Must-Read: Above a Shiller CAPE of 25, we have essentially three observations as to what happens next. Hence “we have little idea what is likely, and past performance is not a reliable guide to future results” is the only sound thing to say. As Jim Powell says: with two data points you have an estimate of the mean and an estimate of the standard error, for you think your two data points are at μ ± σ/2. And then he laughs:

Chandrasekhar Ramakrishnan: The DeLong-Shiller Redux: “2014, Robert Shiller and Brad DeLong…. [Shiller] claims if the value of this [CAPE] ratio is above 25, a major market drop is probably brewing…

…[DeLong] writes “we find that we cannot calculate a ten-year return for the 2007 CAPE peak of 27.54 — we still have three years to go.” Those three years have in the meantime transpired, and we now have the data necessary to calculate the ten-year return for May 2007, when the aforementioned peak occurred. This seems like a good time to revisit the DeLong-Shiller argument….Earnings/price can… be estimated as 1/CAPE. He calls the EMH-expected-returns for a given value of CAPE “warranted returns”, and to visualize his framework, DeLong constructs the following plot, which I’ve updated to include the latest data. This plot shows CAPE vs. 10-year returns and includes a curve to indicate the warranted returns. Reflecting on the fit of the curve, DeLong remarks, “Given the naiveté of the framework, that turns out to be… a remarkably good guide to the central tendency of the distribution of future ten-year returns conditional on the CAPE.” And I would have to agree….

The DeLong Shiller Redux Chandrasekhar Ramakrishnan Medium

Past performance is not an indicator of future performance. Nonetheless, we can see what past performance at today’s CAPE levels would yield. We have earnings data up to the end of Q2 2017 and using that, we can compute CAPE and try the following impossibly naïve model: for a current CAPE value (for which we do not yet have returns data), take the 19 closest values in the past and average these to get a prediction. This is of course not how machine learning should be done…

The DeLong Shiller Redux Chandrasekhar Ramakrishnan Medium

I should point out that my “warranted” returns are for somebody reinvesting their portfolio and holding to ∞, thus eliminating valuation-ratio risk and valuation-ratio mean reversion from the problem. They also assume that reinvested earnings are neither dissipated in corporate empire building nor able to earn supermarket returns via superior information.

When CAPE is high and when your horizon is less than ∞, you should incorporate some estimate of valuation-ratio mean reversion—and that is what Ramakrishnan does…