Another quarter goes by, the market rises further, and the the 10-year forward return falls again.Here are the last eight values: 6.10%, 6.74%, 6.30%, 6.01%, 5.02%, 4.79%, and 4.30%, 3.99%.  At the end of September 2017, the figure would have been 4.49%, but the rally since the end of the quarter shaves future returns down to 3.99%.

At the end of June the figure was 4.58%. Subtract 29 basis points for the total return, and add back 12 basis points for mean reversion, and that would leave us at 4.41%. The result for September month-end was 4.49%, so the re-estimation of the model added 8 basis points to 10-year forward returns.

Let me explain the adjustment calculations.In-between quarterly readings, price movements shave future returns the same as a ten-year zero coupon bond. Thus, a +2.9% move in the total return shaves roughly 29 basis points off future returns. (Dividing by 10 is close enough for government work, but I use a geometric calculation.)

The mean-reversion calculation is a little more complex. I use a 10-year horizon because that is the horizon the fits the data best. It is also the one I used before I tested it. Accidents happen. Though I haven’t talked about it before, this model could be used to provide shorter-run estimates of the market as well — but the error bounds around the shorter estimates would be big enough to make the model useless. It is enough to remember that when a market is at high valuations that corrections can’t be predicted as to time of occurrence, but when the retreat happens, it will be calamitous, and not orderly.

Beyond 10-years, though, the model has no opinion.It is as if it says, past mean returns will occur.So, if we have an expectation of a 4.58% returns, we have one 4.58%/yr quarter drop of at the end of the quarter, and a 9.5% quarter added on at the end of the 10-year period. That changes the quarterly average return up by 4.92%/40, or 12.3 basis points.That is the mean reversion effect.