A recent post on Liberty Street Economics (a blog of the Federal Reserve Bank of New York) attempts to answer that question. The post focuses on statistical analysis of the equity risk premium (ERP). As the following chart illustrates, the ERP is recently at an all-time high of 5.4%, compared to the long-term average of about 3%: To arrive at this conclusion, the authors of the post analyzed 29 different ERP models and weighted them so that the cross-section R-squared was maximized. The authors further concluded that the high level of the ERP is currently driven no so much by dividends (roughly, at the historical average) or dividend growth (anticipated to be slightly above average), but rather by the exceptionally low Treasury yields that result from the Fed’s actions. In other words, while in the traditional CAPM

Re = Rf + β * ERP
where Re = expected return on equity
Rf = risk-free rate
β = beta coefficient, by definition equal to 1 for the equity market

also

ERP = f(Rf)
i.e. the equity risk premium is a function of the risk-free rate, so Re is doubly so.

By various accounts, a long-term average return of the equity market is just over 10%. Subtracting the average ERP of 3%, this would imply a risk-free rate of about 7%. In today’s low-rate environment, the risk-free rate is in the 0.03% to 2.8% range, depending on which Treasury instrument with a maturity from one month to 30 years is used (while many models use three-month T-bills, others may use T-notes or T-bonds depending on the duration of the analysis period).

The following chart shows that the currently expected ERP falls only slightly from the one-month ahead value of 5.4% when the forecast period is extended: Let’s assume that the ERP in the next two years is expected to be about 5% and use a corresponding two-year Treasury note yield of 0.2% as a proxy for the risk-free rate. Adding the two, the expected annualized return of the equity market in that period is about 5.2%, which is significantly below the aforementioned historical average.

So, while the ERP rose to a historically high level, it is still insufficient to compensate for the decline in the risk-free rate. In addition, at 14.3-times estimated next-twelve-month earnings, the price-to-earnings ratio of the S&P 500® is only slightly below the historical average. Therefore, based on the ERP measure alone, one cannot conclude that stocks are cheap now.