I’ve been using wwwdotdatahelperdotcom and also the search engine on the new board to unearth some of Jim’s old posts on PriceToBookValue (PBV) for BRK, in order to record them on the new boards for posterity, or however long the new boards last. It wasn’t an exhaustive search, if others feel inclined to go gold mining then have at it!
I had an email exchange with Mark Wilcox who did datahelper, and if I understood correctly he has an archive of the old board and when the new boards abandon their history he’ll try to help out. But he commented that he doesn’t use the boards any more. Given that everyone has time constraints, it seemed worthwhile trying to preserve some relevant posts now i.e. below.
I wasn’t always able to capture dates in a copy/paste, but never mind, the following text was useful (at least to me).
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Author: mungofitch Date: 08/02/2020 11:50 AM Msg: BH-255100
Subject: Observations Recs: 40
No, not observations in the sense of insights, just some numerical observations in the sense of a science experiment.
I was doing some fiddling about and thought others might find these numbers interesting.
Given the ratio of market price to “peak to date” book per share on any given date in the past, look at the average market price 1-2 years later.
So, it’s a look ahead period of average 1.5 years.
The stock prices and resulting returns are adjusted for inflation and annualized.
Starting dates 2002-01-02 through 2018-07-31
Initial ratio of price to peak book Avg 1.5yr return
1% of time P/peakB from 0.928 to 1.076 30.3%/year
1% of time P/peakB from 1.076 to 1.112 24.2%
1% of time P/peakB from 1.112 to 1.132 24.9% We are in this bucket right now
1% of time P/peakB from 1.132 to 1.144 24.0%
1% of time P/peakB from 1.144 to 1.154 23.5%
5% of time P/peakB from 1.154 to 1.194 21.5%
5% of time P/peakB from 1.194 to 1.248 17.4%
5% of time P/peakB from 1.248 to 1.304 11.6%
5% of time P/peakB from 1.304 to 1.339 7.7%
5% of time P/peakB from 1.339 to 1.361 12.2%
5% of time P/peakB from 1.361 to 1.380 10.9%
5% of time P/peakB from 1.380 to 1.400 7.5%
5% of time P/peakB from 1.400 to 1.432 8.3%
5% of time P/peakB from 1.432 to 1.456 9.0%
5% of time P/peakB from 1.456 to 1.476 8.6%
5% of time P/peakB from 1.476 to 1.499 9.8%
5% of time P/peakB from 1.499 to 1.525 8.9%
5% of time P/peakB from 1.525 to 1.551 3.6%
5% of time P/peakB from 1.551 to 1.604 0.8%
5% of time P/peakB from 1.604 to 1.646 1.9%
5% of time P/peakB from 1.646 to 1.689 0.5%
5% of time P/peakB from 1.689 to 1.741 -0.9%
5% of time P/peakB from 1.741 to 1.805 -1.5%
1% of time P/peakB from 1.805 to 1.818 2.3%
1% of time P/peakB from 1.818 to 1.830 -2.8%
1% of time P/peakB from 1.830 to 1.846 -0.3%
1% of time P/peakB from 1.846 to 1.882 -6.9%
1% of time P/peakB from 1.882 to 2.032 -8.0%
I used the “peak to date” book value for the simple reason that dips in book per share have always
been transient in the past and using the peak-to-date value gives a stronger predictor of forward returns.
A lot of the good returns from purchases come from mean reversion of P/B values.
The interesting things is that the mean reversion is not complete in the 1-2 year time frame.
On average the P/B ratio has moved towards the long run average in that time frame, but not nearly all the way.
Here is a table showing the typical price-to-peak-book ratio from the same buckets as the table above, and the average P/B in the ending period 1-2 years later.
I added a column showing the change in book value ratio, and a column for a formula fit to the change.
Median Average Observed Model
Starting P/B Ending P/B Average Fit of
this bucket Change Change
1% of time 1.044 1.334 +0.290 +0.321
1% of time 1.106 1.328 +0.222 +0.233
1% of time 1.130 1.351 +0.222 +0.203 We are in this bucket right now
1% of time 1.142 1.355 +0.213 +0.188
1% of time 1.152 1.355 +0.202 +0.177
5% of time 1.184 1.347 +0.163 +0.144
5% of time 1.224 1.325 +0.102 +0.107
5% of time 1.292 1.314 +0.022 +0.054
5% of time 1.325 1.312 -0.013 +0.032
5% of time 1.352 1.387 +0.035 +0.016
5% of time 1.372 1.396 +0.024 +0.005
5% of time 1.391 1.364 -0.027 -0.005
5% of time 1.413 1.384 -0.029 -0.016
5% of time 1.446 1.422 -0.024 -0.032
5% of time 1.466 1.447 -0.019 -0.041
5% of time 1.489 1.492 +0.004 -0.051
5% of time 1.514 1.489 -0.025 -0.062
5% of time 1.539 1.435 -0.105 -0.073
5% of time 1.574 1.435 -0.139 -0.089
5% of time 1.629 1.507 -0.122 -0.114
5% of time 1.663 1.507 -0.156 -0.132
5% of time 1.717 1.501 -0.217 -0.164
5% of time 1.786 1.560 -0.226 -0.212
1% of time 1.814 1.678 -0.137 -0.236
1% of time 1.828 1.603 -0.225 -0.248
1% of time 1.842 1.640 -0.202 -0.261
1% of time 1.863 1.538 -0.325 -0.282
1% of time 1.938 1.525 -0.413 -0.369
These aren’t predictions for what will happen in future, just observations of what has happened on average in the last 16.6 years.
The future will probably show the same general effect, but with different specific numbers.
Either way, there seems to be no particular reason to expect good returns within a couple of years if you’re adding shares at higher than about 1.55 times book.
And probably the 1-2 year outlook is pretty good starting at under 1.35 times peak book.
Those two cutoffs would split history in two three sections, with these historical results:
P/B from 0.97 to 1.35 inflation+ 16.7%/year (25% of the time 2002-2018)
P/B from 1.35 to 1.55 inflation+ 9.0% (45% of the time 2002-2018)
P/B from 1.55 to 2.03 inflation -0.4% (31% of the time 2002-2018)
Jim
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Market valuation as a predictor
mungofitch
May 29
I was dusting off an old market prediction model I posted about ten years ago.
https://discussion.fool.com/cheap-stocks-at-a-predictor-or-filter-29492673.aspx
It’s pretty basic: How many of the VL stocks are cheap, i.e., P/E under 10?
Rather surprisingly it’s not a bad predictor of one-year-forward returns.
FWIW, 18.62% of VL stocks are notionally “cheap” on that definition at the moment.
That’s pretty high#somewhere around the 82nd percentile of history.
That is historically consistent with average one year forward returns of around 18.5% to 21.5% for an equally weighted VL stock portfolio, depending on the data smoothing you use.
(emphasis on “average”#an average can hide a lot of variation)
Normally the market valuation level is a terrible predictor of forward returns on time frames under a few years.
(with the exception that very cheap moments tend to lead to good results fairly quickly)
This metric seems to avoid that trap, perhaps specifically because the earnings figures being used are NOT cyclically adjusted.
It captures the apparent current earning power, rather than sustainable earning power: apparent earning power might matter more for price movements.
Incidentally, the predictor works with roughly similar variation and similar numbers among the S&P 500 set.
The percentage of “cheap” S&P 500 stocks right now is only 11.6% measured the same way.
So, to the extent that any of this reasoning holds water, the speculation would be that valuation
levels and forward one year prospects are worse among the S&P 500 set than among the rest of the VL set right now.
So, what would be the lesson? Go small or stay home?
Jim
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232427 of 284296 GoSubject: Cheap stocks at a predictor or filterDate: 8/21/2011 11:21 AM
P/E’s aren’t the very best predictor of individual stock performance or
of the broad market direction, because earnings vary wildly with the
business cycle. On the other hand, they aren’t totally useless.
Right now, earnings are well above trend, meaning stocks are expensive
relative to what they can sustain, but on the other hand stocks are
quite cheap as a function of current earnings which is better than nothin’.
So, I thought I’d look at a simple metric. How many of the Value Line
stocks have current earnings yields over 10%? (P/E under 10x).
Courtesy of the GTR1 backtester, we can see how the market has behaved
based on where this percentage likes. In this case, for “the market”
I took an equally weighted portfolio of all the VL stocks.
I looked at the fraction of stocks trading at a P/E of 10 or less
on any given date, bucketed those percentages, and looked at the
average one-year-forward total returns based on the starting percentage.
Starting percentile % of VL stocks Return
From 0 to 0.02 (0.012 to 0.021) -4.4%
From 0.02 to 0.05 (0.021 to 0.027) -1.7%
From 0.05 to 0.1 (0.027 to 0.036) 6.2%
From 0.1 to 0.2 (0.036 to 0.050) 9.9%
From 0.2 to 0.3 (0.050 to 0.062) 11.7%
From 0.3 to 0.4 (0.062 to 0.073) 9.4%
From 0.4 to 0.5 (0.073 to 0.088) 10.4%
From 0.5 to 0.6 (0.088 to 0.103) 14.8%
From 0.6 to 0.7 (0.103 to 0.121) 14.9%
From 0.7 to 0.8 (0.121 to 0.175) 23.2%
From 0.8 to 0.9 (0.175 to 0.239) 6.5%
From 0.9 to 0.95 (0.239 to 0.289) 18.9%
From 0.95 to 0.98 (0.289 to 0.344) 39.9%
From 0.98 to 1 (0.344 to 0.501) 57.5%
As you can see from the table, there is a clear correlation. If lots
of the stocks are trading at a P/E of 10 or less, the next year is
on average a whole lot better than average for market returns.
Today, there are 396 of 1700 stocks at least that cheap on current earnings.
That’s 23.3%, which is percentile .892 in the table above.
Top quartile in the table above suggests an average forward return of around 20.2% in the next year.
Again, this apparent undervaluation is probably partly a function of
today’s unsustainable earnings levels. But that has happened lots of times
in the past, too, so to a certain extent it’s baked into that projected return.
The trick would be to figure out which firms that are that cheap now on current
earnings will not have any meaningful slide in earnings with the next slowdown.
(not saying we’re about to see one, but there is always one coming).
Those firms should be very good buys right now, because the cheapness
is real, not just a cyclical artefact.
Anybody have a “cyclicality of earnings” metric for all the stocks?
Unfortunately VL’s earnings predictability rank is a short-run thing,
standard deviation of quarterly earnings over 8 years, not a cyclical metric.
But, starting with that, I poked around at a few Value Line reports.
A few that popped out at me were Medtronic, Torchmark, Constellation Brands,
Cracker Barrel, Entergy, Microsoft, perhaps less reliably (for varying
reasons) Best Buy, State Street, and my current fave Intel.
Exxon is a standout, cyclical but on a different kind of cycle.
The process I used is pretty simple: start with over 10% earnings
yield, sort by earnings predictability, pull up the stock report for each,
and look for (a) earnings that haven’t gone [much] down year-to-year in
the last two recessions, and (b) aren’t just flat either.
To cushion the fall a bit for the incorrect picks, I note that 58 of
the 396 firms at a P/E under 10 also have dividend yields of at least 4%.
15 of those are also rated Financial Strength A or better, 10 with A+ or better.
Those 10 comprise 3 oil, 3 guns, 2 drugs, one copper miner and Intel.
It’s quant, even if it’s not really backtestable.
Jim
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mungofitch:
I guess the question you raise is: Are the current earnings actually realistic, or are they cooked because of changes in the corporate climate?
Is it possible to do a similar analysis with free cash flow? This would reduce the variance of earnings which may be deviating recently. This presupposes that earnings are not being evened out by looking at the market as a whole (which may or may not be true)
I think they’re real earnings, not fake or cooked, I just don’t think they’re sustainable.
Any economy has earnings cycles, and the US is at or extremely near the top of one.
Earnings were lower a couple/few years ago, and will be lower again a couple/few
years from now, so today’s on-trend level of earnings is lower than the current observed level.
The trend line ist on the order of $20 lower in earnings on the S&P 500 level;
somewhere around the low $60’s, not the low $80’s which we’re seeing.
This is true only in aggregate, however: some firms will be doing even better
in the next recession than they are now, some about the same, and some will go bust.
It’s probably good to think today about how you can distinguish those classes.
There’s nothing wrong with irregular or cyclical earnings per se, but
it’s even more critical that you value that kind of company on the long
run trend and its likely future trajectory, not on the current level.
Jim
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Is it possible to do a similar analysis with free cash flow? This would reduce the variance of earnings which may be deviating recently. This presupposes that earnings are not being evened out by looking at the market as a whole (which may or may not be true)
Free cash flow is actually more volatile than earnings. The whole purpose of the income statement is to give a smoother picture of cash flow (Matching revenues with expenses). For ex., capital expenditures for Boeing are erratic, with huge amounts of spending lumped together followed by very little spending for several years.
Curious if testing SP500 components might be a more reliable predictor due to size, earnings predictability, liquidity, # analysts, etc… opposed to smaller cap, less liquid companies
Author: mungofitch 8/22/2011 3:34 PM
I checked it.
Extremely similar results, using the count of S&P stocks > earnings yield
10% (rather than count of VL 1700 stocks) to predict average VL stock return.
About the only difference is that at the bottommost percentiles the forward returns aren’t negative.
Percentile range Forward 1yr ret Forward 1yr ret
Using VL Counts Using S&P Counts
From 0 to 0.02 -4.4% 1.9%
From 0.02 to 0.05 -1.7% 7.4%
From 0.05 to 0.1 6.2% 5.0%
From 0.1 to 0.2 9.9% 7.0%
From 0.2 to 0.3 11.7% 12.0%
From 0.3 to 0.4 9.4% 10.2%
From 0.4 to 0.5 10.4% 7.5%
From 0.5 to 0.6 14.8% 12.3%
From 0.6 to 0.7 14.9% 16.6%
From 0.7 to 0.8 23.2% 21.1%
From 0.8 to 0.9 6.5% 7.9%
From 0.9 to 0.95 18.9% 20.8%
From 0.95 to 0.98 39.9% 36.1%
From 0.98 to 1 57.5% 65.3%
The current level is at the 91st percentile.
Jim
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Author: mungofitch
At the moment, it’s just over 30% of the stocks with a stated “Current P/E” ratio listed.
Using the table from the old post…
Starting percentile % of VL stocks Return
From 0 to 0.02 (0.012 to 0.021) -4.4%
From 0.02 to 0.05 (0.021 to 0.027) -1.7%
From 0.05 to 0.1 (0.027 to 0.036) 6.2%
From 0.1 to 0.2 (0.036 to 0.050) 9.9%
From 0.2 to 0.3 (0.050 to 0.062) 11.7%
From 0.3 to 0.4 (0.062 to 0.073) 9.4%
From 0.4 to 0.5 (0.073 to 0.088) 10.4%
From 0.5 to 0.6 (0.088 to 0.103) 14.8%
From 0.6 to 0.7 (0.103 to 0.121) 14.9%
From 0.7 to 0.8 (0.121 to 0.175) 23.2%
From 0.8 to 0.9 (0.175 to 0.239) 6.5%
From 0.9 to 0.95 (0.239 to 0.289) 18.9%
From 0.95 to 0.98 (0.289 to 0.344) 39.9%
From 0.98 to 1 (0.344 to 0.501) 57.5%
…that suggests we’re between percentile 95 and 98, and returns close to 40% would be predicted in the next year.
Don’t hold your breath for that, but at least it’s a bullish sign of hope in these awkward times.
Jim
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mungofitch
May 9
When the market drops, BRK’s book value also drops. So it would take lower price to reach 1.25 or 1.2.
True, but probably not particularly useful.
The ratio of price to “peak-to-date book per share” is a better metric of the company’s value.
Dips in book value at Berkshire tend to be transient.
Also, empirically it has also been a better predictor of forward returns in the past.
Buying at a medium multiple of depressed book value (low multiple of peak book value) has generally worked out very well.
Jim
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do you find this site reliable or calculate by hand:
Berkshire Hathaway Price to Book Value
mungofitch
By eyeball, it doesn’t match mine. Generally yes, but in the finer details no.
At a guess, it seems (?) they are using P/B at (say) Dec 31 2019 being the book value on that date, even though it wasn’t known till a couple of months later.
Personally, I track “published book”: the most recently published figure known on a given date.
Technically speaking, book value is something that exists only on a day that a set of statements is prepared.
And knowable only after that team tells you that result.
This isn’t just price changes in the equity portfolio#there are many accounting adjustments that are done only when a set of books is prepared.
Jim
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mungofitch
Here’s a really simple approach.
(a) If the valuation multiple is not unreasonably high, just invest any saved money immediately.
(b) If it is unreasonably high, wait till it is, letting the cash stack up for a while.
It’s up to you to decide what constitutes “unreasonably high”.
But FWIW, since the credit crunch, the average one year stock price return has been negative in real terms on purchase dates at or above 1.54 times peak-to-date published book per share.
The average one year forward return starting from P/B 1.50 has been inflation + 1.88%.
Jim
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Knighted:
Jim, thanks for the thoughtful responses. I plan to study the option strategy you suggested further. In the meantime, I did some additional backtesting of the approach you stated. I tested two flavors, but unfortunately both seem to be flops. Any thoughts on why that may be? What you state makes logical sense, but I struggle to reproduce a consistent advantage in backtest. I assume that’s because the missed opportunity during periods where P/B remains stubbornly high offsets the advantage by holding cash during these periods and buying in at lower P/Bs. (Note: I haven’t tested your other idea yet of gradually ramping up the P/B thresholds as time passes)
Pick a single P/B threshold, say 1.5. Invest any newly available funds immediately at any P/B below this, and hold onto newly available funds in cash at any level above this, investing the lump sum the first time P/B reaches that 1.5 threshold . I ran this through solver to analyze P/B values from 1.00 to 2.00 from Y2000 and again from Y2005 to date. Surprisingly, this showed negligible total return benefit even with the best parameter: the best produced around 1.5% advantage -total- from 2005, not annual.
Pick two P/B thresholds, say 1.2 and 1.5. Invest any newly available funds immediately at any P/B below 1.5. But if P/B is above 1.5, hold the funds that would have been invested in cash until it reaches 1.2 or below (although future funds would still be automatically invested in the < 1.5 range). I again ran this through solver to analyze all P/B values from 1.00 to 2.00 for each threshold from Y2000 and also from Y2005 to date. The 2005 to date produced a max total return around 8% higher than the baseline for the two optimal P/B thresholds. Still not much of an advantage, but something (+0.4%/yr). I also plotted all runs on a surface in excel to look for the largest cluster of groupings (trying to avoid picking an outlier) - these two special P/B thresholds fell within that. But to stress test the idea, I then ran the same backtest on Y2000 to date data and ended up with very different results. That advantageous P/B from Y2005 to date yields worse results than the baseline from Y2000 to date. This shakes my confidence in the approach, but welcome thoughts on why it should not.
#--------------------------------
BenSolar
I struggle to reproduce a consistent advantage in backtest. I assume that’s because the missed opportunity during periods where P/B remains stubbornly high offsets the advantage by holding cash during these periods and buying in at lower P/Bs.
I expect that’s the case. Berkshire is a stock that generally doesn’t go through a lot of gyrations, and the company is always piling up value, so going ahead and investing at first opportunity is basically as good as the valuation based schemes being proposed.
#------------------------------------
mungofitch:
Bear in mind that I’m not assuming that a multiple of book value remains a pretty good yardstick.
There are many good reasons to assume that a given P/B ratio might not mean the same thing over time, so that would be a bad idea.
Mr Buffett’s warning not to rely on it was a good warning.
Rather, I’m stating that it remains a pretty good yardstick.
That result may be because of a bunch of coincidences, and that might change at any time, but so far there is no divergence between a dumb multiple of book valuation model and what I believe is a pretty sophisticated one taking into account operating earnings, the value of float, cyclical adjustments on various units, etc.
A given P/B multiple is (so far) as good as it ever was, and means about the same as it meant many years ago. There has been no reason to assume that this would be the case, but it is the case so far.
Many expect the fair multiple of book to drift upwards ever so slowly over time.
But if anything, to the extent there is divergence between P/B and other valuation models, based on my figures the fair P/B is either flat or has slid down just a teeny tiny bit in recent years.
There are quite a few moving parts determining the “fair” P/B and its evolution. Over/undervaluation of big equity positions, buybacks, big acquisitions driving the fair P/B down organic growth and capex within subs driving it up, and inflation driving it up.
So far, those things are in balance within my measurement error.
Jim
#---------------------------------------------------
“One-year Forward Returns based on [high] P/E Level” Brooklyn Investor
You probably shouldn’t have been thinking about doing that study. Waste of time.
Earnings are so volatile that the current P/E ratio is pretty darned weak as a metric of market valuation level,
and market valuation in turn is very weak (nearly useless except when dirt cheap) as a predictor of forward one year returns.
When earnings are cyclically low, for example, high P/E ratios make perfect sense: low earnings are temporary.
Look instead a smoothed earnings, versus forward returns over a period longer than a year.
Then it all makes sense.
e.g, even since 1995, ignoring the older data that most people use to define “normal”.
Below, forward real total return ~7 years into the future based on buckets of starting trend earnings yield.
The figures shown display the range of outcomes for start dates with trend-earnings valuations in the buckets indicated.
(ending periods are smoothed, the average index level in a period centred 7 years later, adjusted for dividends and inflation)
Lowest Pctl 10 Average Pctl 90 Highest
Most expensive 5% of time -4.1% -3.8% -3.2% -2.5% -2.3%
Next 10% of time -3.4% -3.1% -2.1% -0.8% -0.1%
Next 10% of time -2.4% -1.9% -0.1% 1.8% 2.2%
Next 10% of time -0.5% -0.1% 1.5% 3.6% 4.3%
[current situation is between these two rows, assuming net margin levels of the last 10-15 years continue]
Next 10% of time 0.6% 0.9% 2.8% 5.2% 5.7%
Next 10% of time 0.9% 1.2% 2.6% 3.5% 6.3%
Next 10% of time 1.4% 1.6% 3.1% 3.8% 7.0%
Next 10% of time 1.8% 2.0% 4.2% 7.5% 7.8%
Next 10% of time 2.1% 2.3% 4.8% 8.6% 9.1%
Next 10% of time 3.2% 3.7% 6.4% 10.3% 11.2%
Cheapest 5% of time 4.7% 5.0% 9.7% 13.2% 13.6%
So, the best return seen starting in the most expensive 5% of the time has been -2.3%/year.
The worst return seen starting in the cheapest 5% of the time has been +4.7%/year.
So, the reasonable conclusions are that:
- Earnings need a cyclical adjustment before they have any utility at all in estimating market valuation levels.
- Valuations at purchase date matter than anything else in predicting forward returns in period over a couple of years.
- Trend earnings yields keep on working as a predictor even in the modern era.
- There is not much evidence that valuation levels, even properly measured, tell you anything much about the next year.
- To the best of my knowledge there is no useful market timing signal based on market valuations.
- You can’t debunk the notion that market valuation levels predict forward returns by looking at a bad model.
Jim