Category Archives: Equity Risk Premium

The Equity Risk Premium (forthcoming book) — slides posted

Yesterday I gave a Zoom talk for a Business school seminar at the Stevens Institute of Technology in New Jersey. My thanks go out to Dan Pirjol, Zack Feinstein, and the other folks from the Business school at Stevens, both for the invitation and attending.

I summarized results from my forthcoming book: “The Equity Risk Premium: Unified Modeling + Python Automation”.
If you’re interested in a preview, here are the slides:

Download “The Equity Risk Premium: slides: Stevens”

THE-EQUITY-RISK-PREMIUM.Stevens.pdf – Downloaded 1169 times – 1.92 MB

US Equity Risk Premiums during the COVID-19 Pandemic

I’ve recently completed a research study

US Equity Risk Premiums during the COVID-19 Pandemic ,

available at This work is a follow-up application of my recent work on

Option-based Equity Risk Premiums, which I posted about here:

The Term Structure of the Equity Risk Premium

The equity risk premium (ERP) is the extra return (above Treasury rates) that investors expect, in order to hold stocks. The health and financial distress associated with the pandemic has been enormous. This has led to record-setting volatility and likely record-setting ERP’s also.  At any point in time, the ERP term structure is a chart of the equity risk premium (as an annual percentage rate) at various time horizons. My time horizons range from one day ahead to about 3 years.

To give a bit of a preview, consider the early days of the pandemic, shown in the timeline below (click on snapshot to view):

Time Line 1
Early timeline events during the COVID-19 pandemic


At this point in time, the US equity market was not too concerned, volatility was more-or-less normal and the associated ERP term structure looked as follows:

US ERP Term Structure on Jan 22, 2020

That January 22 chart shows the ERP’s in a 3-6% range: typical of an unstressed market, and also characteristic of long-run (unconditional) ERP’s. The dotted lines are my point estimates and the gray areas reflect an estimated uncertainty interval.  The main driver of the uncertainty is the degree of risk aversion in a so-called “representative investor”.

Notice that I am using a logarithmic scale for the time axis. The reason for this is that the times are actually the times to various S&P 500 Index option expirations. Those are very closely spaced in the first 30 days ahead. The log scale effectively spreads them apart for greater visibility.

By mid-March 2020, the pandemic had become global, cases and deaths were growing exponentially, and financial markets were close to panic mode. The ERP term structure dramatically inverted:

US ERP Term Structure on Mar 12, 2020

At the short-end of the curve, investors now required an annualized expected return of 500-600% in order to hold equities. This is likely a record, although to say for sure would require applying my same methods to option data during the 2008-2009 Financial crisis. This has not yet been done.







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 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’.