"If you're assuming that the price is ultimately a pretty fair representation of value,..."

Yes, I am assuming that. A plot (log-log) of price versus BV since 1965 has an r^2 of 0.98. That alone doesn't necessarily imply that the trendline is a good estimate of IV. It could be consistently high or low. However when one looks at the points in time when the price has been above trend or below trend, it looks to be about right. For example the price is above trend in June 1998 and below trend in March 2000, above trend in Dec 2007 and below trend in Mar 2009, etc.

"...the message from price in the last 25 years is that the fair book value per share has been falling, not rising, right?"

No, it's been rising, although slowly, from 1.35 in Dec 1999 to 1.59 in Dec 2024. BV has risen by 10.4% annualized over the last 25 years, and IV/BV has risen 0.7%/year, annualized, for a total annualized rise in IV of 11.1%/year.

Here are a couple of points in time for which we can compare price, BV and estimated IV (in my case the trendline of the 1965-2025 plot of P vs BV) and see if we get similar numbers.

As of Dec 31, 1999, BVPS was $37,987 per A-share. The price was $56,100, and P/B was 1.48. The long term trendline of P versus book (my estimate of IV) was $51,456, and the long term trendline of P vs B (i.e., IV) to BV was 1.30.

As of Dec 31, 1024, BVPS was $451,507 per A-share. The price was $680,920, and P/B was 1.51 (As you say, very similar to Dec 1999). The long term trendline of P versus book (my estimate of IV) was $724,435, and the long term trendline of P vs B (i.e., IV) to BV was 1.59.

Please let me know how your estimates compare. Thank you.