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Someone asked for opinions about when to buy [back] in to Berkshire.

I thought this image might be helpful
http://stonewellfunds.com/SmoothedRealValuePerShar...

A long time ago I proposed that the ultimate safe withdrawal rate is to liquidate no more than the amount the value of the shares has increased. Prices might go up and down, but the real value of your holding would never change. You could withdraw money forever, or at least as long as the real value kept rising. Since valuation metrics are themselves pretty volatile, I proposed using a smoothing method. At worst it would be an over- or under-estimate for 2-3 years.

The smoothing proposed was a 16-quarter weighted moving average of real book per share. I also use a 16-quarter weighted moving average of my two-and-a-half column valuation figure. Once they are scaled to match, they match each other very closely. There is a slight divergence lately since book per share has risen a bit faster than my valuation method, because earnings in the subs have been a bit weak in the last couple/few years. For these purposes it makes little difference.

The graph simply shows the real stock price (in today's dollars, log base 10), and the smoothe value. The value is scaled to give the average price:value ratio of 1 in the last 20 years.

This looks almost like a trend line, but there is a crucial difference: if the rate of growth of observable value changes, the smoothed line changes, over a maximum of 4 years but on average less than two. So there is no danger of extrapolating old fast growth rates.

Unsurprisingly, the ratio of price to estimated value is a pretty good predictor of whether you're about to see unusually good or unusually bad price changes.

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

The current valuation level is at percentile 93.5, so around the middle of the "most expensive" bucket above.
The current ratio of price to the value line is 1.187, or 18.7% more richly valued on this metric than the 20 year average.
The 20-year-average valuation level today would correspond to $612733 per share ($408.49 per B). That price (or lower) might perhaps make a good re-entry target?? Of course that number will rise with share value and with inflation as time passes.

Those averages and returns are just observations about what happened in the past. The future may differ.

Jim

PS, this is an older image of the same valuation and smoothing method, from about two years ago.
It shows how similar the two valuation methods are, once they are scaled to match.

http://www.stonewellfunds.com/PriceAndWMAofValue.p...

The single "value" line in the image in the first post is the simple average of the two methods.

Jim

Jim,
Nice work but just for clarification is your 16-quarter weighted moving average equally weighted?

Nice work but just for clarification is your 16-quarter weighted moving average equally weighted?

No, it's a WMA in the sense that chart people mean it. The most recent quarter is weight 16, the second most recent at weight 15, ramping down to weight 1 on the oldest quarter of the 16. So recent data counts the most, but doesn't totally dominate.

If you use equal weighting there is more time lag on average, and you can get meaningless discontinuities when an anomalous quarter shifts from being 16 to 17 quarters earlier.


A small note for those who like to be bullish: a bit of inflation as we saw recently increases the fair P/B ratio just a little. The reason is that still-productive fixed assets, depreciating or not, are rising in nominal output but not rising in nominal book value. The value of any contracts with revenues in fixed dollars falls, but I think Berkshire is smart enough not to have too many of those. The biggest exposure is probably any regulated rates which are not allowed to rise as fast as monetary inflation.

For those who like to be bearish, the big concern is the dire rate of increase of observable value among the operating subsidiaries. Both BHE and BNSF are doing poorly at the same time, and the problems may not be merely cyclical. Taking the whole group, rolling year net earnings on operating subsidiaries are up only 0.81%/year in the last 3 years, and under 4%/year in the last six years. Those figures include cyclical adjustment on underwriting profit so that volatility doesn't ruin the comparison.

Jim

The 20-year-average valuation level today would correspond to $612733 per share ($408.49 per B). That price (or lower) might perhaps make a good re-entry target?? Of course that number will rise with share value and with inflation as time passes.

I just wanted to add to that: the comment above is interesting and perhaps useful, but should not be confused with an estimate of the intrinsic value of a share.

Maybe Berkshire has been undervalued for most of the last 20 years, or overvalued. The comment is merely about the observed average valuation level, for better or worse.

Jim

"I just wanted to add to that: the comment above is interesting and perhaps useful, but should not be confused with an estimate of the intrinsic value of a share."

Nice analysis. Thank you for sharing, Jim.

I'm trying to infer your estimate of current intrinsic value. If I understand you correctly, your 20-year average valuation is intended to give a smoothed valuation level that tracks IV, but which is not necessarily equal to IV. It's apparently the average of your two and a half valuation and 1.5 times the 16 quarter WMA of BV. Is this correct?

Your current valuation level is $612,733, which corresponds to 1.554 times the 16 quarter WMA book value, which I calculate to be $394,284. It is also 1.326 times the March 31 BV/share.

From our recent discussion of IV/BV I understood, or misunderstood, your estimate of current IV to current BV to be flat over the last 25 years at a value of about 1.60. Certainly not 1.32 in Dec 1999 as I suggested.

Would you mind straightening me out? What would be your estimate of current IV to current BV?

FWIW, I'm still holding with an IV estimate of about 1.54x BV, based on a couple of models, but I would not argue with any estimate within 8 or 9 percent of that number.

Thanks for your input.

rrr12345

"FWIW, I'm still holding with an IV estimate of about 1.54x BV, based on a couple of models, but I would not argue with any estimate within 8 or 9 percent of that number."

Here are some other estimates:

person, model, IV estimate, date, IV/BV
Tilson, two-column, May '25, $743K, 1.61x BV
Greg Warren, Morningstar, Apr '25, sum of the parts, $730.5K, 1.58x BV
Bloomstrand, sum of the parts, Dec '24, $783K, 1.73x BV
Highest repurchase price, 1.57x BV
rrr12345, weighing machine, Mar '25, $710K, 1.54x BV

Would other folks here please add more estimates, whether their own or ones they're seen? It would make an insightful histogram. I used to keep track of posted and published IV estimates. Sometimes I'd find as many as 25 estimates, representing over a half dozen different models, including two-column, look through earnings, DCF, sum-of-the-parts, etc. Typically the estimates had a more or less normal distribution with a standard deviation equal to about 9% of the mean. Thanks.

I'm trying to infer your estimate of current intrinsic value. If I understand you correctly, your 20-year average valuation is intended to give a smoothed valuation level that tracks IV, but which is not necessarily equal to IV. It's apparently the average of your two and a half valuation and 1.5 times the 16 quarter WMA of BV. Is this correct?


Yes. I do two valuation methods. I scale each of them to get the best fit to observed 20 year price (inflation adusted). Then I take a simple average of the two scaled smoothings.

Your current valuation level is $612,733, which corresponds to 1.554 times the 16 quarter WMA book value, which I calculate to be $394,284. It is also 1.326 times the March 31 BV/share.

I'll take your word for it : )
I admit that I do another adjustment that I didn't mention in that particular post. The rationale is that when book drops during a recession, it's unlikely to be a lasting drop in value. Book per share just before a drop might be a pinch exuberant, as in 1999, but probably not wildly so. So during a drop in book per share I limit the drop in my "adjusted book" to be no more than 4% of the peak to date. Then I feed those figures into the WMA.

From our recent discussion of IV/BV I understood, or misunderstood, your estimate of current IV to current BV to be flat over the last 25 years at a value of about 1.60. Certainly not 1.32 in Dec 1999 as I suggested.

I think I was speaking of flat in the sense of "no net change", same at start and end. The middle has been very different. The average P/B in the last 20 years is just a hair under 1.40. (using peak-to-date known book, which is generally a better measure of value).


Would you mind straightening me out? What would be your estimate of current IV to current BV?

I can't really say. The only thing my calculations say is that the current price has a relationship to this trend line that is 19% higher than the average such relationship in the last 20 years.

Perhaps surprisingly, I don't usually try to calculate IV as such. As you note, my metric is something that correlates with IV, and rises at the same rate, but is some unknown multiple of true IV. That's because (a) it's impossible to come up with a multiple that's correct for true IV so everybody would pick a different one, and (b) a tracking metric is all I need for my two purposes: how fast is value growing, and what's the current relationship between price and value estimate compared to what is historically typical?

I could make a stab at true IV in the past. For me, intrinsic value is the price that you could pay and sell 5-10 years later at an "average" market multiple and make inflation + 6.5%/year, basically Siegel's constant. So I could tell you what my rough idea of IV was for any date more than 10 years ago : )
Take the average real price in the last 5 years scaled to 2015 dollars, divide by 1.065^7.5= 1.6037, and that's the price 10 years ago that (with hindsight) would have been true IV in my books.

Jim

Fun with crude numbers

"...the ultimate safe withdrawal rate is to liquidate no more than the amount the value of the shares has increased... You could withdraw money forever, or at least as long as the real value kept rising"

......

"...the ratio of price to estimated value is a pretty good predictor of whether you're about to see unusually good or unusually bad price changes.

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"

So, I wondered: as the price:EV has been a pretty consistent long-term trend, then yet another way to think about the sensible "ultimate safe withdrawal rate" would be to add up the last 20 years of results:

0.15 times 0.178 equals 0.0267
0.15 times 0.148 equals 0.0222
0.2 times 0.1 equals 0.02
0.2 times 0.087 equals 0.0174
0.15 times 0.006 equals 0.0009
0.15 times -0.054 equals-0.0081

...with the sum of the RH column being 0.0791, implying an average 7.9% pre-inflation annual withdrawal would have been a sensible USWR 2005 - 2025

As the prices are not normalized for inflation, then the average CPI over the last twenty years of 2.5% needs to be subtracted, for a net USWR of 5 - 5.5%

Of course, this includes the highly questionable assumption that the next 20 years resemble the last 20, as regards Berkshire and the US economy in general and the CPI (which hasn't seen a 2.5% year since 2020).

But hey: you go to war with the data you have.

Anyhow, it further affirms my strategy of selling 1.125% current BRK holdings/quarter* being reasonable for at least the next few years, or until the effects of current policies begin to be reflected in market conditions.**

-- sutton

(*timing occasionally varies to current price/last known book: I sold the June 30 tranche in mid-March @ $522; conversely, I sold none at all during peak pandemic weirdness)


(**please, YWH, let this be at least a month or two before the midterms)

As an example, here is the list of IV estimates that I found for Dec 31, 2012. The document shows a histogram of the estimates as well as a table showing the sources. BV as of Dec 31, 2012 was $114,214, so the average IV estimate of $175K corresponded to 1.53x Dec 31 BV.

https://drive.google.com/open?id=1jR1lLKl3p8j0PnVU...

Oops. Wrong file. Here's the correct one.

https://docs.google.com/document/d/1qb8A-Ggo-2xeT-...

As an example, here is the list of IV estimates that I found for Dec 31, 2012.

Ahh, I remember the time well. Berkshire got cheaper and cheaper and cheaper, with the price having gone nowhere since 2017 but value steadily accumulating. I spent much of 2012 basically doubling my position, figuring that *eventually* the weighing machine would kick in. 2013 and 2014 were most satisfying.

Jim

The devil made me do it, I'm a devil's advocate: "Forget value, just use price. Make a table similar to Jim's."

Below is such a table, I made it using a price-only measure, i.e. no explicit valuation measure is used. It looks pretty similar to Jim's table (and to tables in previous posts where he binned P/B and related this binned ratio to forward returns).

Bin ForwardTwoYearReturn
1  17.8%
2  15.4%
3  13.8%
4  11.4%
5  12.8%
6  12.1%
7  7.9%
8  6.5%
9  5.7%
10 4.1%

To motivate the above table, consider the conventional P/E ratio. For BRK we often use P/B instead of E, where B is book value because book turns out to be a decent surrogate for intrinsic value. Or, get fancier and use Jim's two-and-a-half column valuation figure to stick in the denominator instead of book value. Whatever, stick something in the denominator. The devil told me to stick a price-only measure in the denominator, so the ratio depends only on famously irrational prices i.e. the very thing that value approaches are constructed to avoid.

To make the above table, I used a four year simple moving average (SMA) of BRK price (four years because Jim used 16 quarters to average his two-and-a-half column valuation figure) and I stuck this price SMA in the denominator of P/E for 'E'.
So, the ratio used is
Ratio = Price/SMA
where 'SMA' is a simple moving average of BRK price over the past four years.

I binned this ratio into 10% bins: bin 1 is the 'cheapest' bin i.e. contains the lowest 10% of the Price/SMA values, bin 2 is the next cheapest, and finally bin 10 is the most 'expensive' bin i.e. contains the highest 10% of the ratio's values. The associated return for each bin is the average annualized forward two year price returns within each bin, because Jim used average annualized forward two year returns in his table. I didn't take time to adjust prices for inflation, but I don't think this matters much to the main point of this post. BRK prices are from Yahoo and start 1996-05-09.

CONCLUSION:
The table above looks fairly similar to Jim's table built using his two-and-half-column valuation measure. But the table above was built using the price-only ratio above, which measures how far BRK's current price is above/below its four year simple moving average. No valuation involved. This table has significant predictive power, clearly it's best to buy when BRK is 'cheap' and not so great to buy when BRK is 'expensive', and the average two year forward return pretty much linearly depends on the bin.
Make of it what you will, the devil made made me do it.

I used a four year simple moving average (SMA) of BRK price (four years because Jim used 16 quarters
...
where 'SMA' is a simple moving average of BRK price over the past four years.

Yahoo historical only gives daily, weekly, and monthly. Not yearly.

So how did you do it? Just take the average of the last four December closing prices? Daily average of the last 4 years?


If/when I attempt to redo your interesting table, I'd be inclined to do monthly, maybe the last 48 months closing prices.

"Daily average of the last 4 years?" - Yep
Jim used weighted average, but I just did a simple moving average over the last four years, defined as the last 4*252 trading days.

"Yes. I do two valuation methods. I scale each of them to get the best fit to observed 20 year price (inflation adusted). Then I take a simple average of the two scaled smoothings."

Thank you for answering my questions, Jim. I appreciate it.

One more question, if I may. Have you tried other time intervals besides 20 years, say 30 years. When plotting price against BV I got a higher trendline as of Dec '16 and higher r^2 when the time interval used was 30 years or more. This was for plots of price vs BV through Dec 2016, with starting dates of 2000, 1995, 1990... 1965.

"Have you tried other time intervals besides 20 years, say 30 years."

I realize that using 20 years keeps you within the post 1998 growth period, but the price versus value relationship holds across all three growth periods, 1965-1980, 1981-1999 and 2000-2025. There are knees in BV vs time (semilog) at 1980 and 1999, but price vs BV (log-log) is unaffected.

Very interesting table.

tedthedog, could you give the range of ratio values within each bin?

"Unsurprisingly, the ratio of price to estimated value is a pretty good predictor of whether you're about to see unusually good or unusually bad price changes."

There has certainly been quite a bit of variation in price/value in the last five years. The ratio of price to known BV has ranged from 0.92 on 3/23/20 to 1.78 on 5/2/25, as the stock price rose from $239,440 to $805,883. If your table of forward returns applies for the next two years, then we can expect a total, real return of about -10.5% from the May 2 peak. In fact, we've already seen a -10.5% decline.

"Unsurprisingly, the ratio of price to estimated value is a pretty good predictor of whether you're about to see unusually good or unusually bad price changes."

The ratio is not only a good indicator of when to buy, it is also a good indicator of optimal asset allocation (in tax deferred accounts), if you're into tactical asset allocation. The top 30% of price/value lead to returns that are less that the yield on T-Bills. A Kelly type allocation between BRK stock and T-Bills might look something like the following, VERY CRUDELY, or perhaps a bit more heavily weighted toward BRK stock:

P/value bucket, optimal BRK/T-Bill ratio

bottom 30%, 100%/0%
next 20%, 67%/33%
next 20%, 33%/67%
top 30%, 0%/100%

Buffett might say 90% BRK/10% T-Bills all of the time, but the table says 0% BRK/100% T-Bills when price/value is above the 70th percentile of its range.

<<<Buffett might say 90% BRK/10% T-Bills all of the time, but the table says 0% BRK/100% T-Bills when price/value is above the 70th percentile of its range.>>

But Berkshire stock can rise very dramatically from ANY point at any time, and can keep rising for a very long time at any time regardless of valuation. You don’t have to be a long term owner to see this….just a recent 2 year owner experienced this.

So if you sold in the low $400s some time ago at a point of then high valuation… and you’re waiting for undervaluation you might very well have to pay $650 in a few years when it may be very cheap. Who knows? I’ve seen this play out numerous times over the years. Moving OUT of Berkshire or OUT of stocks in general is extremely risky. History works against you big time with passing time.

Listen to Munger, don’t play this game. This is such a simple game—so much easier than your advisor or your business media can afford to tell you. And if you choose to make it hard you will a
likely lose to default do nothing buy and hold. Fact is if you miss just a few days in equities over years—regardless of valuation— you lose a substantial part of the overall return. It’s very risky getting out, you’re also then forcing yourself to make too many other hard decisions. Why?

Unnecessarily interrupting natural compounding is the biggest mistake investors make, per Munger. The key Munger word there imo is “unnecessary”. You need cash this year, next year, you’re 90% invested in BRK and if declined 50%you’d be screwed—that’s NOT unnecessarily interupting compounding. Opportunistic selling to prudently raise liquidity or diversification sure!

But if it’s your brilliant 160 IQ that makes you think you’re smart enough to unnecessarily interrupt compounding …as Buffett advises sell 30 of those IQ points THEY are unnecessary—and I say—stop.

Is there an easy way to tell what dollar amount almost never will adjust upward for inflation? The only thing I can think of at the moment is current land holdings and current intangible assets. And I could be wrong about those two.

One more question, if I may. Have you tried other time intervals besides 20 years, say 30 years.

There is no particular time interval involved in creating the whole line. As mentioned, this is not a trend line fit, a technique which has no theoretical meaning or predictive power. This is just a moving average of very recent financial figures, average age under 1.5 years.

The 20 years of data was used only to set the scale...to move the entire resulting line up or down so the moving average line overlaps the price line better.

Jim

"and I say—stop."

I take it you're not a fan of tactical asset allocation. :) I'm not either, but even Buffett sells when the price is too far above fair value, as he did with AAPL. I considered trimming a little BRK.B when the P/B was 1.78 on May 2nd, but I didn't. I would have trimmed if the P/B had been 2.0. Too bad I didn't trim, though. Trimming would have saved me a 10% loss on the shares that I would have sold. And if BRK.B had risen 10% from May 2nd instead of fallen 10%, I would have been OK with that. I just have to buy, sell or trim when I think the expected return indicates doing so. It's too late to trim now, imo, as I think that BRK is selling at about fair value, not 15% above fair value. When the expected return on BRK.B or SPY or whatever is less than the expected return on T-Bills, it's time to at least think about trimming. I would definitely trim SPY, or VOO, now. Now is not the time to be heavily invested in the S&P 500. So much for 90% S&P 500/10% short term treasuries. Even though over the long term the S&P 500 will outperform short term treasuries, almost anyone will do better holding less SPY right now.

So if you sold in the low $400s some time ago at a point of then high valuation… and you’re waiting for undervaluation you might very well have to pay $650 in a few years when it may be very cheap. Who knows?

You know, this does not apply just to Berkshire stock but S&P 500 or any broad market index.

Zweig made fun of Cramer thrusting his hips at Buffett during the tech stock runup in 1997-1999. I think the last laugh is on Cramer the idiot savant.

None of us is smart enough to know which specific stock will beat the market in the long run. If you want to delude yourself like Munger did with BABA, go ahead. I am out. I know it's not Berkshire Hathaway.

In the context of this opinion:
Moving OUT of Berkshire or OUT of stocks in general is extremely risky

And it's opposite:
even Buffett sells when the price is too far above fair value, as he did with AAPL ... I would definitely trim SPY, or VOO, now

I find this current FT article vaguely interesting:

https://archive.ph/szVe3#selection-3517.4-3573.1

because I am wondering what that group about which the article is, dip-buyers, are doing:

The rebound in US stocks ... has been “powered by a buy-the-dip dynamic that by some metrics has been even stronger than that seen in the latter stages of the 90s tech bubble,” said BofA equity analyst Vittoria Volta.
...
But dip-buyers are playing a risky game by opting not to cash out when prices surge, according to Rob Arnott, chair of asset management group Research Affiliates.

If they this year bought in such masses and IF they then stay with their stocks (the article does not really claim that - but maybe they do?), who then would be left to buy? Just giving me a hunch of maybe it ending because of soon everybody - apart from this board of course - already being fully invested.

But if it’s your brilliant 160 IQ that makes you think you’re smart enough to unnecessarily interrupt compounding …as Buffett advises sell 30 of those IQ points THEY are unnecessary—and I say—stop.

This could be another winning mini quote!!!

>>>I take it you're not a fan of tactical asset allocation. :) I'm not either, <<

Your assumption is correct., I think it's generally a waste of time. I understand why it may have some value if done every 5,10 years or less frequently. But I suppose that might not quality as "tactical". So, I guess my answer is a firm NO.

I don't believe in cutting roses off at the stem. I don't believe in watering my weeds. Even when the flowers get tall relative to the weeds.

I would have "tactically" sold my Berkshire (now called Class A) at $16,000 when it was massively overvalued. And my "allocation" was WAY out of whack. Probably the only reason I didn't sell was the tax bill. The tax law MADE ME a successful investor lol. It taught me an important life lesson confirmed by life experience and reading. I was LUCKY. Now, in the words of Munger "you don't want to have to be lucky". "Gaming", the in and out timing of investments I've determined suitable for multiple decades, requires luck. Volatility is the gut-wrenching price we pay to be in this club. Its wild. Buffett: "Mae West was right...too much of a good thing is.... wonderful". For me: Rolaids over sell orders to deal with the "too much".

I'm not interested in waiting to buy Berkshire when its demonstrably cheap at $650,000 and it's tactically advantageous.

P.S.--this may be useless--but Manlobbi I hope you like the gratuitous Shrewd Snippets :)

"I don't believe in cutting roses off at the stem. I don't believe in watering my weeds. Even when the flowers get tall relative to the weeds." (LongTermBRK)

"Probably the only reason I didn't sell was the tax bill. The tax law MADE ME a successful investor lol." (LongTermBRK)

"Mae West was right...too much of a good thing is.... wonderful" (Buffett)

P.S.--this may be useless--but Manlobbi I hope you like the gratuitous Shrewd Snippets :)

I read them! And I was just about to involuntarily reply with a message "There you go again, the Shrewd Snippets keep coming!" and then read at the end of the post that you had formulated them intentionally. Highly creative, wise (in our investing-context) and even poetic this time.

- Manlobbi

tedthedog, could you give the range of ratio values within each bin?

Here's the lower limit and upper limit of the ratio values in each bin (with the mean CAGR per bin, as before).

Bin          Lower          Upper        MeanCAGR
  1         0.6609         1.0137         17.8
  2         1.0141         1.0800         15.4
  3         1.0800         1.1144         13.8
  4         1.1145         1.1430         11.4
  5         1.1430         1.1759         12.8
  6         1.1759         1.2128         12.1
  7         1.2128         1.2527          7.9
  8         1.2528         1.3059          6.5
  9         1.3060         1.3684          5.7
 10         1.3684         1.5694          4.1

Here's a link to a scatterplot of CAGR versus the SMA based 'value' measure, i.e. a plot of the data that made the above table
https://www.dropbox.com/scl/fi/nlj5dhm9mpoizonczxe...
One can see a definite trend where BRK has better forward returns when it is 'cheap' than when it is 'expensive'. FWIW, the correlation is -0.42

One can also see that a table that reports the mean value of CAGR in bins of the 'value measure' can provide an unclear view of the data.
Given the relatively short forward return period, such a plot using Jim's value measure would probably also look messy, i.e. a broad smear, but I'd guess less "gappy" in the vertical directions at the ends.

Here is yet another way of showing forward return versus starting P/IV estimate (or metric related to IV).

https://drive.google.com/open?id=1rcBUAK9j8ZmBvHrw...

Sorry, Google keeps using a version of the graph before I corrected some formatting, but I think it's legible. The graph shows the forward, 3-year, nominal, annualized returns starting from Dec 31st 1999. The estimated P/IV comes from the weighing machine model. The returns are:

starting P/IV estimate, mean return
0.7, 18%
1.0, 11%
1.5, 0%

Today the estimated P/IV is 0.98.

Just FWIW.

It's not necessary to estimate P/IV for the x-axis. P/BV works, too. Here's a plot of 3-year return vs P/BV. Once again Google messed up the formatting when I uploaded the file, but it's still legible. Google also changed the trendline to linear from a third order polynomial. Third order polynomials fit normal distributions and skewed normal distributions better than do liner fits, but it's no matter. A third order polynomial just bends the left had end of the trendline up a bit and the right hand end of the trendline down a bit. I used the ending BV for the quarter, but beginning BV for the quarter works just as well.

https://drive.google.com/open?id=1mgbcOlMYUxT5_R1o...

If I could show a third order polynomial trendline, you would see that the trendline changes from being curved upward (on the left) to curved downward (on the right) at a P/ending B of about 1.5, where the 3-year return is 10%. At a P/ending BV of 1.0 the 3-year trendline return is about 22%, and at a price/ending book of 2.0 the 3-year trendline return is about -2%. The tendline return at a P/V 1.4 is about 11%, and at a P/B of 1.6 the trendline return is about 9%.

If I could show a third order polynomial trendline, ...

FWIW, I used to do that a lot, looking at the correlation between past returns and initial starting value and building nice fits.

Ultimately I decided that there was a different way to come up with a reasonable expectation for forward returns that was both more reliable AND vastly simpler to do.

First, the comment about more reliable: the problem with historical forward returns is that in the past, the stock has tended to overshoot. After a period of high valuation, the slide has on averaged continued right on down past the typical valuation range into the cheap range, often very cheap. Thus, the historical record shows that the average return after high valuation levels is not merely bad, but ghastly, as the end point has on average been at a point of substantial cheapness. This overshoot effect might happen again, but more to the point, it might not. A far more conservative and reasonable assumption would be that the end point is merely a normal valuation level, not super cheap.

So, the vastly simpler method. First, pick a value yardstick. I'll use book per share as an example, but it could be whatever metric you prefer. First, estimate what the average valuation multiple will be in the future dates you're interested. Let's say you think that the average P/B in the next few years will be 1.45, a bit higher than the average in the last 20 years because, well, recency bias? Doesn't matter, pick any number. Now, estimate how fast your metric is likely to grow in a typical year. Book per share, as with almost any decent value yardstick, has grown at inflation + 8%/year for ages, so let's pencil in inflation + 7%/year for a bit of conservatism. Then it's pretty easy: Maybe you want to estimate what the likely stock return will be for the next 2-3 years. Take today's level of your preferred metric, add two or three years of growth, multiply by the valuation multiple you think will be normal, and you get a likely future price. Divide that by today's price and annualize the result, and you have probably the best single estimate possible of the likely return in the time frame you're concerned about. Voila!

e.g., using the example figures above, known book per share is $455055 at the moment. Two and three years of 7% growth give future book of about $521k and $557k in today's money. At 1.45 times book that means prices around $755k and $808k in today's money. The price is $715720 at the moment, so the estimated likely 2- and 3-year returns are inflation + 2.7%/year and inflation + 4.1%/year respectively. TIPS would probably get you around inflation + 1.5% in US dollars, so Berkshire stock at this price is a better bet, but not going to make you rich. As the current market price falls, the likely forward rate of return obviously rises.

A fancier share valuation model might improve that guess a bit, but in the end I concluded that fancier methodologies won't. There is no real need to peer really deeply at the historical record other than to inform your sense of what constitutes a reasonable expectation of future valuation multiples. It's true that this method requires you to make a couple of very explicit assumptions about things that are not certain, but other methods make them too, just a bit less obviously.

Jim

"FWIW, I used to do that a lot, looking at the correlation between past returns and initial starting value and building nice fits. Ultimately I decided that there was a different way to come up with a reasonable expectation for forward returns that was both more reliable AND vastly simpler to do."

Thank you, Jim. I also use the method you describe. It works quite well, especially for forecasting returns over longer time periods than 2-3 years.

"This overshoot effect might happen again, but more to the point, it might not. A far more conservative and reasonable assumption would be that the end point is merely a normal valuation level, not super cheap."

With Berkshire repurchasing shares when they're cheap, the overshoot on the cheap side might be more mooted in the future. However, as you know, since Dec '99 the overshoot has been substantial, with P/B ranging from 1.0 to 2.0.

Here are the returns vs P/BV with a 3rd order polynomial, rather than linear, trendline (finally). The returns have a skewed normal distribution.

https://drive.google.com/open?id=1S76nR8b-x-sXR4n3...

However, as you know, since Dec '99 the overshoot has been substantial, with P/B ranging from 1.0 to 2.0.

Indeed. And 2007 especially.

My point is merely that if you look at the historical average of forward returns from any given valuation level, and thinking of that average as a forecast for the future, you are implicitly assuming that there WILL be an overshoot again, at least to some degree. I think a more parsimonious model is to assume a typical valuation level in future.

It took me some years to notice this flaw in what I had been doing...it didn't jump out until I had models of the two different styles which were giving very different expectations for the same forward time frame and built from the same amount of history and same starting valuation level. This led me to ponder which was likely better expectation, which I ultimately decided was "expect the typical". It's purely a bonus that it's dead easy. I have a spreadsheet with thousands of rows and now I only use four of them : )

Jim

in the past, the stock has tended to overshoot. After a period of high valuation, the slide has on averaged continued right on down past the typical valuation range into the cheap range, often very cheap.

This raised my curiosity so I updated my version of Jimīs chart of "Price / smoothed Peak BV":

https://drive.google.com/file/d/1flfn7xrCqY_b0jOid...

According to that
- Itīs price moves around the yellow line, in a channel of "1.2-1.55x smoothed PeakBV"
- Since 2005 (I donīt count that before) it deviated only 4x a lot upwards from the yellow line and reached or broke through the upper border of this channel: 2007/8, 2014/15, 2021/22, 2024/25
- Each of the previous 3x within 1 year (2008 and 2015) or 1/2 year (in 2022) it overshoot itīs typical line and continued to slide down to the lower border or (2009) even lower
- What happens the 4th time (Now!) remains to be seen, but from this history it doesnīt seem unlikely that it may (again) continue itīs slide down to 1.2 x smoothed PeakBV
- Or maybe even lower, as in 2009? The peak before was the only one from which it went not just straight down (as in 2015 and 2022), but held that very high valuation for a long time --- like now! And then it "crashed" completely

- Each of the previous 3x within 1 year (2008 and 2015) or 1/2 year (in 2022) it overshoot itīs typical line and continued to slide down to the lower border or (2009) even lower

Seems right.

But perhaps this is almost a little like sorta a tautology going on here. Recall that my own smoothed value line was scaled up/down to give the best match to stock price history. So more or less by construction, the price is going to be above that trend about half the time, and below the other half. So if it has been up for a while and starts sliding, a move down below the average is necessarily going to happen sooner or later (to keep the average right with equal and opposing ups and downs on average), so it wouldn't be surprising if that were right away while momentum is down.

I guess I would have to agree that an overvalued (technically just more-richly-valued-than-usual) stretch being followed by a cheaper-than-usual stretch is more than a 50/50 shot, but I still prefer to assume agnostically that the price will be typical at the end of the investment interval I'm interested in, rather than try to in effect forecast a future cheap stretch! Enough people call me a permabear already.

Speaking of permabears, I'd be embarrassed to admit how much I've made since May 2 being net short Berkshire stock. Per the reasoning above, that's not a bet on the stock getting cheap, merely a wager that "richly valued" would be followed soon enough by ordinary valuation. I don't think the price slide has anything in particular to do with anything from the annual meeting, just predictable mean reversion (in outcome if not timing). Over time, the price isn't going to rise faster than the value.

Jim

Since the annual meeting on May 3 it has been a steady decline. Down 11% in just about 2 months. From 539.80 to 478.27 on the B shares.

richinmd, you are absolutely right. I just woke up after just 2h. Apparently my unconscious was thinking the same "This canīt be. Where is the 10% drop we experienced"?

As last time I updated this table/chart again a wrong number crawled into my spreadsheet: $716450 as closing price of BRK.A on 03/31/2025. A "little" on the low side. Please wait a little. I already uploaded the corrected chart to my Google drive, but for whatever reason each time I try to post the new link in the "preview" here the old uncorrected chart is shown. Maybe I should log out and in again. I continue to try until it works.

Here now the chart with the correct closing price on 03/31/2025 of $798442 (instead of the
$716450 that crawled into my spreadsheet before):

https://drive.google.com/file/d/1p7k97ln8TkgclzmON...

Far more dramatic as now it even much more resembles the situation of 2008.

>>I guess I would have to agree that an overvalued (technically just more-richly-valued-than-usual) stretch being followed by a cheaper-than-usual stretch is more than a 50/50 shot, but I still prefer to assume agnostically that the price will be typical at the end of the investment interval I'm interested in, rather than try to in effect forecast a future cheap stretch! Enough people call me a permabear already.<<

When you say "typical" price, are you referring the the mean P/BV, which over the last 20 years has been 1.4, or are you referring to the mean analyst estimate of fair value, which is about 1.6?

My own estimate of IV (FWIW) is about 1.54x BV. Berkshire's price was 12% above that (P/BV = 1.78) on May 2, immediately before the annual meeting, and has now fallen to 1.54x estimated June 30th BV, i.e., very close to my estimate of IV. The decline in price began on the first trading day after the annual meeting, which is more than coincidence imo, but that's another story.

So we're left with two questions: (1) How far will the price fall? and (2) at what price will Buffett repurchase stock, as his repurchase price will affect the stock price?

This permabear thinks (or wildly speculates) that the stock will fall lower over the next three months, perhaps by another 12% to 1.35x BV, unless Buffett comes in and repurchases stock at 1.5x BV, as he did in late 2023.

As Yogi Barra said, "Predictions are difficult, especially about the future."

“Far more dramatic as now it even much more resembles the situation of 2008.”

Ronald Coase wold probably agree…

https://www.reddit.com/r/datascience/comments/dv7m...

ciao

When you say "typical" price, are you referring the the mean P/BV, which over the last 20 years has been 1.4, or are you referring to the mean analyst estimate of fair value, which is about 1.6?

The former. I try never to give an opinion on what a share is actually *worth* at any given moment. I tend to look only at what it's likely to trade for, given the usual relationship between a value metric (book or whatever) and market price. Like most observers, I assume that true fair value is higher than the market price most of the time, but I don't try to calculate where.

So we're left with two questions: (1) How far will the price fall? and (2) at what price will Buffett repurchase stock, as his repurchase price will affect the stock price?

Lacking any better information, I assume that the price will fall to a valuation level around 1.4 times book at some point in the not too distant future, something I would probably say no matter what the current level is. It will then go either up or down. At that level, Mr Buffett seems quite happy to be a buyer, with some certainty at any level below about 1.48, so I assume that he will resume buybacks in the not too distant future.

This permabear thinks (or wildly speculates) that the stock will fall lower over the next three months, perhaps by another 12% to 1.35x BV,

That wouldn't surprise me at all. The stock has traded below 1.35 times peak-to-date known book over 40% of the time since January 2008, 17.5 years ago. I just don't find myself with any good reason to have a strong opinion about it happening in any particular time frame. If we see a big bad bear at some point, I expect Berkshire's price will get dragged down with everything else for a while.

Even now, it's not crazy for a person to at least start thinking about bullish positions. For example, January $460 puts would get you about $15.50 today. If exercised, you'd get a net entry price of $444.50, which isn't so bad. If book at year end is (say) $322, you'd be entering at 1.38 times book, a bit below average, which would probably do fine over time. If not, that's a 6.4%/year rate on the cash committed to add to whatever you're already earning on that cash, say 3.5-4%, for a total of ~10%/year rate. Who counts on anything more than that? As the price falls, this type of deal could get more interesting. At some point there's no need to get fancy, the optimal strategy becomes simply "buy the damn stock".

Jim

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