Estimating Equity Risk Premiums with Historical Data and Models
Summary
The document distinguishes ex-post risk premium, which can be calculated from realized returns, from ex-ante risk premium, which must be estimated and is much more difficult to predict. If the premium is assumed constant, a long historical sample can provide an estimate, on the assumption that it captures a representative range of economic conditions. The discussion notes that empirical research instead suggests premiums vary over time.
For equity markets, it describes several estimation approaches: using the difference between earnings yield and bond yield as a proxy, applying dividend discount model variants, and using more complex models that jointly represent equity and bond risk premiums. Long-run market performance is another simple historical approach. The document cautions that even a century of observations leaves considerable estimation error. These are broad methods and caveats rather than a head-to-head evaluation of their predictive accuracy.
Key ideas
- Ex-post premiums use realized returns, while ex-ante premiums must be estimated and are substantially harder to know.
- A long historical average can estimate a constant premium if the sample is assumed to represent relevant economic conditions.
- Evidence cited in the document indicates that risk premiums vary over time.
- Equity premium proxies include the earnings yield less bond yield and dividend discount model estimates.
- Long historical samples still leave considerable uncertainty in the estimated premium.
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Full text
# How is the risk premium of the index estimated? # How is the risk premium of the index estimated? In the construction of an index model, we often use the expected return of a security, including surprises, for analysis. To calculate this, we must estimate the risk premium of the index. Since we only have one data point for each index at each point in time, we only have one of the risk premium, so the only option that is left is to aggregate different data points. But different macroeconomic conditions are reflected at different data points, so how can we calculate the risk premium of the index? ## Answer by Helin (score 1) https://quant.stackexchange.com/a/53642 Estimating ex-post risk premium is easy. Estimating ex-ante risk premium, on the other hand, is the holy grail of investing and is incredibly difficult. As @noob2 has mentioned, if you assume that risk premium is constant, then using a very long-term historical estimates would suffice. Empirical evidence, however, suggests that risk premium is time-varying. There is an extensive literature that goes into estimating risk premium for every asset class. In terms of equity risk premium, a lot of practitioners simply use the difference between earnings yield and bond yield as a proxy. Others depend on more complex models, typically some variants of dividend discount model. See Professor Damodaran's excellent paper "Equity Risk Premiums (ERP): Determinants, Estimation and Implications" and Duarte & Rosa's The Equity Risk Premium: A Review of Models for some good surveys. Even more complex models have been devised that model the risk premium in equities and bonds simultaneously. See Lemke & Werner's The Term Structure of Equity Risk Premia in an Affine Arbitrage-Free Model of Bond and Stock Market Dynamics for an example. ## Answer by nbbo2 (score 0) https://quant.stackexchange.com/a/53603 There is a whole literature on the Equity Risk Premium and its estimation. The simplest method involves looking at the performance of the stock market over very long periods of time (many decades). There is an implicit assumption (but a reasonable one IMHO) that the long term history includes all relevant macroeconomic conditions (an ergodicity assumption). For the US the most commonly quoted estimate of ERP is the Ibboston estimate based on data 1926 to present, some like Dimson have gone back further, to 1900 or before. Even with 100 years of data the estimate has considerable error in it, however.
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