Historically over the last 25 years, when BRK has traded at 1.38 x book, it has average ~15% gain over the next year.

Though technically true, that statement is pretty misleading, as that average return includes all the times that the stock was very much cheaper than 1.38 times book.

The average multiple they mention is valid. Market multiples of book per share used to be high, but that era ended in 2007. The average P/B ratio since January 2008 has been 1.384, using peak-to-date book-per-share for each day.

So, if you have a starting/purchase date at around that average multiple, and you expect the multiple to be at an average level at the end of your holding period, your real return will equal the real rate of growth in book per share during your holding period. That has been inflation + 8.0%/year since the start of 2008, though I would probably pencil in inflation+7%/year as a reasonably sane expectation going forward.

An expectation of around inflation + 7% is a long way from the nominal 15% that the quote suggests one might expect.

As I type, the price is $478.64 per B and P/B is 1.439. If book were to rise inflation + 7% in the next year, and the ending multiple were to end up at the modern average of 1.384, you'd expect a one year return from here of around inflation + 2.91%. Book growth of inflation + 8% and a typical ending multiple gets you one year of inflation + 3.9%.

Maybe book per share will soar this year, maybe multiples will expand. But unless you have information that I don't, it's probably reasonable to expect something in the vicinity of "the usual".

All that being said, it's still a fine investment. The valuation multiple is still pretty close to its modern average if you squint a bit, and the prospect of a pretty long term return of around inflation + 7%/year is not bad at all.

Jim