Historical equity risk premium

What Is Historical Equity Risk Premium?

The historical equity risk premium is the average excess return that equity markets have provided over a risk-free rate during a specified past period. This metric falls under the broader category of financial modeling and portfolio theory, serving as a backward-looking estimate of the additional compensation investors have historically received for taking on the relatively higher risk associated with stock investments compared to safer assets like government bonds. It fundamentally reflects the actual performance difference between equities and risk-free investments over time. Investors assess the historical equity risk premium to gain insight into past market behavior, although past performance is not indicative of future results.

History and Origin

The concept of compensating investors for risk has long been recognized in finance, but the precise empirical measurement of the historical equity risk premium is a more recent development. Reliable data for estimating the historical premium of stocks over bonds only became widely available in the mid-20th century. Pioneers like Edgar Lawrence Smith in the 1920s began documenting the long-run returns of stocks, showing their tendency to outperform bonds. Later, in 1976, academics Roger Ibbotson and Rex Sinquefield published "Stocks, Bonds, Bills and Inflation," a seminal work that provided comprehensive historical data series for various asset classes, making systematic analysis of the historical equity risk premium more feasible²⁷, ²⁸.

The widespread adoption and theoretical grounding of the equity risk premium as a central input in financial models, such as the Capital Asset Pricing Model (CAPM), further spurred its calculation and study. However, this historical evidence also led to what became known as the "equity premium puzzle." This puzzle, highlighted by Rajnish Mehra and Edward Prescott in 1985, noted that the observed historical equity risk premium in the U.S. was surprisingly high and difficult to reconcile with standard economic models of risk aversion²⁵, ²⁶. Despite the puzzle, the data provided a quantifiable measure for the extra return stocks have historically delivered, making it a cornerstone for understanding past market performance.

Key Takeaways

• The historical equity risk premium measures the average excess return of stocks over risk-free assets over a past period.
• It serves as a backward-looking benchmark for understanding the compensation for equity risk.
• The calculation involves subtracting the risk-free rate from the market's historical expected return.
• Estimates can vary significantly based on the time frame, choice of risk-free asset, and averaging method (arithmetic vs. geometric).
• Despite its insights, the historical equity risk premium has limitations, primarily that past returns do not guarantee future performance.

Formula and Calculation

The historical equity risk premium is calculated by determining the average difference between the total returns of a broad-based equity markets index and the total returns of a relatively risk-free asset over a specific historical period.

The basic formula is:

Here:

• Average Historical Stock Market Return typically refers to the average return of a broad market index (e.g., S&P 500) over the chosen period, including both capital appreciation and dividend discount model payments.
• Average Historical Risk-Free Rate is usually represented by the return on long-term government bonds or Treasury bills, considered to have negligible default risk. The choice between short-term bills and long-term bonds can impact the calculated premium, with long-term bonds often preferred for discounting long-duration cash flows²⁴.

Analysts may use either arithmetic or geometric averages when calculating these historical returns. The arithmetic average is the simple mean of annual differences, while the geometric average represents the compound annual growth rate. The arithmetic average typically yields a higher value and is often considered more appropriate for estimating the cost of capital for a single future period, while the geometric average is better for understanding long-term compounded returns²², ²³.

Interpreting the Historical Equity Risk Premium

Interpreting the historical equity risk premium involves understanding what the past suggests about the compensation for taking on equity risk. A positive historical equity risk premium indicates that, on average, investing in stocks has yielded higher returns than investing in risk-free assets over the analyzed period. For example, if the equity markets returned 8% annually and government bonds yielded 3% over the same period, the historical equity risk premium would be 5%. This 5% represents the average extra return investors received for bearing the market volatility and other risks associated with equities.

However, it is crucial to recognize that this is a backward-looking metric. While it provides a factual record of past performance, it does not inherently predict future returns or reflect current market sentiment and economic conditions. Analysts use it as a reference point in financial analysis to gauge what has been possible in terms of risk compensation. The magnitude of the premium can influence expectations about future expected return and capital allocation decisions. A higher historical premium might suggest a greater incentive to invest in equities, while a lower one might temper such enthusiasm.

Hypothetical Example

Consider an analyst reviewing investment performance from 1995 to 2015 to calculate the historical equity risk premium. During this period, a hypothetical broad stock market index generated an average annual return of 10%. Over the same two decades, the average annual return on a portfolio of long-term government bonds was 4%.

To calculate the historical equity risk premium:

1. Identify the average historical stock market return: 10%
2. Identify the average historical risk-free rate: 4%
3. Subtract the risk-free rate from the stock market return: $$\text{Historical ERP} = 10\% - 4\% = 6\%$$

In this hypothetical example, the historical equity risk premium is 6%. This suggests that over the specified 20-year period, investors in this hypothetical market were, on average, compensated an additional 6% per year for investing in equities rather than risk-free government bonds. This figure would then be considered when constructing investment portfolios or evaluating future investment opportunities.

Practical Applications

The historical equity risk premium finds several practical applications within finance and valuation, albeit with the understanding of its backward-looking nature.

• Cost of Capital Estimation: It serves as a foundational input for estimating the cost of capital for businesses, particularly the cost of equity. In models like the Capital Asset Pricing Model (CAPM), the historical equity risk premium is often used as a proxy for the market risk premium, influencing discount rates applied to future cash flows.
• Performance Benchmarking: Investors and portfolio managers use the historical equity risk premium to benchmark the long-term performance of equity markets against risk-free alternatives. This provides context for evaluating whether a given asset allocation strategy has historically delivered adequate compensation for risk taken.
• Academic Research and Economic Analysis: Researchers utilize historical equity risk premium data to study long-term financial trends, test theories about asset pricing, and analyze the impact of macroeconomic factors on returns. It provides empirical evidence for discussions around market efficiency and economic growth.
• Capital Budgeting Decisions: Businesses may use the historical equity risk premium, adjusted for current expectations, to determine the appropriate discount rate for evaluating potential investment projects. This helps ensure that projects are assessed against a realistic hurdle rate that accounts for equity risk.

While useful, its application in forecasting is often cautioned, as highlighted by various financial institutions²¹.

Limitations and Criticisms

Despite its widespread use, the historical equity risk premium faces several significant limitations and criticisms that warrant careful consideration.

• Backward-Looking Nature: The most prominent critique is that historical data, by definition, reflects past performance and does not necessarily predict future returns. Market conditions, investor sentiment, and economic structures evolve, meaning that a premium observed in the past may not persist into the future²⁰. Aswath Damodaran of NYU Stern emphasizes that while historical premiums are widely used, their underlying assumption that investor risk premiums have not changed over time is flawed¹⁹.
• Data Period and Survivorship Bias: The chosen time period for calculation significantly impacts the result. Using a longer period may increase statistical precision but can obscure changes in risk aversion or market regimes¹⁷, ¹⁸. Conversely, shorter periods are noisier. Additionally, focusing solely on successful markets like the U.S. can introduce survivorship bias, inflating the observed premium as poorly performing markets or companies are excluded¹⁵, ¹⁶.
• Choice of Risk-Free Rate: The selection of the risk-free rate proxy (e.g., Treasury bills vs. government bonds) also influences the premium. Different choices reflect different investment horizons and liquidity characteristics, leading to varying historical equity risk premium estimates¹⁴.
• Averaging Method: Whether an arithmetic or geometric average is used can lead to materially different premium figures, with the arithmetic average typically being higher. The choice depends on the intended application (single-period vs. multi-period forecasting), but it highlights the ambiguity in arriving at a definitive "historical" value.
• Equity Premium Puzzle: As noted earlier, the observed magnitude of the historical equity risk premium, particularly in the U.S. over long periods, has puzzled economists, suggesting it is too high to be explained by conventional models of risk aversion alone¹³. This "equity premium puzzle" suggests that the historical premium may reflect unforeseen gains or a level of risk compensation that is not economically rational or sustainable in the long term¹¹, ¹². The Brookings Institution discusses this puzzle and its implications for understanding investor behavior [https://www.brookings.edu/articles/the-equity-premium-puzzle/].

These limitations underscore that while the historical equity risk premium provides valuable context, it should be used in conjunction with other forward-looking methodologies for robust financial analysis.

Historical Equity Risk Premium vs. Forward-Looking Equity Risk Premium

The historical equity risk premium and the forward-looking equity risk premium are two distinct approaches to estimating the additional return expected from equity investments over a risk-free rate. The primary difference lies in their temporal perspective.

The historical equity risk premium is a backward-looking measure, calculated based on the actual average excess returns of the stock market over risk-free assets from a past period. It quantifies what has happened—the empirically observed compensation for equity risk over a defined period. ¹⁰It is straightforward to calculate given readily available data but may not accurately reflect current or future market conditions or investor expectations.
⁹
In contrast, the forward-looking equity risk premium is a prospective estimate of the additional return investors expect to receive from equities in the future. ⁸This approach aims to capture current market sentiment, economic forecasts, and prevailing market volatility. Methods for calculating the forward-looking premium include using current market prices in relation to expected future cash flows (e.g., through a dividend discount model or earnings-based models), or through surveys of market participants. ⁷Unlike its historical counterpart, the forward-looking premium is inherently subjective and involves assumptions about future variables, making it more challenging to derive a single, definitive figure.
⁶
While the historical equity risk premium provides a factual baseline, many practitioners and academics argue that a forward-looking premium is more relevant for making current investment decisions and for accurate valuation purposes, as it directly attempts to incorporate future expectations into the analysis.
⁵

FAQs

What does a high historical equity risk premium imply?

A high historical equity risk premium implies that, over the period studied, equity markets significantly outperformed risk-free rate assets, providing substantial additional compensation to investors for taking on stock market risk. However, it does not guarantee similar performance in the future.

Can the historical equity risk premium be negative?

While less common over long periods for developed markets, the historical equity risk premium can theoretically be negative if equity markets have performed worse than government bonds over a specific duration. This would mean that investors were not compensated for the additional risk of holding stocks during that time.

Why is the time period chosen for calculation important?

The time period chosen is crucial because market cycles, economic conditions, and investor risk aversion change over time. Different periods can yield vastly different historical equity risk premium values, highlighting the sensitivity of the calculation to the chosen data window. ⁴Using a longer period generally reduces noise but might not reflect recent market shifts.
³

How does the choice between arithmetic and geometric mean affect the historical equity risk premium?

The arithmetic mean calculates the simple average of annual excess returns, while the geometric mean calculates the compound average. The arithmetic mean will almost always be higher than the geometric mean and is generally preferred for estimating the expected return for a single period, while the geometric mean is better for understanding long-term compounded growth for investment portfolios.
²

Is the historical equity risk premium used in modern finance?

Yes, the historical equity risk premium is still widely used in modern finance as a reference point, especially in academic research and as an input for the Capital Asset Pricing Model (CAPM) when estimating the cost of capital. However, it is often complemented or challenged by forward-looking and implied equity risk premium estimates to provide a more comprehensive view.¹