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A while back there was a post on the long run trend of Berkshire.
I added a comment to the effect that it's a bad idea to use the long run trend line to say anything about current value levels.
I later realized that my comment may have been taken as a bit harsh and dismissive, which was definitely not my intent.
I just wouldn't want someone to make investment decisions using a method which could go very badly awry, which I think is a real danger there.

So, in a more constructive vein, have a look at this chart for something I would suggest as a substitute
www.stonewellfunds.com/PriceAndWMAofValue.png

The blue line is just a chart of the average real stock price in each calendar quarter.
The smoothed value lines look a lot like a long run trend, but it's just a smoothing with an average lag of 1.25 years, so it will adapt reasonably quickly if/as Berkshire's trend rate of value growth slows.
There isn't nearly as much danger of extrapolating a happy long run trend and being way off base when valuations stay below that.

The smoothing is constructed like this:
First, the pink smoothing line.
For each quarter, I start with book per share.
Adjust each historical figure for inflation at the end-of-quarter date to get real book, call that "A".
Create a separate column for peak-to-date real book per share, and then multiply those by 0.9. Call that 90%-of-peak for each quarter "B".
Why 90%?
The theory on this is: during really good markets book per share may be an overoptimistic estimate of value per share...but almost certainly not by more than 10%.
Any drop in book per share of more than 10% is almost certainly a transient mark-to-market issue and isn't something to worry about.
Next, take as your value for each quarter the maximum of current real book per share ("A") and 90%-of-peak ("B").
Next, for the smoothing: do a WMA16 of that series.
For those who aren't familiar with the jargon, that's a weighted moving average using 16 data points.
The most recent data point is given weight 16, the second-last is given weight 15, the third last 14, and so on down to a weight of 1 for the oldest data point.
This reacts to changes quite a bit more quickly than a simple moving average. Think of it as something in the middle grounds between the raw data set and a simple moving average of the data set.
And last step: take that WMA and multiply by 1.50.
Why 1.50?
I looked for the multiple that gave the best fit to price data.
I gave squared errors in the fit to the price data 1999-2003 a weight of 1, 2003-2008 a weight of 2, and 2008 to date a weight of 3.
The best fit result was a multiple of 1.5004 times the weighted moving average of real book. We're among friends, so call it "one and a half".

It is my belief that this moving average line is much more reliable than the long run trend line.
That is, if the stock price is meaningfully below this trend line, the stock is very probably trading at a better-than-average valuation multiple and vice versa.
It reacts to slow periods in observable growth in value reasonably quickly, generally without assuming that value per share actually falls in a bear market.
The current price is roughly 3% below the trend line.

The yellow line on the graph is the same type of WMA as the pink line.
The only differences are
* I started with my quarterly "two and a half column" value metric rather than book per share.
This values operating subs as a multiple of their earnings rather than book, and includes (among other things) a haircut on large stock holdings at high valuation multiples, notably Apple and Coke.
* I assumed that this metric is never a cyclical overestimate of more than 7% rather than the 10% I used for book value: the "2.5 column" metric is a bit more stable.
This 7% number is selected based on the size of the impact from the largest stock overvaluation haircut I have done to date.

You can see that both methods give very similar results once the smoothing is done.
Book may diverge from fancier metrics of value over time, but this similarity so far is the source of my frequent comments to the effect that book per share may no longer be a theoretically sound yardstick of value, but so far (and only by coincidence) it gives results which are not meaningfully different.
For now, rules of thumb about valuation at various multiples of book are as good as they ever were. So far.

Jim

Nice analysis. I do have a question about the pink line as of Q1 2000, though. The high and low prices during Q1 2000 were $57,800 and $40,800 respectively, and the beginning and ending BV/share were $87,987 and $37,013 respectively. That puts the low P/B during the quarter at 1.07 using the beginning BV/share and 1.10 using the ending BV/share. At its low price for the quarter on March 10th BRKA stock was pretty clearly undervalued. I even recall Warren offering to buy back stock if anyone wanted to send in their certificates. However the pink line suggests that BRKA was overvalued. Where do you think the discrepancy lies?

Also, do you think that it would help to go back to, say, 1995, just for perspective? BRKA stock was clearly overvalued in Q2 1998 at a P/B as high as 2.8. I think that it helps to see the value estimate at points in time when BRKA was clearly overvalued, such as Q2 1998 and Q4 2007, and at times when BRKA was clearly undervalued, such as Q1 2000, Q1 2009 and Q1 2020. In addition, in terms of value growth rate there was a sharp knee to a lower growth rate in about mid 1998. Just a suggestion.

Thanks for sharing,
rrr12345

The high and low prices during Q1 2000 were $57,800 and $40,800 respectively, and the beginning and ending BV/share were $87,987 and $37,013 respectively. That puts the low P/B during the quarter at 1.07 using the beginning BV/share and 1.10 using the ending BV/share.
At its low price for the quarter on March 10th BRKA stock was pretty clearly undervalued. I even recall Warren offering to buy back stock if
anyone wanted to send in their certificates. However the pink line suggests that BRKA was overvalued. Where do you think the discrepancy lies?

Good point.

The main thing is that I scaled the pink line to make it (on average) match observed prices mainly 2008 to date when valuation multiples have been much lower.
There was a time when 1.45 times book was a low valuation multiple, but in recent years that counts as above average.
What once looked low now looks not so bad. Using history to assess what counts as "cheap" is a tricky business.

A smaller secondary thing is that the lowest part of the price dip in Q1/2000 was quite a bit lower than the average price in Q1 or Q2 (which is what the blue line tracks).
The 2000-Q1 low was 18% lower than the 2000-Q1 average, and 27% lower than the 2000-Q2 average.

Also, do you think that it would help to go back to, say, 1995, just for perspective?

Frankly, no, since you ask : )
The growth rates and multiples were huge back then, and equities were more than book value.
Those factors no longer have anything to say about the valuation or prospects of Berkshire stock. It's not really the same business.
Consequently I don't really think it's meaningful to go back more than about 15 years for a baseline.
There seems to have been a big and permanent step downward step in valuation levels at the onset of the credit crunch, so for now it seems that "2008 to date" is what seems most useful as a definition of normal.

Usually you'd expect the valuation multiples to fall back as the business results moderate. But nope.
Oddly enough, value has risen faster and faster in the last decade than in the previous one, but valuation levels remain very modest by pre-2008 standards.
The ten year rate of change of smoothed real book has gone from inflation+6.1% in 2010 to inflation+7.9% ending in 2015 to inflation+9.4% ending in 2020.
Similar lately.
Those are inflation adjusted numbers, so the recent spike in inflation should if anything have caused the recent data to look bad.
Heck, we're probably due a few years of poorer growth rates in real observable value. Things have been suspiciously good lately.
I generally count on inflation + 7% over time, and hope for inflation + 8%.

Jim

As with any trend line of value that roughly tracks price over time, it's not a bad predictor of stock returns.
I calculated the stock price divided by a simple average of the two smoothed value methods since 2008.
I used the value estimate for a given quarter starting on the release date of those statements, not when the quarter ended.
Dividing all start dates since January 2008 into 25 equally sized buckets, these are the average one year forward returns:

Inflation + 32.5%  (starting the 4% of days with the lowest ratio of price to smoothed value estimate)
Inflation + 26.1%
Inflation + 23.1%
Inflation + 19.8%
Inflation + 18.7%
Inflation + 13.2%
Inflation +  9.8%
Inflation +  7.1%
Inflation +  6.0%
Inflation +  3.1%
Inflation +  6.6%
Inflation +  6.8%
Inflation +  2.7%
Inflation +  1.7%
Inflation +  0.6%
Inflation +  0.2%
Inflation   -1.8%
Inflation   -5.6%
Inflation   -6.5%
Inflation   -8.8%
Inflation  -13.3%
Inflation  -24.1%
Inflation  -26.9%
Inflation  -19.1%
Inflation  -32.2%   (starting the 4% of days with the highest ratio of current price to smoothed value estimate)

Depending on whether you look at data from 1999 or 2003 or 2008, models applied to today's ratio suggests one might anticipate a one year forward return of inflation + 14.0% to inflation + 14.9% from here.
That's starting from a price of $480795 (320.53 per B) and CPI 301.836.

That's if the next year resembles the range of the last 15 or so years in both value growth rates and valuation multiples, which it might not.
In essence, this value model is highly dubious of the recent drop in book per share as an indicator of a lower value per share.
Consequently it thinks the current valuation multiple is a bit below the average of recent years, maybe 5%, not a bit above.

Jim

Thanks Jim, appreciate you posting this.

Are there other stocks beyond BRK that you've had success in applying this approach to predict likely forward return?

Jim, as you know at times I'm a tad over in the cynical side LOL. But the info you publish here is quite extraordinary for when to buy and maybe sell Berkshire. So...

Do you have any the data as to the longer term (and the longer the better) outcome of you personally doing this assuming it is a tax free operation? It would be quite fun to have this seen.

Nice, Jim. Quite a range of 1-year returns, and quite a strong dependence on starting price/value estimate.

I did a similar analysis looking at forward 1-yr, 3-yr, 5-yr and 10-yr returns versus P/estimated value over periods between 1965 and 2022. For the estimated value I used the trendline (power law) of the plot (log-log) of price versus book value since 1965. Price versus book value has an extremely good fit. For 1-yr returns versus P/value over the period Dec 1999 to Sept 2022 I get similar results to yours. As you might guess, the 3-yr forward return versus P/value had considerably less scatter than the 1-yr return vs P/value. Plots for the period Dec 1999-Sept 2022 were much flatter than the plots for Dec 1964-Sept 2022.

The extremely good fit of price versus value is what makes this analysis useful as a predictive tool. Several year ago I looked at price versus sales, book value, operating income and net income for the companies in the S&P 500 from 1962 to 2017. Berkshire Hathaway's price versus book value had the highest r^2, 0.994, of any price versus metric of the S&P 500 companies.

Are there other stocks beyond BRK that you've had success in applying this approach to predict likely forward return?

There are different kinds of stocks.
Berkshire is in a relatively small category of firms with a relatively steady and extrapolatable value growth trend, yet with high volatility in "blatant" short term results.
The problem here is just picking a suitable type of smoothing, which the top post attempts to do.
Just enough smoothing to get a relatively stable line--
but not enough to let the level of the trend line be too out of date compared to recent business results or to let you erroneously count on a given growth rate lasting longer.
The metric you use can vary a lot--earnings are most common, but for other firms the better metric is cash flow or book or sales or (rarely) even dividends.
Maybe Alphabet might fall into this category, using sales as the underlying metric (as their net margins are quite variable) and assuming that multiples will fall gently over time.

Other categories of firm it wouldn't be much use.
Some firms are relatively predictable--relatively steady progress in some obvious metric.
For those, you don't really even need an smoothing. Sometimes a simple P/E will tell you what you need to know. Think of Costco.
Is the observable range sensible given the speed of value growth, and is the current multiple higher or lower than its historical average?

Some firms have volatile short term results, but the overall trajectory of the firm isn't that predictable so smoothing won't help you.
Commodity firms will always track the unpredictable pricing cycles of the commodities in question, so smoothing will mislead.
Some firms really too much on very big concentrated bets, say Softbank or Fairfax, so smoothing isn't much use.
Some are at the mercy of unpredictable fashion whims, like Crocs.

And lastly, some firms look at first like steady growers but their business model is headed for a cliff.
The Schumpeter type, where stability leads inevitably to instability.
This often includes roll-ups, firms massaging their earnings, and fast-growth concept restaurants or specialty retailers.
Or fad-like tech firms riding a trend you know will end or at least top out.
Beware any bank-like entity growing much faster than the economy it serves.

The best source for ideas on this pick-a-metric-and-smoothing approach to mean reversion investing is probably Ned Davis.
They have a book, now somewhat dated, that shows the best metric to use and its range of multiples over time for many large cap stocks.
This is included in some of their services, though it's too expensive for most individuals, including me.

Jim

Do you have any the data as to the longer term (and the longer the better) outcome of you personally doing this assuming it is a tax free operation? It would be quite fun to have this seen.

Well, having an idea of the most likely expectation for the returns in the next year is a far cry from having a stock trading system.
An average can hide a whole lot of sins. A high valuation can be followed by a year of high returns sometimes. (see below)

I did once suggest swapping some of your stock to calls when P/B gets below 1.35.
For example, you might put half your BRK allocation into long dated calls with 2:1 leverage, giving you overall 1.5:1 leverage on your Berkshire position.
Then unwind that leverage and putting the proceeds back into plain stock again when P/B next got above 1.55.
Which might be several years later, of course.
That was a speculation, and when tested on some data was confirmed to have been not a bad "system" in the past.

The additional profits were large enough that the tax is the tail, not the dog: better to pay tax than not make more profit.
The bigger disadvantage is that once you start trading, you have to have the discipline to not make dumb trades.
To a first approximation, the average person's long run returns go down steadily with how many trades they do.

But really, the best advice would be:
(1)Whenever Berkshire stock is really really cheap, buy as much as you can. Then just never sell it : )
(2)If you have to sell some (to raise money to buy a jet, say...), try to do it when the multiples are high or at least above average.

On the subject of how good the predictor is---
Here is a slightly different table.
For start dates January 2008 to last year, what is the annualized forward return in the next 1.5 years?
For this table, I took the average (real) market price 1-2 years after the purchase date as the assumed sell price.
This gets rid of squiggles due to the randomness of the price on the precise 1.5 year anniversary.
In effect, it's the average annualized rate of return you'd get if you bought a bunch of shares on day 1 and sold 1/365th of them each day during the whole period 1-2 years later.
The addition to this table is that it show the worst, average, and best return from having purchased at each valuation level.
Start dates are divided into 25 buckets based on the starting valuation level, with equal numbers of purchase dates in each bucket.
All returns are inflation adjusted and expressed as annualized rates.

  Min       Avg       Max
 18.0%     27.7%     42.9%
 10.0%     24.4%     34.1%
  8.1%     19.5%     30.6%
  0.8%     15.7%     26.5%
 -1.8%     16.3%     23.4%
 -3.0%     12.9%     22.1%
 -4.4%      9.9%     21.5%
 -5.4%      8.1%     20.0%
 -6.2%      7.6%     16.8%
 -6.8%      4.9%     15.4%
 -6.3%      5.4%     14.2%
 -6.7%      6.1%     13.8%
 -7.1%      4.7%     13.1%
 -7.4%      3.6%     12.6%
 -7.7%      2.0%     11.8%
 -8.9%      0.6%      9.6%
-11.6%     -0.6%      7.5%
-12.4%     -2.0%      3.8%
-13.4%     -3.3%      2.5%
-14.8%     -4.3%      1.5%
-15.7%     -6.6%      0.4%
-17.6%    -13.1%     -1.3%
-21.2%    -16.0%     -2.0%
-23.3%    -13.6%     -3.5%
-26.1%    -24.5%    -22.4%

The lesson is that if you buy at a low valuation, the return you get is pretty reliably good, provided you sell on an "average" day rather than a specifically bad one.
And the reverse. (even more strongly so: there were no good returns starting from the highest valuation levels)
In the middle range, things are pretty variable.

Jim

Do you have any the data as to the longer term (and the longer the better) outcome of you personally doing this assuming it is a tax free operation? It would be quite fun to have this seen.


I posted on the the old MI board some trade history for one of my IRAs where I have been executing a similar strategy to what Jim suggests. If anyone is interested I can repost here if I can find it through DataHelper.

The quick summary is I purchased my first BRK position in that account on 1/16/2014 using all funds in the account to purchase BRK calls. Since that date I have owned a mix of BRK shares and calls the entire time putting on leverage when it looked attractive and pulling back on leverage when it seemed appropriate.

As of today my CAGR in that account is 23.7% at the closing bell for the weekend. I believe the S&P500 CAGR over the same period is about 9% plus dividends. I remain very pleased with the results and owe Jim a beverage of his choice should we cross paths (or maybe two tickets to Canada's Wonderland the next time he is on this side of the pond).

Jeff

"Depending on whether you look at data from 1999 or 2003 or 2008, models applied to today's ratio suggests one might anticipate a one year forward return of inflation + 14.0% to inflation + 14.9% from here."

Another variable that affects Berkshire's forward 1-year returns, besides starting P/B, is the return of the broad stock market, or more specifically the return of Berkshire's equity portfolio. Berkshire's equity portfolio, net of deferred taxes, still makes up about half of Berkshire's IV. In 2022 the S&P 500 declined 18%, while Berkshire's equity portfolio declined about 17% and BRKA stock rose just over 3%. Plotting the annual returns of BRKA stock versus the return of the S&P 500 from 1994 to 2022, the trendline return of BRKA when the S&P 500 returns -18% is -4%. Therefore one question regarding Berkshire's return over the next 12 months is, "What will the S&P 500 return over the next 12 months?"

The starting point for forecasting the return of BRK stock is value growth and P/value, which are currently about 10%/yr and 1.0, suggesting a forward return of 10%, but with the S&P 500 trading at a trailing P/E of 24, suggesting a return for the S&P of about 4% (considerably less if there is a correction in the next 12 months) I would lower the forecast for BRKA, possibly quite a bit.

Theoretically speaking, why would one look at alleged overvaluation of the S & P 500, if BRK does not hold the S & P 500? We can determine the P/E of almost all of BRK's public holdings directly, if we're worried about how forward returns are affected by present P/E.

If there is some empirical claim that the relationship nevertheless has value, I'm not seeing it.

"If there is some empirical claim that the relationship nevertheless has value, I'm not seeing it."

When the broad market declines or has a low return, all stocks tend to have lower than normal returns, whether overvalued or undervalued.

Jim, when you refer to "annual forward return", do you mean returns arising from

(1) looking at the trend line where the trend line is defined over the whole time period

or

(2) from looking at the trend line where the trend line is defined using data only available prior to each date?

The second one is "walk forward" and uses data only available to date.

(2) from looking at the trend line where the trend line is defined using data only available prior to each date?
The second one is "walk forward" and uses data only available to date.

Definitely this one...it would be useless otherwise, like one of the flaws of the dangerous/dumb "BMW method" charts with their crystal ball effect.

Similarly, in my tests the data for a given reporting period start getting used only when the statements are out, not when that financial quarter ended.

Jim

If anyone is interested I can repost here if I can find it through DataHelper.

It's a slow day at work and I was able to find the old posts in DataHelper. I found it valuable to reflect on my own actions so I'm reposting here with a current update at the end. I think I will try to keep updating periodically even if it is only for my own benefit :)

For anyone interested in the full discussion thread I think you'll be able to get to it through this link to one of the posts in DataHelper.

http://www.datahelper.com/mi/search.phtml?nofool=y...

''''''''''''''
Author: bluehorseshoe2 Date: 04/16/2021 06:25 PM Msg: MI-280987
: Re: brkb plus mechancial Recs: 4
I really learned a lot from this thread a few years ago and because historical options pricing is nearly impossible to find I thought it might be helpful to some to see an update of my transactions.

I did not own any BRK.b in this account prior to this trade.

01/16/2014: Buy Jan16 80s for $39.60 P/B 1.36x
12/14/2015: Sell Jan16 80s for $51.65 P/B 1.31x

Seemed like a good time to roll
12/14/2015: Buy Jan18 90s for $49.00 P/B 1.31x
12/01/2017: Sell Jan18 90s for $104.72 P/B 1.56x

It didn't seem like a great time to roll so I bought shares instead on 12/01/2017 for $193.67.

05/03/2018: Sold some shares for $190.13.
05/03/2108: Buy Jan20 120s for $79.25 P/B 1.36x (half my original leap position)

I bought too early once again but it was the first quarterly drop in book since 2011 and I believed it was temporary.

10/26/2018: Buy Jan21 130s for $82.00 P/B 1.37x (other half of my original leap position)


On 10/26/2018 I owned the following contracts:
Jan20 120s for $79.25
Jan21 130s for $82.00

9/30/2019: Sell Jan20 120s for $89.10

My estimate of Q3 ending book value had P/B at 1.33x so I took the opportunity to capture the bit of remaining premium and roll up and out.

9/30/2019: Buy Jan22 130s for $89.50

Before we look at the next transactions, let's just remember BRK.b dropped to $159.50 on 3/23/2020. I have to say I appreciate the advantage of un-callable leverage way more now.

1/12/2021: Sell Jan21 130s for $103.15

Jim might say to exercise that close to expiration but this is a retirement account and I'm limited in what trades I can do. With expected P/B at 1.22x at the time I chose to just roll up and out.


1/12/2021: Buy Jan23 150s for $92.90

As the share price has increased this year I decided today that it was a good time to pull back a little on my leverage with P/B being at its highest level since May of 2019. My personal estimate of IV is around $280 per B share and BRK has rarely traded this close to my estimate of IV.

4/16/2021: Sell Jan22 130s for $142.85
4/16/2021: Buy shares at $272.00 (56 shares for every contract sold because I had a bit of cash in the account)

So now I control a few less shares but I'll be waiting for another time when the forward returns with leverage look appealing to me. I still have my Jan23 150s for now for a pinch of leverage should the run up continue.

''''''''''''-

Activity after the post on 4/16/2021:

Well the run up did continue as BRK price and BV continued to rise as equity prices increased. I raised my estimates for BV and IV for Q2 and decided to sell half my shares and buy back half my leap position at about 1.32x P/B for Q2.

6/24/2021: Buy Jun23 200s for $87.50

The share price stayed flat even though BV and IV were increasing. I decided to sell my Jan23s and a few shares to increase my leverage by rolling up and out to the Jan24s and increased my contracts by 50% with P/B at about 1.32x for Q3

9/28/2021: Sell Jan23 150s for $130.00
9/28/2021: Buy Jan24 200s for $93.00

Now we get to the spring of 2022 and BRK is getting to multiples of P/B and IV that we had not seen in a long time. I decide it's time to reduce leverage.

3/9/2022: Sell Jun23 200s for 135.20
Buy shares at $326.04 with the proceeds

I also sell covered calls for the first time against my holdings. At the time I believed IV was forecasted to be about ~$350 for 2022 year end and BRK rarely if ever trades at my IV estimate.

3/9/2022: Sell Jan23 340s for $23.90
3/11/2022: Sell Jan23 340s for $24.65

The price of BRK continues to rise and I decide to reduce leverage further by selling 1/3 of the Jan24s I've only owned for 6 months.

3/17/2022: Sell Jan24 200s for $156.10
I did not buy any shares this time using the proceeds. With P/B at 1.51 I thought I would have a better opportunity.

The share price dropped quickly going into May so I decided to capture the the premiums from my covered calls. I moved much too early in hindsight.

5/2/2022: Buyback Jan23 340s for $14.45

I also buy a few shares as the price gets back under median P/B at the time.

5/9/2022: Buy shares for $314.55

Now the share price is falling quickly and soon we are trading at P/B below 1.3x. I never thought it would happen so quickly but I decide to start putting my leverage back on.

6/10/2022: Buy Jan24 200s for $113.50

As I've said before, I like to have expiration dates spread out for my leaps when possible so I take that opportunity here. Interest costs were higher than we had seen in a long time too so shorter duration looked more attractive.

6/14/2022: Buy Jun23 200s for $91.55

As the price of BRK started to rise in April this year I decided to capture the bit of remaining time premium on my Jun23 calls.

4/13/2023: Sell Jun23 200s for $118.25

And with P/B being at about median levels for what I expect Q1 BV to be I decided to roll up and out to Jan25. By far the most time premium I've paid but the most likely outcomes still look attractive to me.

4/13/2023: Buy Jan25 220s for $119.15.

In summary, I now have Jan24 200s and Jan25 220s for leverage and I own more shares than I have at any point in the past. I hope to hold onto my Jan24 calls until the Jan26 are available so I can continue to spread out the expiration dates, or maybe we will get lucky and BRK will return to higher multiples and I will reduce leverage again.

Jeff

Jim,

Thanks for verifying, it's what I expected. Please don't take any of my comments/questions as criticism, it's just that your results are so beautiful that I want to understand every detail. In the same vein, how about data used in this one, how was the 1.5 picked?
And last step: take that WMA and multiply by 1.50. Why 1.50? I looked for the multiple that gave the best fit to price data.

Also, are results e.g. the forward return bucket results, fairly robust to changing the WMA16? That's sort of an open-ended question, to be more specific in a worst case of sophistication, hopefully just a SMA still shows a significant trend?

A prior question to which Jim had replied is:
Also, do you think that it would help to go back to, say, 1995, just for perspective?
Side comment:
As many have noticed, a plot of price to book (logged), or even just share price (logged), versus time shows a distinct change in slope at the end of 1998. The GenRe acquisition was, perhaps coincindentaly, at end of 1998.

@ Value Trend
Several year ago I looked at price versus sales, book value, operating income and net income for the companies in the S&P 500 from 1962 to 2017. Berkshire Hathaway's price versus book value had the highest r^2, 0.994, of any price versus metric of the S&P 500 companies.
Wow, that analysis sounds extremely interesting! You don't happen to have any of the results of that lying around that you could post?

@Bluehorseshoe
I think I will try to keep updating periodically even if it is only for my own benefit :)
We'd all benefit if you would so generously continue to share.

because historical options pricing is nearly impossible to find
Actually, it's not so hard anymore to find historical options data at a semi-reasonable price. But I've found that it's hard to find good historical options data. Maybe data from ivolatility.com or other quite high priced shops are better. Data from, e.g. https://historicaloptiondata.com, and even data from the CBOE "datashop" (just google it), is NBBO data i.e. "National Best Bid Offer Data". You can read some anecdotes about NBBO data in Flash Boys (I re-read it recently, and found the book pretty disturbing). I've seen weird stuff going in historical NBBO data, e.g. Bids greater than Ask, also NBBO values that are silly (and changing) values even when volume and open interest are zero. The last is understandable if one realizes the data is NBBO i.e. national best bid/offer and not actual transaction data. Bid/Offer data is whatever the market makers (now algorithms) decide to post, and they seem to post some weird stuff some not insignificant part of the time, well, assuming that the historical data is an accurate record which may or may not be a good assumption. In a backtest of e.g. SPX, one can start off with some quite reasonable option, say something not too far ITM or OTM and with good volume and open interest, and then follow it in the historical record, and find that it enters a period of zero volume. And NBBO values can get whacky. What do you do in a backtest? Perhaps say that if volume goes to zero then you hold (because if you don't, at what whacky historical Volume=0 data value do you close the trade?). But, if you do that, what if Volume=0 right through to expiration (which isn't just a one-off thing), how do you close out the back test? Perhaps in response to this, CBOE uses something called VWAP data (Volume Weighted Average Price data) for some of their indices that track option strategies, see https://www.cboe.com/us/indices/benchmark_indices/ My understanding, which could be wrong, is that VWAP data is actual transaction data that's volume weighted over some time period, e.g. the half hour before noon. They use this apparently odd choice of time period to avoid whacky stuff that occurs at say the half hour before close. But when I asked CBOE if their VWAP data, which you can buy at greater cost from them than their NBBO data, would allow me to reproduce some of their option strategy backtests (https://www.cboe.com/us/indices/benchmark_indices/) the answer was emphatically "No!". The reasons were never made clear to me, and resolving the issue of whether and where I can get good historical options data will have to wait until I summon the energy to get back into the very gory details of such data. Meanwhile, I'm not sure I trust any of my option backtests, and by extension, currently am suspicious of much of what has been published in peer-reviewed business school academic papers on option backtests.

In the same vein, how about data used in this one, how was the 1.5 picked?
...
And last step: take that WMA and multiply by 1.50. Why 1.50? I looked for the multiple that gave the best fit to price data.

I guess my explanation wasn't very clear...

The WMA calculation is just a yardstick of value. An arbitrary number that it intended to rise at the same rate as observable intrinsic value.
Phrased another way, it's a number which, multiplied by an unknown constant, would give you the true intrinsic value.

Rather than trying to estimate what the correct constant would be for true intrinsic value, I picked the constant (a bit lower I presume) which best fits the history of market price data in the last several years.
Coincidentally that came out to almost precisely 1.50 times the WMA smoothing calculation.
So, in the interval I considered (mainly 2008 to date, with a bit of consideration for earlier dates), the price was above the 1.5 line about half the time.
I used RMS error to get the multiple which was the best fit to the price history, and out popped 1.5.

The practical use is this: if the current price is below the current WMA calculation scaled by 1.50, the implication is that it's cheaper than usual and shortish term results should be expected.
Assuming multiples and growth rates remain somewhat similar to those in recent years, of course.


Also, are results e.g. the forward return bucket results, fairly robust to changing the WMA16? That's sort of an open-ended question, to be more specific in a worst case of sophistication, hopefully just a SMA still shows a significant trend?

Yes and no.
It's not sensitive in terms of how well it "worked" in the past, but I chose the 16 quarter figure quite carefully.
With more smoothing from a longer lookback, you start to get a line that doesn't react for many years when the growth rate changes.
Since the growth rate has been remarkably steady in the past, this wouldn't have been a problem, but the whole idea was to find something that was just smooth enough but not too smooth.
With smoothing that uses too little data (shorter history), the problem is that it starts to squiggle around. You get quite visible dips in recessions.
At the extreme, you're simply using quarterly book per share as reported.
Four years (which I later changed to 16 quarters since I had the data) seemed a sensible compromise.
Dips in short term mark-to-market book per share during bear markets tend to come out as flat spots, sometimes with VERY slowly growing value per share in the early part of the dip.
That sounds sensible to me.
I personally don't think that the true value of Berkshire drops in recessions (or at least, hasn't in the past) so I'm looking for a metric which chimes with that belief.
But no more optimistic than that, no more.

Incidentally, the smoothing method was created some time ago, as a tool to solve a different problem: how much stock can you sell for income while never running out of money?
The answer is based on this thinking:
"... the fairly simple notion that ultimately what you can withdraw is a function of how much value your portfolio is generating.
If you value it sensibly on a regular basis, you can withdraw any gain and never run out of money."

Original post from 2015
http://www.datahelper.com/mi/search.phtml?nofool=y...
A follow-up of how it would have worked as a "safe withdrawal rate" method
http://www.datahelper.com/mi/search.phtml?nofool=y...

Jim

Very clear, thank you Jim!

Thanks Jim for sharing this terrific data with those of us that have lost our peak math and stats skills many years ago. The last link especially hits home personally & provides solid guidance and reassurance.

Cheers to all shreds who are part of the loyal BRK family! Making the pilgrimage to Omaha tomorrow for the festivities and might even order a medium-rare T-bone with a double order of hash browns in honor of our dear host. Looks like we may be lucky wrt the Weather- mid-high 70's with a good bit of sunshine.

Making the pilgrimage to Omaha tomorrow for the festivities and might even order a medium-rare T-bone with a double order of hash browns in honor of our dear host.


Enjoy! My neighbor works for a BRK company and they were invited to the meeting this year for the first time. Rumor is this is likely the last year Warren and Charlie will be doing the Q&A on stage. Could just be corporate gossip but you may be witnessing the final dance. We shall see.

Jeff

"A follow-up of how it would have worked as a "safe withdrawal rate" method"

Thank you for sharing, Jim. The survival of my retirement nestegg is of great importance to me, as I'm sure it is to many board members, and ideas on how safely to withdraw funds is very useful.

May I ask a question about the table of values in your 3/23/2021 post? The value shown as of the end of 2020 of 409719 looks to be inconsistent with the value shown in the chart at www.stonewellfunds.com/PriceAndWMAofValue.png. I'm sure that it's not, and that I'm just reading the chart wrong, but could you please help me? If I'm reading the chart correctly, the value, by both measures, looks to be very close to the price at the end of 2020, which was $347,815. The difference between that and 409719 cannot be the inflation adjustment, as the 3/23/2021 post was less than four months after the end of 2020. Where is my error? (See, I do try to read your posts carefully.)

Thank you for correcting my misreading, and thank you for sharing your estimates of value. I'm impressed at how well your estimates of value agree with the price history.

Sincerely,
rrr12345

The value shown as of the end of 2020 of 409719 looks to be inconsistent with the value shown in the chart at www.stonewellfunds.com/PriceAndWMAofValue.png. I'm sure that it's not, and that I'm just reading the chart wrong, but could you please help me?

I haven't delved into it, but it's the same method.
The two most likely differences are
* I probably used a different multiplier constant. The rate of change of increase should be the same between the two summaries.
* This is a different year, with a difference CPI level, so the inflation adjustment to the level of 2023 dollars gives different numbers.
Again, it should be the same slope with a slightly different final multiplier.


For any given analysis, just make sure that the prices are adjusted for inflation with the same final CPI number as the value estimates : )
It doesn't matter which date--which size of dollars--you use as long as it's consistent between the two.

Speaking of currency effect adjustments---
Though I'm sure nobody cares, I don't track my portfolio or net worth in US dollars.
The dollar itself is a bit volatile cyclically.
I calculate my portfolio value in dollars, then also convert it to euros, and take the simple average of the two numbers for each date.
The biggest currency movements are usually one of those two (usually the dollar), so the midpoint is a much better track of true purchasing power over time.
I nicknamed the simple average "mid Atlantic currency units", or MACU.
It sounds bizarre, but it gives a much less volatile and (I believe) more meaningful result.
No matter who you are or where you live, if the dollar tanks for a couple of years then a mattress full of euros has more purchasing power than a mattress full of dollars.
And vice versa, of course.
For a sense of the swings in the US dollar, check out this graph.
https://stockcharts.com/h-sc/ui?s=%24USD&p=D&st=20...
The US dollar index is the level of the dollar relative to all its trading partners, which is in effect a measure of the dollar movements since the average of all others can be considered a constant.
There is a big difference between the purchasing power implied by level 72 and the purchasing power implied by level 114.

Jim

Thank you.

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