How to Estimate the Equity Risk Premium for Any Market

The equity risk premium (ERP) is the additional return investors expect for holding stocks over risk-free assets. It's one of the three inputs in the capital asset pricing model (CAPM), which is used to estimate the cost of equity in absolute valuation models.

If you get the ERP wrong, the entire cost of equity shifts. A higher ERP increases the cost of equity, lowers the present value of future cash flows, and produces a lower valuation. A lower ERP does the opposite. Growth companies are especially sensitive because a larger share of their value sits in distant future cash flows.

For most U.S.-focused investors, the ERP can be estimated using historical stock and bond returns or by backing it out of current market prices. But the concept gets more nuanced when you're valuing companies with significant non-U.S. exposure, where country-specific risk needs to be layered in.

Below, we'll cover how the ERP is calculated, the main estimation approaches and their trade-offs, and how to handle non-U.S. markets.

What Is the Equity Risk Premium?

The ERP is the compensation investors demand for bearing equity market risk above the risk-free rate. It's calculated as the difference between the expected market return (E(r_m)) and the risk-free rate (r_f):

ERP = E(r_m) - r_f

where:

• ERP = equity (aka market) risk premium
• E(r_m) = expected market return
• r_f = risk-free rate

When plugged into the CAPM, the ERP is scaled by a company's beta (β) to determine the stock-specific risk premium, which is then added to the risk-free rate to estimate the cost of equity.

How to Estimate the Equity Risk Premium

There are six primary ways to estimate the ERP:

1. Historical ERP: Calculates the average difference between stock market returns and risk-free rates over a specific period. Assumes past performance is indicative of future results.
2. Historical returns-based forecasts: Uses time series patterns in historical returns and measures of stock "cheapness" (like P/E ratios) to predict future returns and ERPs.
3. Federal Reserve model: Compares the earnings yield (E/P ratio) to the Treasury bond rate, with the difference representing the ERP.
4. Implied ERP: Forward-looking approach that estimates the ERP based on current market prices and expected future cash flows, including dividends, buybacks, and earnings growth forecasts.
5. Modified historical ERP: For non-U.S. markets, combines a base premium for mature equity markets with a country-specific risk premium (CSRP).
6. Surveys: Relies on surveys from academics and institutional investors. Services like Ibbotson Associates (now part of Morningstar), Duff & Phelps, and Graham-Harvey provide regular survey-based ERP estimates.

The most widely used methods for estimating the cost of equity are the historical ERP, implied ERP, and modified historical ERP. We'll cover each in detail below.

Historical Equity Risk Premium

The most common approach to estimating the ERP is to base it on historical data. This method assumes that past performance is indicative of future results, and that returns will revert to historic norms over time (i.e., "mean reversion").

Historical ERPs can be calculated in two different ways:

Arithmetic vs. Geometric Averages

Arithmetic Average

The simple average of returns over a given period:

A = (r₁ + r₂ + ... + r_n) / n

where:

• A = arithmetic average return
• r₁ through r_n = individual period returns
• n = number of periods

Useful for estimating expected returns in any single future period, but overstates actual investment growth over time because it ignores compounding.

Best suited for short time horizons when using the Treasury bill rate as the risk-free rate.

Geometric Average

The compound average of returns over a given period:

G = [(1 + r₁) × (1 + r₂) ... (1 + r_n)]^{(1 / n)} - 1

where:

• G = geometric average return
• r₁ through r_n = individual period returns
• n = number of periods

Accounts for the compounding effect of gains and losses, making it the more accurate measure of actual investment performance over multiple periods.

Best suited for long time horizons when using the Treasury bond rate as the risk-free rate.

Example: Suppose the S&P 500 has the following annual returns over three years: 10%, -5%, and 15%.

• Arithmetic average: (0.10 + (-0.05) + 0.15) / 3 = 6.67%
• Geometric average: (1.10 × 0.95 × 1.15)^1/3 - 1 = 6.42%

The geometric average will always be equal to or lower than the arithmetic average. The gap between them widens as return volatility increases.

Historical ERP Data

Using historical returns on the S&P 500 (with dividends) against the 10-year U.S. Treasury bond, the arithmetic and geometric average ERPs across different time periods are:

Arithmetic Average Historical Returns

• 1928-2023 (95 years): S&P 500 returned 11.66%, 10-year Treasury returned 4.86%, ERP of 6.80%.
• 1974-2023 (49 years): S&P 500 returned 12.54%, 10-year Treasury returned 6.59%, ERP of 5.95%.
• 2014-2023 (9 years): S&P 500 returned 12.98%, 10-year Treasury returned 1.81%, ERP of 11.17%.

Geometric Average Historical Returns

• 1928-2023 (95 years): S&P 500 returned 9.80%, 10-year Treasury returned 4.57%, ERP of 5.23%.
• 1974-2023 (49 years): S&P 500 returned 11.10%, 10-year Treasury returned 6.12%, ERP of 4.97%.
• 2014-2023 (9 years): S&P 500 returned 11.91%, 10-year Treasury returned 1.46%, ERP of 10.44%.

The historical ERP ranges from 5.95-11.17% (arithmetic) and 4.97-10.44% (geometric), depending on the time period. That's a wide range, which brings us to the core problem with historical data.

Flaws of Relying on Historical Data

Relying on historical data to estimate the ERP in the CAPM is generally a flawed approach. Here's why:

• Noisy estimates: Returns can vary greatly depending on the chosen time period (e.g., last 10, 20, 50, 100 years). Including or excluding significant recessions (e.g., 2001, 2008) will significantly impact your estimate. Even over long periods, the derived risk premium will have substantial standard error. Between 1928 and 2023 (95 years), for instance, the ERP would fall somewhere between 2.53% and 11.07%, with 95% confidence (6.80% ± 2 × 2.15%).
• Survivorship bias and limited data: Historical data often comes from successful markets like the U.S., potentially overestimating future returns. For other markets, reliable historical data can be limited or even non-existent (e.g., some emerging markets). European markets are often dominated by a few large companies with thin trading.
• Changing market dynamics: Past performance doesn't account for structural changes in the economy or markets. Factors like globalization and the rise of technology companies have significantly altered market compositions.
• Black swan events: Rare, high-impact events like the COVID-19 pandemic can skew historical data and may not be representative of future patterns.

Despite its flaws, historical data remains the standard for estimating the ERP due to its simplicity and widespread acceptance. It provides an easily understandable, data-driven starting point. Investors can also average returns across different time periods to provide a more balanced view and reduce the impact of any single period's performance.

Implied Equity Risk Premium

The implied ERP method is a forward-looking approach that incorporates current market expectations. Instead of relying on historical data, it assumes the market is correctly priced and calculates the discount rate that equates the present value of expected future cash flows (dividends and buybacks) to the current market index price.

Implied ERP Formula

The implied ERP formula employs a two-stage model: an explicit forecast period where cash flows grow at analyst-estimated rates, followed by a terminal value where growth converges to a stable long-term rate. You solve for the discount rate (r) that makes both stages equal the current index price:

Index Price = Σ [E(CF_t) / (1 + r)^t] + E(CF_n+1) / [(r - g) × (1 + r)ⁿ]

where:

• Index Price = current price of an index (e.g., S&P 500 Index)
• n = number of periods in the explicit forecast period
• t = time period, ranging from 1 to n
• E(CF_t) = expected cash flows (dividends + buybacks) at time t
• r = discount rate (aka required rate of return)
• g = perpetual earnings growth rate

Solving for "r" gets you the implied expected stock market return (E(r_m)). Subtract the risk-free rate (r_f) to solve for the implied ERP:

Implied ERP = E(r_m) - r_f

Note: Damodaran provides an implied ERP calculator (Excel) that automates this process. You can also view S&P 500 monthly valuations and implied ERP estimates on RPubs for a visual breakdown of how the implied ERP changes over time.

Step-by-Step Process

The steps to estimate the implied ERP for any market are:

1. Find the current (or start of current year) price of the relevant market index (e.g., S&P 500 Index) for the country where the company is primarily listed or operates. Set this equal to the index price in the implied ERP formula.
2. Find and sum the total amount of adjusted dividends and stock buybacks over the last twelve months (LTM). This represents the base year cash flows (dividends + buybacks) equity investors receive from owning the index.
3. Decide on the number of periods to forecast cash flows (dividends + buybacks). 5 years is standard.
4. Find consensus analyst estimates on earnings growth for the relevant market index. Grow the cash flows (dividends + buybacks) by these growth rates over the next "n" number of years.
5. Scale down the cash flow growth to the current risk-free rate (r_f) by the end of the forecast period (e.g., year 5), which acts as a proxy for the normal growth rate of the relevant economy.
6. Solve for the discount rate (r), which represents the implied expected return on the stock market index (E(r_m)).
7. Subtract the risk-free rate (r_f) from the implied expected market return (E(r_m)) to calculate the implied ERP.

To capture a more "typical" ERP, you can choose to calculate the implied ERP over the past 5-15 years, then calculate an average over this period to estimate the implied ERP.

Implied ERP Example

Use the following information to calculate the discount rate (r):

• Current price of S&P 500 Index on 01/01/2024: $4,742.83
• Risk-free rate (r_f) on 01/01/2024 (U.S. 10-year Treasury bonds): 3.88%
• Dividends + buybacks in 2023: $164.25
• Number of periods (n): 5 years
• Analyst earnings CAGR estimate over the next 5 years: 8.74%

Growing the base year cash flows of $164.25 at 8.74% per year and then scaling down to the risk-free rate by year 5, the projected cash flows are: $178.61, $194.22, $211.19, $229.65, and $249.72. The terminal value uses the year 5 cash flow grown at the risk-free rate (3.88%).

Solving for r yields 8.33%. Subtract the risk-free rate to get the implied ERP:

8.33% - 3.88% = 4.45%

So the implied ERP for the U.S. equity market as of January 1, 2024, is ~4.45%. You can find Damodaran's historical implied ERP estimates on his website, which provides annual implied ERP calculations going back decades.

Implied ERP Pros and Cons

Pros

• Current market reflection: Incorporates real-time investor expectations and market conditions.
• Universal applicability: Usable in any market without requiring historical data.
• Better long-term predictive power: Demonstrates stronger correlation (0.6713) with 10-year future returns, compared to historical ERPs which show a negative correlation (-0.5509).
• Positive future correlation: Shows positive relationship with future stock returns, unlike historical ERPs.

Cons

• Model sensitivity: Requires future growth rate assumptions for expected cash flows (dividends + buybacks).
• Data quality dependence: Accuracy hinges on reliable forecasts of future cash flows and growth rates.
• Short-term volatility: Produces unstable estimates over short periods due to market fluctuations.
• Limited short-term utility: Weak correlation (0.1746) with one-year future returns limits short-term predictive value.
• Market sentiment influence: Can be skewed by temporary investor optimism or pessimism.

Overall, the data supports the idea that the implied ERP method has merit, especially for long-term predictions, but it's not a perfect tool and has limitations, particularly for short-term forecasts.

Modified Equity Risk Premium (Non-U.S. Markets)

The modified ERP is used to estimate ERPs for companies exposed to markets outside developed economies, particularly emerging markets where country-specific risk is significant.

The ERP in any equity market can be written as:

ERP = Base Premium for Mature Equity Market + Country-Specific Risk Premium (CSRP)

where:

• Base premium for mature equity market: The ERP of a mature market, such as the U.S.
• Country-specific risk premium (CSRP): The additional risk associated with investing in a specific country's market, reflecting factors such as political instability, economic volatility, currency risks, and regulatory uncertainties.

How to Approach the CSRP

There are two approaches to apply the CSRP:

1. Location-based CSRP: Attach a CSRP to a company based on its country of incorporation.
2. Operation-based CSRP: CSRP for a company is based on the weighted average of the CSRPs of the countries in which it does business, with weights based on revenues or operating income.

How to Estimate the CSRP

There are two methods to estimate the CSRP. Both rely on Damodaran's country default spreads and risk premiums table as a key data source.

Method #1: Default Spread on Country Bond

The simplest approach is to set the CSRP equal to the rating assigned to a country's debt by a credit ratings agency (i.e., S&P, Moody's, and Fitch).

These ratings measure default risk (not equity risk) but are affected by many of the same factors that drive equity risk (stability of country's currency, budget and trade balances, political stability, etc.).

Country vs. corporate bond spreads:

• You can choose to use country bond spreads if you want a reflection of the market's current view of risk in the market.
• Some investors use corporate bond spreads instead, because there's generally more market participants than the country bond markets, which means it's less volatile on a period-by-period basis.

The flaw of this approach is that ratings may lag markets when it comes to responding to changes in the underlying default risk, and the focus on default risk may obscure other risks that could affect equity markets.

India example:

Estimate the CSRP and ERP for India, where:

• Base premium for the U.S. (mature equity market): 4.45%
• Credit rating: Baa3 by Moody's on 07/01/2024
• Default spread (and CSRP): 2.07%

The ERP is 6.52% (4.45% + 2.07%).

Method #2: Default Spread Adjusted for Equity Risk

An adjustment to the default spread is necessary because equity markets typically carry more risk than bond markets, implying a country's ERP should exceed its bond default spread.

To quantify this additional risk, compare the volatility of the country's equity market to its bond market. Use this ratio to scale the default spread for a more appropriate country ERP estimate:

CSRP = Default Spread × (σ_Equity / σ_{Country Bond})

where:

• CSRP = country-specific risk premium
• Default Spread = difference between the yield on the country's sovereign bonds and a risk-free rate
• σ_Equity = standard deviation of returns in the country's equity market
• σ_{Country Bond} = standard deviation of returns in the country's bond market

India example:

Estimate the CSRP and ERP for India, where:

• Base premium for the U.S. (mature equity market): 4.45%
• Credit rating: Baa3 by Moody's on 07/01/2024
• Default spread: 2.07%
• Annual std dev in S&P Emerging BMI Index (SCRTEM) over previous year: 11.20%
• Annual std dev in iShares JP Morgan USD Emerging Markets Bond ETF (EMB): 9.24%

The CSRP is 2.51% (2.07% × (11.20% / 9.24%)). The ERP is 6.96% (4.45% + 2.51%).

CSRP will increase (decrease) if the country rating drops (improves) or if the relative volatility of the equity market increases (decreases).

CSRP also varies across time horizons. For longer periods (e.g., 10-year cash flows), use standard deviations of equity and bond prices over that timeframe. Relative volatility typically decreases for longer horizons, causing the ERP to converge towards the country bond spread for long-term expected returns.

Note: You can explore global default spreads and risk premiums on RPubs for a visual breakdown of country-level risk data.

Weighted Average CSRP for Multinationals

For multinational companies, the CSRP should reflect the geographic mix of revenues, not just the country of incorporation. You calculate a revenue-weighted average CSRP across all regions where the company operates.

Nvidia (NVDA) example:

Using revenue data from Nvidia's 10-K annual report:

• U.S.: 44.3% of revenue, CSRP of 0.00%, total ERP of 4.45%.
• Taiwan: 22.0% of revenue, CSRP of 0.73%, total ERP of 5.18%.
• China (including Hong Kong): 16.9% of revenue, CSRP of 0.86%, total ERP of 5.31%.
• Other Countries: 16.8% of revenue, CSRP of 3.00% (estimate), total ERP of 7.45%.

The weighted average CSRP is 0.81%, giving a total ERP of 5.26% (4.45% + 0.81%). This is higher than using the U.S. ERP alone (4.45%), reflecting Nvidia's significant international revenue exposure.

Company Exposure to Country-Specific Risk

After estimating the CSRP, you need to assess how individual companies within a country are exposed to country-specific risk. This is necessary because not all companies face the same level of exposure to country risk.

For example, Indian firms earn roughly 72% of revenue from the domestic market according to Morgan Stanley, but this varies widely across individual companies. Similarly, Chinese companies face growing pressure to globalize their revenue bases, which affects how much country-specific risk each firm actually bears.

There are five main approaches, each incorporating the CSRP differently into the modified CAPM formula for cost of equity (r_e):

1. Constant exposure, location-based: r_e = r_f + β_L × (Mature ERP) + CSRP. Adds the full CSRP on top of the standard CAPM. Assumes every company in the country faces the same country risk.
2. Constant exposure, operation-based: Same as above, but uses a revenue-weighted average of CSRPs across the countries where the company operates.
3. Beta exposure, location-based: r_e = r_f + β_L × (Mature ERP + CSRP). Scales the CSRP by beta, assuming companies with higher betas also have higher country risk exposure.
4. Beta exposure, operation-based: Same as above, but uses a revenue-weighted CSRP across operating countries.
5. Lambda (λ) exposure: r_e = r_f + β_L × (Mature ERP) + λ × (CSRP). Uses a lambda factor (λ = % of revenues domestically for the firm / % of revenues domestically for the average firm) to scale each country's CSRP based on how exposed the specific company is relative to the average firm in that country.

The lambda approach is generally preferred because it provides the most nuanced assessment of a company's actual exposure to country risk, rather than assuming uniform or purely beta-driven exposure.

Common ERP Estimation Mistakes

These are the key mistakes to avoid when estimating ERPs:

1. Third-party overreliance: Blindly using service-provided ERPs (e.g., Ibbotson, Duff & Phelps, etc.) without understanding the implicit assumptions or data sources.
2. Static ERP application: Using the same ERP (e.g., 6-7%) across all assets and time periods, ignoring changing market conditions and asset-specific risks.
3. Convenience over accuracy: Choosing familiar or easily defensible methods (e.g., historical ERP) rather than more predictive approaches (e.g., implied ERP), due to comfort or simplicity.
4. Purpose misalignment: Using short-term ERP estimates for long-term valuations, or vice versa, leading to inaccurate risk assessments.
5. Inappropriate CSRP application: Assigning full CSRP to multinational companies based solely on incorporation location, rather than considering global revenue distribution.

The Bottom Line

The equity risk premium (ERP) is the compensation investors demand for bearing equity market risk above the risk-free rate. It's a key input in cost of equity calculations, particularly through the CAPM.

For U.S. valuations, the two primary estimation methods are historical and implied. Historical ERPs are simple and widely used but suffer from noisy estimates, survivorship bias, and sensitivity to the time period chosen. The implied ERP is forward-looking and has demonstrably better long-term predictive power, but requires assumptions about future cash flows and growth rates.

For non-U.S. markets, you need to add a country-specific risk premium (CSRP) on top of the base ERP for a mature market. The CSRP can be estimated using the default spread on country bonds or, more precisely, by adjusting the default spread for the relative volatility of equities versus bonds in that market.

Whichever method you use, the ERP should not be a static number pulled from a textbook. It should reflect current market conditions, the specific geography of the company's operations, and the time horizon of your valuation.