I am finishing up a book: “The Equity Risk Premium: An Options-based Approach“. I expect to release it sometime this year.
As part of that book, I estimate the term structure of the ERP for the US broad equity market, as proxied by the S&P 500 Index. That is, at trade date t we can estimate the ERP for horizons T, using the listed options market. This is abbreviated \textnormal{ERP}_{t,T}. Just as we do with interest rates, regardless of the horizon, the values are displayed as annualized and in percent.
I have done this for every market day over the 11+ year period from Jan 3, 2012 through Apr 28, 2023. This produces a lot of term structures — in fact, 2823 of them. This is way too much data to review in detail in the book, so I limit myself there to interesting periods like the COVID-19 Pandemic era (esp. Mar 2020), the “Volpocalypse” (Feb 5, 2018) and so on.
However, you can view the ERP term structure on any of the 11-year study dates by visiting the ERP app (historical) (Once the app is “woken up”, I believe it’s pretty responsive).
Here is a partial screenshot from the app after loading: (Click to fully view). It shows the US market ERP term structure close to the Covid pandemic peak inversion in Mar 2020. With the date selector you can choose any date in an 11+ year study period.
I estimate the ERP by inferring a forward-looking risk-neutral density for SPX returns from the options market. Then, this density is converted to a real-world density by an exponential tilt with a parameter. The parameter is an estimate of the Coefficient of Relative Risk Aversion for a representative investor, often written as the Greek letter \gamma, so we have \textnormal{ERP}_{t,T}(\gamma).
Based on a historical estimator, I use \gamma = 3 for some midpoint estimates and \gamma \in (2.5,3.5) for a ballpark uncertainty band. These values are charted at the App and also visible in a displayed data table. For example, the midpoint estimate is shown in the table with column header ERP3.0 and so on. The table has other elements that are discussed in the book.
I am working on some additional ERP apps. When they are deployed, I will update this post or make some new ones.
Update (Aug 17, 2026). The book is now released. See the landing page for this site for selling site links. A second supplementary app is available. It demonstrates how well Gaussian mixture models fit option smiles. Here is the link: ERP App (GMM Fit Demo).
Known issues. Apps make take 30 seconds to “wake up”. If you then see a blank page with “Loading…” in the upper left corner, try refreshing your browser window. (This may be peculiar to MS Edge; the Chrome browser did not exhibit this glitch in my tests. However, refreshing the browser window is a good catch-all fix for many app issues).
