The Equity Risk Premium

Publié le par Estelle Verdier

The equity risk premium (ERP) is defined by Goetzmann and Ibbotson (2006) as “the extra return needed to induce investors to risk their money in the stock market”. Thus, it is the difference between stock returns and returns on a risk free investment.


ERP = stock return – return of a riskless bond (*)

(*) The 10 year governemtn bond is usually considered as the riskless bond.


The ERP will depend on both extrinsic and intrinsic elements. Regarding the first category, we can underline that the ERP will reflect collective risk aversion of investors, the predictability of the overall economy (related to inflation, interest rates, and macro-economic performances) and the degree of information transparency in certain situations (Damodaran, 2009).

Besides, intrinsic extra-risks that a stock bears can be due to three main factors:

- The volatility of returns in the short term

- The residual claim position of stockholders in comparison to bondholders.

- The variability of dividends: the company is free to decide not to give dividends unless it is written in the agreement between the stockholder and the company.

Concerning this last point we can notice that there are fewer dividends distributed nowadays. Actually, firms often prefer to reward their stockholders through share buybacks. Consequently, the role of dividends in ERP estimates has to be relativized.

Stock specific risk premiums are usually quite close for equities within a particular sector. On the contrary, across sectors the ERP varies due to the sector sensitivity to market crisis. Thus, high technology industry stocks are said to be more exposed, given that in the turmoil companies are more likely to cut their investments in new technologies as far as they are not vital for their business. On the other hand, the insurance or the health care industry are supposed to be less exposed to market fluctuations.




There is still no consensus on how to measure the risk in an investment and how to convert it into an equity risk premium. We will present below the main methods to estimate the ERP.


Ex-post calculation: the historical approach

An average realized ERP can be calculated thanks to historical databases. Under this method, the difference between actual returns earned on stocks over a long time period and actual returns earned on T-bonds is calculated. In the USA, market returns data are usually those collected by Ibbotson Associates on S&P 500 index going back to 1926.


On the US market the arithmetic average long-term premiums for stocks, from 1928 to 2008, is 5.64% (Damodaran, 2009). The unexplainably high level of this estimation led Mehra and Prescott (1985) to wonder if the observed ERP was compatible with the theory. They have argued that such a high ERP reflects implausibly high risk-aversion coefficients. To explain what they called “the equity risk puzzle” Damodaran (2009) sets forth five potential explanatory elements:


- Statistical artefact: this calculation suffers from a “survivor bias” because it is based on the “winning market”, i.e. the American market which is one of the most successful equity markets of the last century.

- Disaster insurance: the volatility of the observed market does not consider the potential volatility that could be related to a rare but disastrous event.

- Taxes: the declining marginal tax rate could have led to an increase of returns.

- Alternative preference structure: people prefer lower and more stable level of wealth. Riskier behaviours thus have to be highly rewarded.

- Myopic loss aversion: individuals’ loss aversion becomes more pronounced when the frequency of their monitoring increases.

Given these remarks, estimations of future ERP based on historical data might be biased. Actually, the ERP estimated on other timeframes and geographical areas can show great discrepancies. For example, the global ERP calculated by Dimson, Marsh, Staunton and Wilmot (2009) over 17 markets from 1969 to 2008 is estimated at 0.10% (Damodaran, 2009). It has to be underlined, however,  that this rate is heavily impacted by the recent market collapse.


Ex ante calculations: Implied equities premiums

Ex ante calculus is a way to assess the superior expected profitability of a stock over a government bond. The calculation can either be based on the dividend discount model (DDM) or on the earning based approach.


Under the dividend discount approach it is assumed that the stock price is fixed as a multiple of dividends. Thus the total stock return encompasses both the dividend yield and the expected growth in dividends. Based on the Gordon constant growth model the equity yield is the dividend yield (D/P) plus the long-term growth of dividends (g). The risk free rate (rf) should then be deduced from it.

ERP = ( D/P + g) - rf

Using potential dividends (including buybacks), according to this calculation, Damodaran (2009) charted the implied premiums in the S&P 500 from 1960 to 2008:





An alternative approach is the earning based approach. Under this method, the equity yield is equal to the earnings per share divided with the stock price. The real risk free rate (i) then has to be deduced from the equity yield.


ERP = E/P - i



The relevance of the equity risk premium

The crisis of 2008 provided another illustration of the difficulties surrounding the estimation of the ERP. Damodaran (2009) underlines that the ERP rose more during 2008 than during any year of the prior 50 years. Most of the change was concentrated in the last three months of the year. This reminds us that estimations of the ERP based on extrapolations (of historical data) are risky because it assumes that there are no changes, no shocks taking place in the broad environment, which is far from reality.


Besides, the historical ERP approach does not consider that structure of asset supply and demand might have varied. This is an important issue given that ERP is also defined thanks to the supply and demand mechanism.


Another issue regarding the ERP concerns the adoption of the 10-year government bond yield as the risk free rate. Patrick Artus (2009) now recommends using big companies (with a A rating) bond yields as the interest rate reference. According to him arbitrage is nowadays much more between these bonds and stocks. If we consider this "risk free" reference, it erases the four years of above-trend ERP values experienced since the burst of the dotcom bubble.


Lastly, evaluations based on the national or regional indices might suffer from a sector bias. The sector composition of the S&P500 and of the EuroStoxx, for example, are very different. And it must be underlined that the ERP varies a lot between geographical areas, especially between western countries and emerging markets.





Artus, P., 2009, Comment juger la prime de risque actions, Natixis Special Report, 20 janv. 2009.


Damodaran, A., October 2009, Equity Risk Premiums (ERP): Determinants, Estimation and Implications - A post-crisis Update.


Harper, D., 2009, An Overview of the Equity Risk Premium, available on on the 22/11/2009.


Goetzmann, W. N., and Ibbotson, R. G., 2006, The Equity Risk Premium.


Kholler, T., Goedhart, M., Wessels, D., Valuation: measuring and managing the value of companies, Hoboken, NJ: John Wiley & Sons.

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