The Term Structure of the Equity Risk Premium

What is the equity risk premium, abbreviated ERP? It’s the market’s best point estimate, today, of what “stocks in the aggregate” will return in the future — after subtracting a risk-free interest rate.  By “stocks in the aggregate”, I am taking a US perspective, so thinking about an equity investment matching the  S&P500 (after dividends are accounted for).

If the future is very distant, say the next 20 years, a widely held belief is that the ERP will average around 4-6% per year.  The ERP has often been called “the most important number in finance”.

Speaking of interest rates, it’s well-known that rates vary in time and, at each time, have a term structure. For example, if r was a US Treasury rate, we would write r_{t,T} to denote the annual yield at time t for a Treasury bond maturing at time T.

Just like interest rates, the ERP is also time-varying and has a term structure —  so we also write \mbox{ERP}_{t,T}. For example, we could ask, what is the ERP today for holding stocks over the next 6 months? Regardless of the horizon, which might be very close, the convention is to quote the ERP as an annualized percentage rate. This is the same convention as for interest rates: even if you are borrowing money for just a couple weeks, your borrowing cost will be quoted as an annualized percentage rate.

The fact that the ERP has a term structure is not widely appreciated. In contrast, the term structure of interest rates is well-known and readily visible. For example, just look in the Wall Street Journal for the current term structure of US Treasury rates  — or find it in many places on the web.  The ERP term structure is not directly visible and needs to be estimated. Exactly how? That’s the question I answer in a new research paper, recently posted at the arXiv, titled:

Option-based Equity Risk Premiums

As an example, I show below my estimate of the (US) ERP term structure for Feb 7, 2018,  2 days after the so-called `Volpocalypse’.  That Feb 5, 2018 volatility event was the day of the Dow Jones Industrial Average’s largest point loss ever, although the percentage loss was less than 5%. The two charts show the same ERP, but the bottom uses a log time scale in order to better show the various, closely-spaced, option expirations.  As you can, the ERP is declining from about 26% per year for the nearest dates (2 days away) toward the longer-term values mentioned above. The  dark lines are central estimates and the red lines estimate the uncertainty. My assumptions and other details are found in the article.

The ERP term structure, estimated for Feb 7, 2018, two days after the ‘Volpocalypse’.