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I thought I'd share some charts regarding Berkshire's price and BV history. The first chart shows price and BV per A-share from Oct '64 (fiscal year end) to Dec '24. (I estimated BV for Dec '24 to be about $451K.) The knees in the curves at 1975 and 1999 also appear if one plots the S&P 500 index versus time. The second chart, P/B, shows the high and low price for the quarter to the ending BV. I apologize that you have to copy and paste the link. This is my first time trying to use a Google account to share documents.

https://docs.google.com/document/d/1fjyrqEMxDyhtTz...

The third chart, Price versus BV, shows the price/share plotted against the BV/share. Note the high r^2. The fourth chart shows the ratio of the price to the trendline of the P versus BV curve. While the fit of price versus BV is very good over the long term, there are significant excursions from the trendline in the short term, notably in 1975 (below trend), 1999 (above trend), 2000 (below trend), 2007 (above trend), 2009 (below trend) and 2020(below trend). As of Dcc 31, 2024 the stock price was on trend at a stock price of $681K, a P/B of 1.51 and a price/(P vs BV trendline) of 0.97.

https://docs.google.com/document/d/1ed5MS6b_vz3d0o...

I argue that the trendline of P versus BV can be used as a reasonable estimate of IV. The trendline corresponds currently to 1.56x BV. As an etimate of IV this value matches pretty well with Berkshire's repurchases. Berkshire repurchased shares in March '24 at 1.567x ending BV and issued shares in Sept '24 at 1.565x ending BV.

Comments appreciated.

rrr12345

I guess you don't have to copy and paste the link.

I think it's great context for understanding how book and price to book have evolved over time.

I think it's reasonable, within error bars, to think that the multiples seen in the last 10 or 20 years are probably not a bad guess of what you might see in the next five.

I think the log-real-book trend line is an amazing thing to behold and ponder...for the past.

But one warning about this sort of work...

I would be very much opposed to the dangerous notion that the relationship between current price and the trend line has any predictive value at all, despite what has happened in the past.

The linearity of log real book since 1998 is truly amazing, but there is no reason to think that it will continue like that. However, there IS a pretty good reason to think that price will continue to bear some sort of relationship to current book or recent peak book: because book is a not-too-terrible yardstick for value. This sensible relationship can hold whether book rises faster or slower than the old trend line in future, which a long-baseline trend line won't handle.

If the growth rate of real book suddenly halves and stays at that new lower rate, following PB will still get you useful valuation information, but following price to trend line would soon have you buying at overvalued levels thinking they were cheap.

Jim

Thank you for your input, Jim. Just to be clear, I was using nominal P and BV. I agree that the growth rate of BV can change at any time. Historically there have been three, fairly distinct periods of growth: a lumpy period from 1965 to 1979 at a CAGR of about 15%/yr, a fairly straight line (exponential) period from '79 to '99 at a CAGR of 27%/yr and a fairly straight line period from '99 to '24 with a CAGR of 10%/yr. The next period could be lumpy or straight line (exponential), and with an unknown CAGR. However I am encouraged in the analysis that the trendline (log-log) of P versus BV continued to be straight through the two knees in BV and P versus time in 1975 and 1999. Still, as you point out, we need to be cautious about putting too much trust in the trendline remaining straight (log-log). Further, to bolster your point, the trendline changes with the starting date of the regression, so this analysis needs some way to determine the best starting date.

Thank you again for your input.

rrr12345

When I hit those links, google says "sorry file does not exist"

Can you send me the files directly or links to the files on google directly?

Thanks!

Hi rr, or should I call you Mr 12345,

These two links don't work anymore. google says "sorry, the file you requested does not exist."

https://docs.google.com/document/d/1fjyrqEMxDyhtTz...
https://docs.google.com/document/d/1ed5MS6b_vz3d0o...

Is there any chance you could either refresh the links to something that does work, or just email me back the documents as attachments? I am very interested to see what you havce.

Thanks,
R:)

I'm having trouble with my Google account. I'll send the charts to your email.

"I'll send the charts to your email."

I'm having trouble doing that, too. Sorry.

Just one more comment about price and BV. Most of you will remember that John Kish posted estimated IVs from Dec 1981 to Dec 2014. He used both discounted cash flow and two-column. The IVs from both models track BV extremely well, with r^2 above 0.99, even though BV is not used in his IV calculations. This is further evidence that IV tracks BV extremely well.

Will the Annual Report be released on 2/22? I think it was released 2/24/24. Cannot wait, Thanks!

Highly likely to be Saturday, February 22.

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