetically received by investing in smaller companies compared to larger ones over this period, indicating the presence of a positive size risk premium.
Practical Applications
The size risk premium, as a recognized factor in asset pricing models, has several practical applications in finance and investing:
- Portfolio Construction: Investors and asset managers may consciously allocate a portion of their portfolio to small-cap stocks to potentially enhance long-term returns, viewing the size premium as an additional source of return beyond broad market exposure. This is a common aspect of factor investing strategies.
- Performance Attribution: Analysts use factor models, which include the size factor, to explain why a particular fund or portfolio performed as it did. If a fund targeting smaller companies outperforms its benchmark, part of that outperformance might be attributed to its exposure to the size risk premium.
- Valuation: In corporate finance, when valuing private companies or divisions that are small relative to publicly traded peers, valuation experts might incorporate a size premium as an adjustment to the discount rate or expected return to account for the inherent differences in size and associated risks.
- Academic Research: The size premium continues to be a subject of ongoing academic inquiry, examining its persistence, drivers, and relationship with other factors. For example, the Federal Reserve Bank of San Francisco has discussed how factor investing, including the size factor, can be applied in various contexts.
7## Limitations and Criticisms
Despite its historical prominence, the size risk premium is not without its limitations and criticisms. One significant debate revolves around its persistence. While initially robust, some studies suggest that the size premium has diminished or even disappeared in certain periods, especially in developed markets since the late 20th century., 6T5his has led to questions about whether the premium was merely a statistical anomaly or if its drivers have changed over time.
Another critique focuses on the definition and measurement of small-cap stocks. Some researchers argue that the observed premium is largely concentrated in micro-cap stocks—the very smallest companies—which are often less liquid and more prone to specific biases in historical data, such as delisting biases. If th4e premium primarily exists in the most illiquid and difficult-to-access segments of the market, its practical applicability for many investors becomes limited.
Furthermore, some critics propose that any observed outperformance of small-cap stocks might be attributed to other underlying factors not fully captured by simple size sorts, such as a higher exposure to "junk" (low-quality) companies or specific liquidity risk that is not adequately compensated. The p3resence of an outperformance may also be cyclical, with periods of strong small-cap performance followed by extended periods of underperformance, leading to investor frustration and the potential for "tracking error regret" for those who tilt their portfolio diversification towards this factor. Resea2rch Affiliates, for instance, has explored the future of various equity risk premiums, including the size premium, acknowledging the challenges to its consistent realization.
S1ize Risk Premium vs. Small-Cap Effect
The terms "size risk premium" and "small-cap effect" are often used interchangeably, but there's a subtle distinction in their emphasis. The small-cap effect refers to the initial empirical observation that small-cap stocks have historically outperformed large-cap stocks. It is a descriptive term for the phenomenon itself. The size risk premium, on the other hand, implies an underlying economic rationale for this outperformance—that investors are being compensated with higher return for bearing the additional risk associated with investing in smaller, less liquid, or more volatile companies. While the small-cap effect describes what happened, the size risk premium attempts to explain why it happened. Both terms relate to the same fundamental concept within factor investing, but the "premium" explicitly links the outperformance to a form of risk compensation.
FAQs
Is the size risk premium guaranteed?
No. While historically observed over long periods, the size risk premium is not guaranteed to persist in the future. Financial markets are dynamic, and past performance is not indicative of future results. Investors should approach factor-based investment strategy with an understanding of this uncertainty.
Why do small-cap stocks sometimes underperform?
Small-cap stocks can underperform for various reasons, including their higher volatility and sensitivity to economic downturns. They may also face greater challenges in terms of funding or competition compared to larger, more established companies. Periods of market preference for large, stable companies can also lead to small-cap underperformance.
How do investors gain exposure to the size risk premium?
Investors typically gain exposure to the size risk premium by investing in portfolios or funds that specifically target small-cap stocks. This can include small-cap index funds, small-cap exchange-traded funds (ETFs), or actively managed small-cap mutual funds. Some factor investing strategies specifically tilt portfolios towards smaller companies to capture this premium.
Is the size premium related to the efficient market hypothesis?
The existence of a size premium (and other factor premiums) is often debated in the context of the efficient market hypothesis. If markets were perfectly efficient, all available information would be immediately priced into assets, and persistent outperformance based on readily observable characteristics like size would not exist without corresponding higher risk. Proponents of the premium argue it's a compensation for unmeasured risk, while critics sometimes suggest it's an anomaly that has been arbitraged away or was due to data mining.