What Is Historical Equity Risk Premium?
The Historical Equity Risk Premium (ERP) is a widely used measure within portfolio theory and financial valuation that quantifies the additional return investors have historically earned from holding a broad market portfolio of equities, such as the S&P 500, compared to a so-called "risk-free rate." It represents the compensation for the perceived higher risk associated with equity investments over a specified historical period. This historical equity risk premium serves as a backward-looking estimate, reflecting past market conditions and investor behavior.
History and Origin
The concept of an equity risk premium has been central to finance theory for decades, particularly with the development of models like the Capital Asset Pricing Model (CAPM). The practice of calculating a historical equity risk premium emerged as a practical approach to estimate this premium, relying on observed past performance. Academics and practitioners began analyzing long-term data sets of stock market returns and government bond yields to determine the average excess return of equities. For instance, extensive research by academics like Elroy Dimson, Paul Marsh, and Mike Staunton, as well as Professor Aswath Damodaran, has provided comprehensive historical data sets spanning over a century for various markets globally, contributing significantly to the understanding and application of the historical equity risk premium.12,11 These analyses have shown that, despite variations across countries and timeframes, a substantial premium has historically existed.
Key Takeaways
- The historical equity risk premium measures the average excess return of stocks over risk-free assets in the past.
- It is a backward-looking estimate, based on realized returns from equity markets and risk-free investments like Treasury bonds.
- While simple to calculate, its main limitation is the assumption that past performance is indicative of future returns.
- The selection of the equity index, the risk-free proxy, and the historical period significantly impact the calculated premium.
- It serves as a foundational input in various financial models, particularly in determining the expected return on equity.
Formula and Calculation
The historical equity risk premium is calculated as the arithmetic or geometric mean of the difference between historical equity market returns and historical risk-free rates over a chosen period.
The basic formula is:
Where:
- Average Historical Stock Market Return: The average annualized return of a broad market index (e.g., S&P 500) over a specific historical period.
- Average Historical Risk-Free Rate: The average annualized return of a proxy for a risk-free asset (e.g., long-term U.S. Treasury bonds or Treasury bills) over the same period.
The choice between arithmetic and geometric mean can significantly affect the result. Arithmetic mean represents the average return in any single year, while geometric mean represents the compound annual growth rate over the entire period.10
Interpreting the Historical Equity Risk Premium
Interpreting the historical equity risk premium involves understanding that it reflects what investors have earned, not necessarily what they will earn. A higher historical equity risk premium suggests that, on average, equities have provided a significantly better return than risk-free assets over the past. This historical data provides a benchmark for assessing the potential returns from equity investments. However, market conditions, economic environments, and investor sentiment are dynamic, meaning that the future equity risk premium may deviate from its historical average. Therefore, while providing valuable context for asset allocation decisions, its direct application as a forecast requires careful consideration and often adjustment.
Hypothetical Example
Consider an investor analyzing market data to estimate the equity risk premium for use in a valuation model. They gather historical data for the S&P 500 and U.S. 10-year Treasury bonds over the last 50 years.
- Assume the average annual return of the S&P 500 over this period was 9.5%.
- Assume the average annual return of U.S. 10-year Treasury bonds over the same period was 3.0%.
Using the formula:
In this hypothetical scenario, the historical equity risk premium would be 6.5%. This suggests that, over the past five decades, equity investors have, on average, received an extra 6.5 percentage points of return per year for taking on stock market risk compared to investing in long-term government bonds. This figure would then be used as an input for determining the discount rate for future cash flows.
Practical Applications
The historical equity risk premium is primarily used as an input in several critical financial calculations and analyses. Its most common application is in determining the cost of equity within the Capital Asset Pricing Model, which is essential for corporate finance decisions like capital budgeting and company valuation.9 Financial analysts often use historical data to derive a foundational ERP, which is then adjusted for current market conditions and forward-looking expectations.
While some consider historical estimates less reliable for forecasting future returns, they offer a useful starting point for understanding long-term trends in market performance. They also provide a baseline for comparing different asset classes and understanding the historical compensation for volatility. Organizations like New York University Stern School of Business's Professor Aswath Damodaran provide regularly updated historical data on equity risk premiums, which are widely referenced by practitioners and academics.8
Limitations and Criticisms
Despite its simplicity and widespread use, the historical equity risk premium faces significant limitations and criticisms. A primary concern is its backward-looking nature; past performance is not necessarily indicative of future results.7,6 Market conditions, economic structures, and investor behavior change over time, meaning that a premium observed over a long historical period may not accurately reflect current or future expectations. For example, periods of high inflation, recessions, or significant technological shifts can skew historical averages.
Another criticism centers on the selection of the historical period and the type of average used (arithmetic vs. geometric). Different time frames can yield vastly different historical equity risk premiums, leading to inconsistencies in analysis.5,4 Furthermore, historical data can be influenced by "luck" or unanticipated gains, which may not repeat in the future.3 Experts like Robert Arnott of Research Affiliates argue that forecasting the future ERP solely based on past excess returns is a "pernicious blunder" and that current valuations are better indicators of future returns.2 Some studies even suggest that sophisticated machine learning models often fail to outperform the simple historical average benchmark in out-of-sample forecasts, highlighting the inherent challenges in predicting future equity risk premiums.1
Historical Equity Risk Premium vs. Implied Equity Risk Premium
The historical equity risk premium and the implied equity risk premium represent two distinct approaches to estimating the additional return investors expect from equities. The fundamental difference lies in their temporal perspective and methodology.
Feature | Historical Equity Risk Premium | Implied Equity Risk Premium |
---|---|---|
Perspective | Backward-looking | Forward-looking |
Methodology | Calculated from observed past returns of equities and risk-free assets. | Derived from current market prices and expected future cash flows (e.g., dividends or earnings) of the overall market. |
Assumptions | Assumes future performance will resemble past performance. | Assumes the market is correctly priced and uses that price to infer the market's expectation of the premium. |
Data Source | Historical time series data of market indices and bond yields. | Current market prices, analyst forecasts for earnings/dividends, and risk-free rates. |
Key Advantage | Simplicity, uses readily available actual data. | Reflects current market sentiment and expectations. |
Key Disadvantage | May not reflect current or future market conditions; influenced by past "luck." | Relies on assumptions about future cash flow growth and the efficiency of market pricing. |
While the historical equity risk premium provides a long-term average, the implied equity risk premium offers a dynamic, real-time estimate of investor expectations. Many financial professionals often consider both when making decisions related to investment horizon and portfolio diversification.
FAQs
Why is the length of the historical period important when calculating the Historical Equity Risk Premium?
The length of the historical period is crucial because it affects the stability and representativeness of the calculated premium. A very short period might be skewed by recent market anomalies or short-term volatility, while a very long period may smooth out short-term fluctuations but might also include economic regimes that are no longer relevant. Analysts typically use periods of 50 years or more to capture multiple economic cycles and provide a more robust average.
Can the Historical Equity Risk Premium be negative?
Theoretically, yes, if the average historical returns of risk-free assets were higher than equity returns over the chosen period. While this is uncommon over very long periods, it could occur over shorter, specific time frames, especially during prolonged bear markets or periods of exceptionally high bond yields relative to stock performance.
How does inflation affect the Historical Equity Risk Premium?
Inflation can impact both equity returns and risk-free rates. When calculating the historical equity risk premium, it's important to consider whether the returns are nominal (including inflation) or real (adjusted for inflation). If both are nominal, the inflation component largely cancels out when taking the difference. However, real historical equity risk premiums provide a clearer picture of the actual purchasing power gained from investing in equities versus risk-free assets. Understanding mean reversion in real returns can be insightful.
Is the Historical Equity Risk Premium the same for all countries?
No, the historical equity risk premium varies significantly across countries due to differences in economic development, political stability, market maturity, and investor risk aversion. Developed markets with long, stable histories tend to have more reliable and often lower historical equity risk premiums compared to emerging markets, which may exhibit higher, but also more volatile, historical premiums.