(1) Get previous 16 quarters of inflation adjusted book per share
(2) Get previous 20 years of PE multiples
(3) WMA = triangular weighting of (1)/(sum of weights) * average(2) for each quarter
(4) Do a least squares match of offset of (3) to price over same timeframe (any smoothing)?
(5) Calculate the standard deviation of the offset line in (4) vs price (assume gaussian spread).

More or less.



(1) Yes. An elaboration I didn't mention but isn't material: I assumed that any book-per-share drop of more than 4% below peak to date was transient, so I replace big book dips with 4% less than peak to date. The assumption is that even though book per share isn't rising, the actual value is rising. Or at the very least it isn't actually falling. This means the smoothed line is (to date) always rising, never falling.
(2) doesn't apply, not needed anywhere.
(3) right
(4) yes, but it's just the final scale factor to minimize the error between the smoothed line and the historical prices. Book per share, especially smoothed book per share, is a whole lot lower than the average price.
(5) I didn't do a step like this.

So, my process could be revised as what I did to create the graph:
(1) Get previous 16 quarters of inflation adjusted book per share
(2) Replace any low book values (dips during bear markets) with 96% of the peak-to-date real book-per-share.
(3) WMA of the prices. (most recent book*16 + previous quarter's book * 15 + ... + oldest book * 1))/136. Using the "no big dips" book values adjusted by step 2.
(4) Find the scale factor to apply to the smoothed line which makes the best fit to the real price history. I used 20 years of history for this, to get a single simple single multiplier factor.
...and optionally:
(5) For each day in the last 20 years, calculate the ratio of then-current real price to the then-current point on that scaled smoothed line. The average of this ratio is by construction 1. Look at the correlation between that ratio and the forward stock returns. Unsurprisingly, a high ratio of current-price-to-smoothed-value-line has usually given low average returns for the next year or two, and vice versa.
Step 5 just gives the typical returns from my post at the Berkshire board:

In the last 20 years,
Cheapest 15% of the time: Two year forward real total return average 17.8%/year
Next 15% of the time: Two year forward real total return average 14.8%/year
Next 20% of the time: Two year forward real total return average 10.0%/year (just a little cheaper than average)
Next 20% of the time: Two year forward real total return average 8.7%/year (just a little more expensive than average)
Next 15% of the time: Two year forward real total return average 0.6%/year
Most expensive 15% of the time: Two year forward real total return average -5.4%/year

Jim