In The Siren’s Song of the Unfinished Half-Cycle John Hussman has a great annotated chart comparing the **ten-year returns estimated by the Shiller PE to the actual market returns that emerged over the following ten years from each estimate (from 1940 to present):**

Hussman estimates the ten-year return using a simple formula:

**Shorthand 10-year total return estimate = 1.06 * (15/ShillerPE)^(1/10) – 1 + dividend yield(decimal)**

He justifies his inputs to the simple formula as follows:

Historically,nominal GDP growth, corporate revenues, and even cyclically-adjusted earnings (filtering out short-run variations in profit margins) have grown at about 6% annuallyover time. Excluding the bubble period since mid-1995,the average historical Shiller P/E has actually been less than 15.Therefore, it is simple to estimate the 10-year market return by combining three components:6% growth in fundamentals,reversion in the Shiller P/E toward 15 over a 10-year period, and thecurrent dividend yield.It’s not an ideal model of 10-year returns, butit’s as simple as one should get, and it still has a correlation of more than 80% with actual subsequent total returns for the S&P 500.

Here is Hussman’s application of the simple formula to several notable points on the chart and comparison to the subsequent returns:

For example, at the 1942 market low, the Shiller P/E was 7.5 and the dividend yield was 8.7%. The shorthand estimate of 10-year nominal returns works out to 1.06*(15/7.5)^(1/10)-1+.087 = 22% annually. In fact, the S&P 500 went on to achieve a total return over the following decade of about 23% annually.

Conversely, at the 1965 valuation peak that is typically used to mark the beginning of the 1965-1982 secular bear market, the Shiller P/E reached 24, with a dividend yield of 2.9%. The shorthand 10-year return estimate would be 1.06*(15/24)^(1/10)+.029 = 4%, which was followed by an actual 10-year total return on the S&P 500 of … 4%.

Let’s keep this up.At the 1982 secular bear low, the Shiller P/E was 6.5 and the dividend yield was 6.6%. The shorthand estimate of 10-year returns works out to 22%, which was followed by an actual 10-year total return on the S&P 500 of … 22%. Not every point works out so precisely, but hopefully the relationship between valuations and subsequent returns is clear.

Now take the 2000 secular bull market peak. The Shiller P/E reached a stunning 43, with a dividend yield of just 1.1%. The shorthand estimate of 10-year returns would have been -3% at the time, and anybody suggesting a negative return on stocks over the decade ahead would have been mercilessly ridiculed (ah, memories). But that’s exactly what investors experienced.

The problem today is that the recent half-cycle has taken valuations back to historically rich levels. Presently, the Shiller P/E is 22.7, with a dividend yield of 2.2%. Do the math. A plausible, and historically reliable estimate of 10-year nominal total returns here works out to only 1.06*(15/22.7)^(.10)-1+.022 = 3.9% annually, which is roughly the same estimate that we obtain from a much more robust set of fundamental measures and methods.

Simply put, secular bull markets begin at valuations that are associated with subsequent 10-year market returns near 20% annually. By contrast, secular bear markets begin at valuations like we observe at present.It may seem implausible that stocks could have gone this long with near-zero returns, and yet still be at valuations where other secular bear markets have started – but that is the unfortunate result of the extreme valuations that stocks achieved in 2000. It is lunacy to view those extreme valuations as some benchmark that should be recovered before investors need to worry.

The actual return deviates from the estimated return at several points, including the most recent ten-year period from 2002. Hussman comments:

Note that there are a few points where the estimate of prospective market returns would have differed from the actual market returns achieved by the S&P 500 over the following decade.These deviations happen to be very informative. When actual returns undershoot the estimate from a decade earlier, it is almost always because stocks have moved to significant undervaluation. When actual returns overshoot the estimate from a decade earlier, it is almost always because stocks have moved to significant overvaluation.Note the overshoot of actual market returns (versus expected) in the decade since 2002. The reason for this temporary overshoot is clear from the chart at the beginning of this weekly comment: the most recent 10-year period captures a trough-to-peak move: one full cycle plus an unfinished bull half-cycle.

While Hussman’s formula is exceedingly simple, with a correlation of more than 0.8 it’s also highly predictive. It’s currently estimating very attenuated returns, and investors should take note.