I’d be very interested, and assume many others as well.
There is an upload button, not sure what happens if you don’t upload a pic but try a pdf.
There is a hyperlink button but I assume you don’t have your own website?
I suppose dropbox or some other file share could work.
2 Likes
Thank you for your interest. Unfortunately the paper is a bit long, 16 pages, to upload into a post, and I don’t have my own website. I’d rather not use a file share app like Dropbox or Google Drive. Maybe I could just upload a few figures that tell the story.
1 Like
Very nice; thanks for the work and the thread.
Looking at your last plot:
And addressing the bottom-right corner, or the time that P/B has been the lowest over the last 25 years or so:
I think I can identify in it the macro trends of the 2008 housing bubble and the 2020 pandemic.
But the 1999 P/B drop was before both 9/11 and the 2000-011 dot-com crash…so I’m assuming that was (appropriate) GenRe pushback?
(And what happened in 2012, anyway?)
IIRC, BRK was added to the S&P 500 only ca 2009 (around the time of the BNSF purchase), so arguably became more sensitive to secular trends then
My thesis: as long as the corporate culture remains intact, then buying on a secular drop with BRK P/B <1.2 demonstrably safer than any other publicly listed equity I can think of
–sutton
4 Likes
Wow. Very nice, thank you!
A few questions prompted by you generously sharing your work:
Do you happen to have handy the unlogged version of the “Price/Share vs BV/Share” plot? If not, no worries, I’m not suggesting work! Just curious.
The “Price/Trendline, Oct 1964-June 2022” plot computes the trendline using all the data, then plots the ratio of the price on a given date to the trendline value on a given date, correct?
On any particular date one has data only on or before that date, so one can imagine computing the trendline on some date in say 1995 using data only on or before that date and no future data. You had remarked on importance of starting with sufficient data covering many business cycles, e.g. 30 years (1964 through 1994), that’s why I started with a hypothetical date in 1995. There’s about another 28 years of data from 1994 to now, almost equal to the initial 30 years.
Have you happened to have looked at the associated residual plots, QQ plots, etc?
Good thesis. Yes, 2012 was a head scratcher. Q1 2000 was, too. The market herd piled into tech and telecom in early 2000, calling Berkshire, Gillette and Coke “old economy” companies. Don’t we wish that we had bought in 1975?
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What happened in 2012?
As I recall, everyone was convinced “Buffett had lost it”. And maybe it was a fair argument going into 2012.
At the end of Sept. 2011 the trailing 4yr book value cagr was 5.7%, bottom decile of all trailing 4yr values since the listing of the B shares in 1996 through today. The R12 book value growth at the end of Sept. 2011 was 0%. IV only increases maybe 7% that year. Clearly the old man had lost it because shortly after the end of Q3 that year they announced the 1.1x buyback threshold.
Fast forward to the end of 2012, and R12 book growth was 14.4%, 4yr trailing book growth was 12.8%, R12 IV grew about 19%, and the old man increased the buyback threshold to 1.2x. Seems he was convinced the market wasn’t valuing Brk appropriately.
Maybe a similar situation today, or maybe not. Book value growth this year seems likely to be down or flat at best, however IV continues to increase steadily.
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I’m still in process of following up on Jim’s analysis, and @cwags02, and @rrr12345. Am using Morningstar data from 1990-05-31 to 2022-09-30.
I keep coming back to the following observations about a qualitative difference between pre December 1998 and post December 1998 BRK behavior. FWIW, the GenRe acquisition was reflected in BRK’s accounting in last quarter 1998. I thought I’d see what other people think of the following.
Here’s a plot of Price/Book (from Morningstar) over time, logged, i.e. log(P/B))
Blow up period 1998-1999
Clearly, something went on with a big increase in Book in last quarter 1998, more on that in a moment.
Here’s a plot of BRK’s A-share price, logged
share price (logged)
Eyeballing trend lines of log(price) against time: the trend looks steeper pre-1998 and shallower after.
Above is Morningstar price data.
I pulled down price data from Yahoo, it actually went back farther, and it show similar trend break
I don’t separately have Book data, my data is just PriceToBook = Price/Book, from Morningstar.
I can get Book by forming the ratio: Price/PriceToBook
Here’s a plot of Book
Zooming in on that big blip towards end of 1998 shows a big rise in Boook:
What’s up with that?
Here’s a quote for the 1998 annual report:
"Our gain in net worth during 1998 was 25.9 billion, which increased the per-share book value of both our Class A and Class B stock by 48.3%. (snip)
Normally, a gain of 48.3% would call for handsprings – but not this year. (snip)
To explain: Our stock sells at a large premium over book value, which means that any issuing of shares we do – whether for cash or as consideration in a merger – instantly increases our per-share book-value figure, even though we’ve earned not a dime. What happens is that we get more per-share book value in such transactions than we give up. These transactions, however, do not deliver us any immediate gain in per-share intrinsic value, because in this respect what we give and what we get are roughly equal. Charlie Munger, Berkshire’s Vice Chairman and my partner, and I can’t tell you too often (though you may feel that we try), it’s the per-share gain in intrinsic value that counts rather than the per-share gain in book value.(snip)
On December 21, we completed our 22 billion dollar acquisition of General Re Corp. (snip)
"
Comment 1: Point dislocations
Buffett explains a rise in book as basically an artifact associated with the GenRe acquisition and that it’s not related to an equivalent rise in IntrinsicValue. BRK made other significant acquisitions, e.g. GEICO, so one might expect other single point disclocations in BookValue due to these artifacts as well.
Comment 2: Trend dislocation
What’s bothering me is that there also seems to be a trend differences pre-1998 and post-1998. IOW, there seems to be more going on than just single point artifacts.
One sees this in a plot of log(Price), earlier.
One sees this in a plot of Book over time (admittedly, I infer Book from my Price/Book data, so what happens in Price is reflected in my Book):
and here it is again with log(Book)
One sees this in a plot of log(Price) vs log(Book)
One see’s a difference around log(Book)=10.5 or so.
Turns out those points to the left of 10.5 or so are from dates before Dec 1998, and to the right are after 1998. To show this, here’s a plot of data after Dec 1998:
slope=0.88036
Here’s pre-1998
slope=1.18913
Comment:
If you break the data into “before Dec 1998” and “after Dec 1998” then the regressions look much better (as one might expect, if there was one trend before and a different trend after). But what I mean by ‘better’ is not just that they’re visually nicer, but if you look at plots of the residuals, i.e. the “noise” around the regression line, then the noise is much closer to nice looking Gaussians (if you regress using all the data and look at the noise, it most definitely is not Gaussian looking). Ordinary least square regression assumes Gaussian noise. Conclusions about statistical significance of coefficients e.g. slope, or how much variance is explained i.e. the R^2, will be suspect if the Gaussian assumption is violated.
Clearly, you can still run a line no matter what the ‘noise’ is, it’s just that you can’t believe the usual verbiage about statistical signficance etc that came with assumption of Gaussian noise. Also, ordinary least squares, which gives the regression lines plotted above, is quite sensitive to outliers, and Buffett is telling us to expect outlier points as artifacts of acquisitions. I’m kind of OK with outlier points, what bothering me is a difference in trend lines.
Question: Point dislocations versus trend dislocations
Buffett explains some point dislocations in Book as artifacts associated with acquisitions. BTW, such point artifacts will affect any ordinary least square regression trend line. We could try to handle them either by using robust regression techniques, and/or by using our “domain knowledge” of BRK and do some kind of hand adjustments (it’s a pity Jim isn’t posting here, but we have other BRK experts who may want to chime in on the latter).
Perhaps someone can independently confirm this other behavior, i.e. a qualitative trend difference before Dec 1998 and after Dec 1998?
FWIW, B shares were issued in 1996, i.e. sort of near this trend break time, conceivably this may have something to do with it?
Anyway, I’m fretting about trend dislocations. Point dislocations seems a simpler issue.
6 Likes
I forgot to say, the reason I’m interested in trend issues is @rrr12345 explanation that trendline Price from a plot of Price vs Book is a good approximation to IntrinsicValue.
Where I’m going with this is:
assume that’s the case and then compute trend line using data only to the past of each date of interest, reserving the first X-years as a burn-in period to establish gross trend. So in principle one could reserve 1964-1994 as the trend burn-in period. Then compute a new trend line for each date after 1994 through present and estimate IV from each new trendline. Also record, in the spirit of Jim’s analysis, the future average one year forward return from each date for which you’ve just determined an IV using this ‘walk-forward’ process.
Question: Does using this estimate of IV gives us a tighter relation between present ‘value’ and average forward one year return than Jim found using book?
4 Likes
Thanks for sharing all this work. I did a quick scan, don’t have time to look at the details right now. I noticed you graphed log(P/B) over time. I’m not sure I understand why you would take log of P/B for that graph? We would expect P and B to both grow exponentially at the about the same rate. It’s true that P/B has appeared to drop over time, but is that somehow picked up better in a log(P/B) graph?
It makes sense that trying to fit a single line to the entire series (199x - present) is not going to look as nice as using just more recent data, say 2012-present. BRK was a different company in the 90s growing at a faster rate. Jim said that there was a change in average P/B around 2012, so if your intention is to get the line that’s going to give you the best forecast going forward, probably sticking to 2012-present data will work best. Sorry if I’m not helpful. I’m responding after scanning your post, so maybe misconstrued your ideas.
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Linear plots of both price/share and BV/share versus time show knees (change in slope) at about 1977 and 1999. So does a plot of calculated IV/share. The S&P 500 index shows these knees, too. A log-log plot of P/share versus BV/share does not show these knees. That is, the slope of IV versus time changes at 1977 and 1999, but the slope of IV versus BV, in a log-log plot, does not.
I think that you are right to look for factors such as the purchase of Gen Re to explain the change in slope of price and book value against time in 1999, but we also need to ask why the S&P 500 index changes slope after 1999. I doubt that it is coincidental.
5 Likes
O
Oops. I meant semi-log plots, with exponential trendlines.
With a power law trendline.
Sorry for messing up the cut and paste of the quotes.
I can’t recall, have you shared the P/B time series you are using? I’d be interested in taking a look at it over the weekend if there’s a way to share it. I’d like to see what I come up with.
I’ve plotted 5-year and 10-year forward returns versus P/B and P/IV, but I haven’t plotted forward 1-year returns. My guess is that one would get similar trends, ie, forward returns decreasing with increasing P/B or P/IV, but with more scatter for 1-year plots than for 5-year or 10-year plots. The way that you, Jim and cwagso2 do it, ie, plotting real, forward 1-year return versus P/B is perfectly reasonable. However I might prefer using the semi-log plot of BV/share versus time for making a 1-year forecast. From Dec 1999 to Jun 2022 the exponential growth in BV has been fairly smooth at about 10.6%/year, nominal. The large scatter in all of the plots of forward return vs BV/share derive more from changes in P/B over the 1, 5, or 10 year periods than it does from the underlying growth in BV/share. Another way to forecast the 1-year return would be to assume 10.6% nominal growth in BV/share +/- the expected, percentage change in P/B. This approach would have sources of scatter, too, in both the BV/share growth and in the change in P/BV, but it would make an interesting comparison. That’s all you need, unsolicited suggestions for more work 
Good luck with your analysis,
rrr12345
3 Likes
@johnIII No reason for the log other than I guess I had been typing ‘log’ a lot. For that graph log makes little difference, in fact below I show the blown up part in unlogged form
1 Like
Price/Book
Date,Name,Close,High,Low,Open,Volume,PB,
04/30/1990,Berkshire Hathaway Inc Class A,"6,700","7,025","6,575","6,700","4,470",1.599392,
05/31/1990,Berkshire Hathaway Inc Class A,"7,150","7,675","6,700","6,700","4,440",1.706814,
06/29/1990,Berkshire Hathaway Inc Class A,"7,200","7,425","6,910","7,100","5,600",,
07/31/1990,Berkshire Hathaway Inc Class A,"7,000","7,325","6,875","7,200","5,500",1.48281,
08/31/1990,Berkshire Hathaway Inc Class A,"6,400","7,075","6,000","7,075","7,700",1.355712,
09/28/1990,Berkshire Hathaway Inc Class A,"5,875","6,425","5,550","6,400","6,500",,
10/31/1990,Berkshire Hathaway Inc Class A,"5,950","6,300","5,500","6,100","9,400",1.418671,
11/30/1990,Berkshire Hathaway Inc Class A,"6,345","6,350","5,825","5,860","5,200",1.512852,
12/31/1990,Berkshire Hathaway Inc Class A,"6,675","6,900","6,250","6,275","6,700",1.446723,
01/31/1991,Berkshire Hathaway Inc Class A,"7,400","7,400","6,550","6,675","6,700",1.603858,
02/28/1991,Berkshire Hathaway Inc Class A,"8,075","8,250","7,400","7,575","6,700",1.750156,
03/29/1991,Berkshire Hathaway Inc Class A,"8,025","8,275","7,775","8,125","4,600",,
04/30/1991,Berkshire Hathaway Inc Class A,"8,125","8,225","7,760","8,125","4,600",1.760993,
05/31/1991,Berkshire Hathaway Inc Class A,"8,750","8,750","8,000","8,200","4,200",1.896454,
06/28/1991,Berkshire Hathaway Inc Class A,"8,400","8,750","8,300","8,650","4,700",,
07/31/1991,Berkshire Hathaway Inc Class A,"8,525","9,000","8,400","8,500","2,500",1.847688,
08/30/1991,Berkshire Hathaway Inc Class A,"8,775","9,000","8,500","8,550","5,300",,
09/30/1991,Berkshire Hathaway Inc Class A,"8,875","9,000","8,325","8,775","7,000",1.923546,
10/31/1991,Berkshire Hathaway Inc Class A,"8,570","9,000","8,400","8,925","5,700",1.857441,
11/29/1991,Berkshire Hathaway Inc Class A,"8,350","8,545","8,150","8,500","9,500",,
12/31/1991,Berkshire Hathaway Inc Class A,"9,050","9,125","8,300","8,425","4,600",1.405344,
01/31/1992,Berkshire Hathaway Inc Class A,"8,850","9,100","8,575","9,050","6,100",1.374287,
02/28/1992,Berkshire Hathaway Inc Class A,"8,725","8,875","8,625","8,875","3,500",,
03/31/1992,Berkshire Hathaway Inc Class A,"8,950","9,000","8,675","8,675","3,500",1.348679,
04/30/1992,Berkshire Hathaway Inc Class A,"9,125","9,200","8,850","8,950","3,900",1.375049,
05/29/1992,Berkshire Hathaway Inc Class A,"9,100","9,150","8,912","9,025","3,000",,
06/30/1992,Berkshire Hathaway Inc Class A,"9,225","9,300","8,875","9,080","4,700",1.3197,
07/31/1992,Berkshire Hathaway Inc Class A,"9,525","9,525","9,075","9,300","3,300",1.362617,
08/31/1992,Berkshire Hathaway Inc Class A,"9,125","9,950","9,050","9,550","5,500",1.305394,
09/30/1992,Berkshire Hathaway Inc Class A,"9,400","9,425","9,075","9,100","3,700",1.323114,
10/30/1992,Berkshire Hathaway Inc Class A,"9,475","9,550","9,150","9,425","2,700",,
11/30/1992,Berkshire Hathaway Inc Class A,"10,725","11,050","9,375","9,475","2,700",1.509617,
12/31/1992,Berkshire Hathaway Inc Class A,"11,750","11,750","10,375","10,475","4,300",1.517569,
01/29/1993,Berkshire Hathaway Inc Class A,"12,100","12,850","11,350","11,750","4,500",,
02/26/1993,Berkshire Hathaway Inc Class A,"12,475","12,600","11,875","12,450","2,800",,
03/31/1993,Berkshire Hathaway Inc Class A,"12,750","13,200","12,400","12,450","3,100",1.652457,
04/30/1993,Berkshire Hathaway Inc Class A,"12,650","12,800","11,800","12,700","4,500",1.639496,
05/31/1993,Berkshire Hathaway Inc Class A,"15,000","15,150","12,600","12,750","4,600",1.944067,
06/30/1993,Berkshire Hathaway Inc Class A,"15,400","16,200","14,000","15,700","4,400",1.952561,
07/30/1993,Berkshire Hathaway Inc Class A,"16,000","16,050","15,100","15,100","2,600",,
08/31/1993,Berkshire Hathaway Inc Class A,"17,525","17,800","15,950","15,950","4,100",2.221989,
09/30/1993,Berkshire Hathaway Inc Class A,"16,675","17,550","16,350","17,400","3,100",2.05477,
10/29/1993,Berkshire Hathaway Inc Class A,"17,250","17,700","16,520","16,700","2,800",,
11/30/1993,Berkshire Hathaway Inc Class A,"17,250","17,800","17,100","17,300","2,700",2.125624,
12/31/1993,Berkshire Hathaway Inc Class A,"16,325","17,550","16,200","17,300","2,800",1.844084,
01/31/1994,Berkshire Hathaway Inc Class A,"16,200","16,800","15,700","16,350","3,000",1.829964,
02/28/1994,Berkshire Hathaway Inc Class A,"15,450","16,500","15,250","16,400","2,700",1.745244,
03/31/1994,Berkshire Hathaway Inc Class A,"15,925","16,900","15,150","15,400","3,000",1.79599,
04/29/1994,Berkshire Hathaway Inc Class A,"16,100","16,700","15,400","15,925","3,600",,
05/31/1994,Berkshire Hathaway Inc Class A,"16,100","16,500","16,100","16,400","2,400",1.815726,
06/30/1994,Berkshire Hathaway Inc Class A,"16,100","16,550","16,100","16,500","2,500",1.758062,
07/29/1994,Berkshire Hathaway Inc Class A,"19,600","19,700","16,100","16,475","3,800",,
08/31/1994,Berkshire Hathaway Inc Class A,"19,100","19,750","18,250","19,500","4,500",2.085652,
09/30/1994,Berkshire Hathaway Inc Class A,"18,950","19,100","18,750","18,850","2,300",1.956879,
10/31/1994,Berkshire Hathaway Inc Class A,"20,250","20,475","18,200","18,950","14,780",2.091124,
11/30/1994,Berkshire Hathaway Inc Class A,"20,525","21,070","19,650","20,350","1,990",2.119522,
12/30/1994,Berkshire Hathaway Inc Class A,"20,400","20,525","19,550","20,250","3,380",,
01/31/1995,Berkshire Hathaway Inc Class A,"24,600","24,650","20,300","20,400","6,050",2.440341,
02/28/1995,Berkshire Hathaway Inc Class A,"22,275","26,050","21,350","25,850","6,385",2.209699,
03/31/1995,Berkshire Hathaway Inc Class A,"22,650","22,900","21,160","22,000","4,800",2.056837,
04/28/1995,Berkshire Hathaway Inc Class A,"21,600","22,609","21,500","22,400","2,440",,
05/31/1995,Berkshire Hathaway Inc Class A,"22,700","23,250","21,650","22,200","3,250",2.061377,
06/30/1995,Berkshire Hathaway Inc Class A,"23,450","24,450","22,125","22,725","2,070",1.904416,
07/31/1995,Berkshire Hathaway Inc Class A,"24,750","24,750","23,400","23,400","2,350",2.009992,
08/31/1995,Berkshire Hathaway Inc Class A,"25,500","25,500","24,200","25,100","2,960",2.0709,
09/29/1995,Berkshire Hathaway Inc Class A,"29,400","30,600","25,500","25,700","3,550",,
10/31/1995,Berkshire Hathaway Inc Class A,"29,500","29,950","29,250","29,850","2,880",2.177054,
11/30/1995,Berkshire Hathaway Inc Class A,"31,300","32,600","28,850","29,400","5,070",2.309892,
12/29/1995,Berkshire Hathaway Inc Class A,"32,100","33,400","23,600","31,700","4,380",,
01/31/1996,Berkshire Hathaway Inc Class A,"31,900","32,250","29,800","32,100","8,040",2.212254,
02/29/1996,Berkshire Hathaway Inc Class A,"35,500","35,800","31,600","31,800","6,890",2.461913,
03/29/1996,Berkshire Hathaway Inc Class A,"33,850","38,000","32,800","36,000","6,220",,
04/30/1996,Berkshire Hathaway Inc Class A,"33,500","35,300","31,100","33,850","4,010",2.234527,
05/31/1996,Berkshire Hathaway Inc Class A,"30,500","36,000","30,000","33,600","5,260",2.03442,
06/28/1996,Berkshire Hathaway Inc Class A,"30,700","33,200","30,100","30,100","3,320",,
07/31/1996,Berkshire Hathaway Inc Class A,"30,900","32,750","30,500","31,900","3,160",1.869599,
08/30/1996,Berkshire Hathaway Inc Class A,"31,300","33,500","30,700","31,000","2,320",,
09/30/1996,Berkshire Hathaway Inc Class A,"32,150","32,800","31,000","31,300","2,160",1.837111,
10/31/1996,Berkshire Hathaway Inc Class A,"32,400","32,800","31,500","32,000","4,440",1.851397,
11/29/1996,Berkshire Hathaway Inc Class A,"33,200","33,900","32,300","32,350","3,140",,
12/31/1996,Berkshire Hathaway Inc Class A,"34,100","36,500","32,200","33,300","4,310",1.793691,
01/31/1997,Berkshire Hathaway Inc Class A,"34,800","35,100","33,000","34,100","4,490",1.830512,
02/28/1997,Berkshire Hathaway Inc Class A,"35,500","37,400","34,500","34,800","3,660",1.867333,
03/31/1997,Berkshire Hathaway Inc Class A,"36,200","37,900","35,400","36,000","4,030",1.84406,
04/30/1997,Berkshire Hathaway Inc Class A,"38,000","38,500","35,900","36,400","4,540",1.935754,
05/30/1997,Berkshire Hathaway Inc Class A,"43,000","44,100","37,700","38,000","4,730",,
06/30/1997,Berkshire Hathaway Inc Class A,"47,200","48,600","42,800","43,000","4,390",2.076356,
07/31/1997,Berkshire Hathaway Inc Class A,"47,200","48,300","46,000","47,400","2,530",2.076356,
08/29/1997,Berkshire Hathaway Inc Class A,"41,500","47,600","41,300","47,500","3,520",,
09/30/1997,Berkshire Hathaway Inc Class A,"44,800","45,500","41,300","41,500","3,240",1.974103,
10/31/1997,Berkshire Hathaway Inc Class A,"43,700","47,200","42,500","44,800","2,960",1.925632,
11/28/1997,Berkshire Hathaway Inc Class A,"45,300","46,400","43,700","44,300","2,370",,
12/31/1997,Berkshire Hathaway Inc Class A,"46,000","47,100","45,400","46,000","2,230",1.804783,
01/30/1998,Berkshire Hathaway Inc Class A,"50,300","50,500","45,800","46,000","4,250",,
02/27/1998,Berkshire Hathaway Inc Class A,"55,800","55,800","50,800","51,900","4,130",,
03/31/1998,Berkshire Hathaway Inc Class A,"67,200","69,300","55,900","56,400","6,820",2.398212,
04/30/1998,Berkshire Hathaway Inc Class A,"68,600","71,000","65,800","67,500","4,270",2.448175,
05/29/1998,Berkshire Hathaway Inc Class A,"70,700","74,600","68,000","69,300","4,390",,
06/30/1998,Berkshire Hathaway Inc Class A,"78,305","84,000","70,400","70,500","10,210",2.632727,
07/31/1998,Berkshire Hathaway Inc Class A,"70,100","78,500","68,300","78,005","12,729",2.357032,
08/31/1998,Berkshire Hathaway Inc Class A,"60,500","72,800","60,300","70,300","7,020",2.034098,
09/30/1998,Berkshire Hathaway Inc Class A,"59,600","65,300","57,000","59,900","12,270",2.399566,
10/30/1998,Berkshire Hathaway Inc Class A,"64,500","68,500","57,700","59,000","10,460",,
11/30/1998,Berkshire Hathaway Inc Class A,"68,100","70,100","64,600","64,700","6,200",2.733733,
12/31/1998,Berkshire Hathaway Inc Class A,"70,000","71,000","58,400","67,200","13,990",1.519878,
01/29/1999,Berkshire Hathaway Inc Class A,"65,000","71,000","61,900","68,350","15,490",,
02/26/1999,Berkshire Hathaway Inc Class A,"71,100","77,500","66,600","67,000","9,680",,
03/31/1999,Berkshire Hathaway Inc Class A,"71,400","81,100","71,200","71,200","8,850",1.874181,
04/30/1999,Berkshire Hathaway Inc Class A,"76,400","78,100","71,100","72,100","6,210",2.005426,
05/31/1999,Berkshire Hathaway Inc Class A,"72,000","78,600","71,000","76,700","6,040",1.88993,
06/30/1999,Berkshire Hathaway Inc Class A,"69,100","74,400","68,300","71,900","4,550",1.804161,
07/30/1999,Berkshire Hathaway Inc Class A,"67,805","73,000","67,200","69,000","6,300",,
08/31/1999,Berkshire Hathaway Inc Class A,"64,200","67,705","61,700","67,400","4,500",1.681091,
09/30/1999,Berkshire Hathaway Inc Class A,"55,000","65,000","54,600","64,000","7,320",1.511656,
10/29/1999,Berkshire Hathaway Inc Class A,"63,900","63,900","54,200","55,500","8,750",,
11/30/1999,Berkshire Hathaway Inc Class A,"57,300","66,900","57,000","64,400","8,280",1.574871,
12/31/1999,Berkshire Hathaway Inc Class A,"56,100","58,200","52,000","57,000","11,000",1.476835,
01/31/2000,Berkshire Hathaway Inc Class A,"51,200","57,600","51,000","56,100","7,460",1.347842,
02/29/2000,Berkshire Hathaway Inc Class A,"44,000","52,000","43,000","51,800","17,780",1.158302,
03/31/2000,Berkshire Hathaway Inc Class A,"57,200","57,800","40,800","44,000","17,980",1.545349,
04/28/2000,Berkshire Hathaway Inc Class A,"59,300","60,200","53,400","56,000","11,460",,
05/31/2000,Berkshire Hathaway Inc Class A,"58,600","60,000","51,800","59,200","7,370",1.583244,
06/30/2000,Berkshire Hathaway Inc Class A,"53,800","60,800","52,700","58,800","6,610",1.420771,
07/31/2000,Berkshire Hathaway Inc Class A,"55,100","58,200","52,000","53,700","9,550",1.455102,
08/31/2000,Berkshire Hathaway Inc Class A,"57,700","63,200","54,700","55,300","11,050",1.528069,
09/29/2000,Berkshire Hathaway Inc Class A,"64,400","64,400","55,100","57,900","10,110",,
10/31/2000,Berkshire Hathaway Inc Class A,"63,700","64,400","53,500","64,000","9,820",1.635754,
11/30/2000,Berkshire Hathaway Inc Class A,"65,900","66,500","60,950","63,200","10,120",1.692931,
12/29/2000,Berkshire Hathaway Inc Class A,"71,000","71,300","64,900","65,800","8,730",,
01/31/2001,Berkshire Hathaway Inc Class A,"68,400","74,500","64,700","70,000","8,970",1.691305,
02/28/2001,Berkshire Hathaway Inc Class A,"70,300","72,000","67,500","68,200","5,030",1.738286,
03/30/2001,Berkshire Hathaway Inc Class A,"65,450","72,100","63,000","70,000","6,320",,
04/30/2001,Berkshire Hathaway Inc Class A,"68,000","69,700","62,800","65,450","4,860",1.777955,
05/31/2001,Berkshire Hathaway Inc Class A,"68,700","69,790","66,800","68,400","4,360",1.796582,
06/29/2001,Berkshire Hathaway Inc Class A,"69,400","69,800","64,750","68,600","4,460",,
07/31/2001,Berkshire Hathaway Inc Class A,"69,200","70,900","67,600","69,400","4,650",1.799181,
08/31/2001,Berkshire Hathaway Inc Class A,"69,400","69,990","67,700","69,400","3,970",1.804734,
09/28/2001,Berkshire Hathaway Inc Class A,"70,000","70,800","59,000","69,400","16,510",,
10/31/2001,Berkshire Hathaway Inc Class A,"71,200","75,300","68,400","69,500","14,390",1.904131,
11/30/2001,Berkshire Hathaway Inc Class A,"70,000","73,000","66,600","70,800","5,690",1.872949,
12/31/2001,Berkshire Hathaway Inc Class A,"75,600","75,600","67,500","70,000","4,780",1.993671,
01/31/2002,Berkshire Hathaway Inc Class A,"73,900","75,600","71,200","73,900","4,890",1.948839,
02/28/2002,Berkshire Hathaway Inc Class A,"73,000","74,000","72,100","73,900","4,290",1.925105,
03/29/2002,Berkshire Hathaway Inc Class A,"71,100","74,500","69,000","73,000","7,320",,
04/30/2002,Berkshire Hathaway Inc Class A,"73,450","73,500","69,700","70,900","6,770",1.861852,
05/31/2002,Berkshire Hathaway Inc Class A,"74,600","78,500","72,600","73,700","7,510",1.891002,
06/28/2002,Berkshire Hathaway Inc Class A,"66,800","75,400","66,500","74,900","8,677",,
07/31/2002,Berkshire Hathaway Inc Class A,"68,300","70,600","59,600","67,800","14,430",1.679837,
08/30/2002,Berkshire Hathaway Inc Class A,"73,000","75,600","68,000","68,800","5,290",,
09/30/2002,Berkshire Hathaway Inc Class A,"73,900","75,900","69,900","74,300","5,450",1.8104,
10/31/2002,Berkshire Hathaway Inc Class A,"74,190","75,000","67,800","74,200","9,210",1.81783,
11/29/2002,Berkshire Hathaway Inc Class A,"72,300","74,700","69,700","73,800","6,060",,
12/31/2002,Berkshire Hathaway Inc Class A,"72,750","73,200","69,100","73,000","6,130",1.743464,
01/31/2003,Berkshire Hathaway Inc Class A,"67,600","73,005","66,500","72,300","9,010",1.620044,
02/28/2003,Berkshire Hathaway Inc Class A,"61,700","68,490","60,600","67,600","8,080",1.478649,
03/31/2003,Berkshire Hathaway Inc Class A,"63,800","69,500","62,900","63,000","8,180",1.498284,
04/30/2003,Berkshire Hathaway Inc Class A,"69,815","73,600","64,305","64,600","8,210",1.639716,
05/30/2003,Berkshire Hathaway Inc Class A,"71,000","74,200","69,700","70,100","9,410",,
06/30/2003,Berkshire Hathaway Inc Class A,"72,500","75,500","70,850","71,000","8,660",1.576236,
07/31/2003,Berkshire Hathaway Inc Class A,"72,010","74,500","70,900","72,505","11,110",1.565918,
08/29/2003,Berkshire Hathaway Inc Class A,"75,775","76,400","71,700","72,000","9,580",,
09/30/2003,Berkshire Hathaway Inc Class A,"75,000","76,300","74,300","75,400","6,720",1.60005,
10/31/2003,Berkshire Hathaway Inc Class A,"77,810","78,100","75,150","75,200","5,960",1.66062,
11/28/2003,Berkshire Hathaway Inc Class A,"83,750","84,500","78,100","78,100","5,490",,
12/31/2003,Berkshire Hathaway Inc Class A,"84,250","84,700","82,100","84,100","5,300",1.668399,
01/30/2004,Berkshire Hathaway Inc Class A,"89,490","90,500","84,000","84,500","7,830",,
02/27/2004,Berkshire Hathaway Inc Class A,"94,500","95,700","89,000","89,200","5,060",,
03/31/2004,Berkshire Hathaway Inc Class A,"93,300","94,900","90,700","94,500","5,840",1.799097,
04/30/2004,Berkshire Hathaway Inc Class A,"93,390","95,650","91,800","93,200","5,020",1.801141,
05/31/2004,Berkshire Hathaway Inc Class A,"89,000","93,700","85,100","93,700","6,800",1.716474,
06/30/2004,Berkshire Hathaway Inc Class A,"88,950","90,300","86,000","89,100","3,820",1.700282,
07/30/2004,Berkshire Hathaway Inc Class A,"87,250","90,750","86,550","89,100","5,260",,
08/31/2004,Berkshire Hathaway Inc Class A,"87,000","87,010","83,400","86,600","4,960",1.66335,
09/30/2004,Berkshire Hathaway Inc Class A,"86,650","87,500","85,900","86,800","5,080",1.65185,
10/29/2004,Berkshire Hathaway Inc Class A,"84,250","86,600","81,150","86,500","6,650",,
11/30/2004,Berkshire Hathaway Inc Class A,"83,700","86,350","81,600","84,600","8,070",1.595613,
12/31/2004,Berkshire Hathaway Inc Class A,"87,900","89,500","83,250","83,500","10,560",1.574582,
01/31/2005,Berkshire Hathaway Inc Class A,"89,900","90,500","85,400","87,910","7,170",1.610408,
02/28/2005,Berkshire Hathaway Inc Class A,"90,200","92,000","89,800","89,800","5,070",1.616294,
03/31/2005,Berkshire Hathaway Inc Class A,"87,000","91,050","84,500","90,500","9,560",1.548927,
04/29/2005,Berkshire Hathaway Inc Class A,"84,350","88,900","82,000","86,500","14,620",,
05/31/2005,Berkshire Hathaway Inc Class A,"84,100","86,210","82,400","84,900","8,590",1.497679,
06/30/2005,Berkshire Hathaway Inc Class A,"83,500","84,700","82,300","84,300","5,920",1.459477,
07/29/2005,Berkshire Hathaway Inc Class A,"83,500","85,450","83,350","83,800","3,930",,
08/31/2005,Berkshire Hathaway Inc Class A,"83,150","85,200","82,400","83,825","6,480",1.453552,
09/30/2005,Berkshire Hathaway Inc Class A,"82,000","84,600","78,800","83,290","13,380",1.410519,
10/31/2005,Berkshire Hathaway Inc Class A,"85,900","85,900","82,100.102","82,500","9,670",1.477998,
11/30/2005,Berkshire Hathaway Inc Class A,"89,390","90,900","85,790","85,990","9,870",1.538047,
12/30/2005,Berkshire Hathaway Inc Class A,"88,620","91,200","88,350","89,500","6,500",,
01/31/2006,Berkshire Hathaway Inc Class A,"89,490","90,300","88,250","88,550","7,450",1.50714,
02/28/2006,Berkshire Hathaway Inc Class A,"86,800","89,190","86,200","89,100","5,120",1.462028,
03/31/2006,Berkshire Hathaway Inc Class A,"90,350","90,600","86,700.102","86,800","9,090",1.460136,
04/28/2006,Berkshire Hathaway Inc Class A,"89,000","90,650","85,400","90,500","8,820",,
05/31/2006,Berkshire Hathaway Inc Class A,"92,290","93,100","88,000","89,000","13,470",1.49194,
06/30/2006,Berkshire Hathaway Inc Class A,"91,659","92,600","89,500","92,340","9,620",1.447372,
07/31/2006,Berkshire Hathaway Inc Class A,"91,600","92,100","89,400","91,800","7,980",1.447089,
08/31/2006,Berkshire Hathaway Inc Class A,"96,097","96,700","91,300","91,600","7,360",1.518132,
09/29/2006,Berkshire Hathaway Inc Class A,"95,800","97,100","92,875","95,900","6,420",,
10/31/2006,Berkshire Hathaway Inc Class A,"105,475","105,500","95,200","95,200","9,530",1.591171,
11/30/2006,Berkshire Hathaway Inc Class A,"107,100","108,800","103,300","105,475","8,760",1.615685,
12/29/2006,Berkshire Hathaway Inc Class A,"109,990","114,500","105,900","107,300","7,560",,
01/31/2007,Berkshire Hathaway Inc Class A,"110,050","110,600","106,100","109,700","8,480",1.565856,
02/28/2007,Berkshire Hathaway Inc Class A,"106,190","110,700","103,800","110,200","8,070",1.511112,
03/30/2007,Berkshire Hathaway Inc Class A,"108,990","109,700","104,800","105,100","7,200",,
04/30/2007,Berkshire Hathaway Inc Class A,"109,200","110,000","107,600","108,300","5,800",1.533265,
05/31/2007,Berkshire Hathaway Inc Class A,"109,490","110,490","108,000","109,000","11,680",1.537337,
06/29/2007,Berkshire Hathaway Inc Class A,"109,475","109,900","107,200","109,500","8,160",,
07/31/2007,Berkshire Hathaway Inc Class A,"110,000","112,000","108,600","109,500","8,620",1.476527,
08/31/2007,Berkshire Hathaway Inc Class A,"118,390","120,800","109,400","110,000","10,850",1.589146,
09/28/2007,Berkshire Hathaway Inc Class A,"118,510","120,200","116,300","118,700","5,880",,
10/31/2007,Berkshire Hathaway Inc Class A,"132,500","132,500","118,400","119,000","9,590",1.710064,
11/30/2007,Berkshire Hathaway Inc Class A,"140,100","140,700","131,000","131,800","18,100",1.80815,
12/31/2007,Berkshire Hathaway Inc Class A,"141,600","151,650","131,600","140,900","14,110",1.81519,
01/31/2008,Berkshire Hathaway Inc Class A,"136,000","145,000","126,100","143,500","17,054",1.743403,
02/29/2008,Berkshire Hathaway Inc Class A,"140,000","145,900","134,000","136,700","11,567",1.795911,
03/31/2008,Berkshire Hathaway Inc Class A,"133,400","139,000","127,100","138,500","14,969",1.730757,
04/30/2008,Berkshire Hathaway Inc Class A,"133,850","135,500","126,300.01","134,800","14,452",1.736707,
05/30/2008,Berkshire Hathaway Inc Class A,"134,650","135,000","121,200","133,950","19,433",,
06/30/2008,Berkshire Hathaway Inc Class A,"120,750","135,450","119,450","134,800","12,015",1.585032,
07/31/2008,Berkshire Hathaway Inc Class A,"114,450","120,710","111,000","119,600","19,331",1.502334,
08/29/2008,Berkshire Hathaway Inc Class A,"116,600","120,100","112,900","115,200","14,941",,
09/30/2008,Berkshire Hathaway Inc Class A,"130,600","147,000","115,500","118,500","31,606",1.683899,
10/31/2008,Berkshire Hathaway Inc Class A,"115,490","140,900","102,010.01","132,500","42,774",1.489078,
11/28/2008,Berkshire Hathaway Inc Class A,"104,000","119,200","74,100","115,490","42,374",,
12/31/2008,Berkshire Hathaway Inc Class A,"96,600","107,500","90,000","96,000","25,088",1.369636,
01/30/2009,Berkshire Hathaway Inc Class A,"89,502","102,600","85,000","90,700","21,689",,
02/27/2009,Berkshire Hathaway Inc Class A,"78,600","91,300","73,500","86,901","28,798",,
03/31/2009,Berkshire Hathaway Inc Class A,"86,700","91,900","70,050.008","74,300","34,502",1.310282,
04/30/2009,Berkshire Hathaway Inc Class A,"94,000","95,500","83,957","85,800","23,991",1.420605,
05/29/2009,Berkshire Hathaway Inc Class A,"91,600","95,499","87,310","93,400","17,160",,
06/30/2009,Berkshire Hathaway Inc Class A,"90,000","93,010","85,155","92,700","15,670",1.219409,
07/31/2009,Berkshire Hathaway Inc Class A,"97,000","97,900","84,600","89,900","16,151",1.314254,
08/31/2009,Berkshire Hathaway Inc Class A,"100,850","108,450","96,500","97,950","18,703",1.366417,
09/30/2009,Berkshire Hathaway Inc Class A,"101,000","104,875","95,270","100,350","18,135",1.243125,
10/30/2009,Berkshire Hathaway Inc Class A,"99,000","102,370","97,870","100,300","17,569",,
11/30/2009,Berkshire Hathaway Inc Class A,"100,600","105,980","98,400","99,750","23,520",1.237604,
12/31/2009,Berkshire Hathaway Inc Class A,"99,200","101,300","97,950","101,300","23,764",1.17415,
01/29/2010,Berkshire Hathaway Inc Class A,"114,600","116,650","97,205","99,190","59,762",,
02/26/2010,Berkshire Hathaway Inc Class A,"119,800","120,155","107,416","116,640","138,654",,
03/31/2010,Berkshire Hathaway Inc Class A,"121,800","125,252.5","118,700","119,850","36,744",1.362808,
04/30/2010,Berkshire Hathaway Inc Class A,"115,325","122,907.99","113,506","122,210","17,286",1.290389,
05/31/2010,Berkshire Hathaway Inc Class A,"105,910","118,116","102,751","116,190","18,670",1.185043,
06/30/2010,Berkshire Hathaway Inc Class A,"120,000","122,300","104,502","105,389","23,790",1.384706,
07/30/2010,Berkshire Hathaway Inc Class A,"117,000","120,266","114,448","119,394","19,226",,
08/31/2010,Berkshire Hathaway Inc Class A,"118,675","121,385","113,622.01","118,400","12,505",1.369525,
09/30/2010,Berkshire Hathaway Inc Class A,"124,500","128,730","118,446","118,900","17,386",1.370803,
10/29/2010,Berkshire Hathaway Inc Class A,"119,300","126,568","118,201","124,850","12,497",,
11/30/2010,Berkshire Hathaway Inc Class A,"120,200","125,649","118,259","119,500","13,611",1.323515,
12/31/2010,Berkshire Hathaway Inc Class A,"120,450","122,070","118,789.01","121,122","12,092",1.261878,
01/31/2011,Berkshire Hathaway Inc Class A,"122,425","125,036","118,792","120,550","12,735",1.282568,
02/28/2011,Berkshire Hathaway Inc Class A,"131,300","131,463","123,000","123,000","9,847",1.375875,
03/31/2011,Berkshire Hathaway Inc Class A,"125,300","131,400","121,500","131,400","10,981",1.290677,
04/29/2011,Berkshire Hathaway Inc Class A,"124,750","126,100","119,683","126,000","10,616",,
05/31/2011,Berkshire Hathaway Inc Class A,"118,775","123,830","115,860.01","123,100","8,265",1.223571,
06/30/2011,Berkshire Hathaway Inc Class A,"116,105","118,340","109,925","118,020","11,233",1.176152,
07/29/2011,Berkshire Hathaway Inc Class A,"111,500","117,250","111,246","115,230","9,086",,
08/31/2011,Berkshire Hathaway Inc Class A,"109,769","113,445","100,265","113,400","19,962",1.111976,
09/30/2011,Berkshire Hathaway Inc Class A,"106,800","111,751","98,952","109,374","15,839",1.102442,
10/31/2011,Berkshire Hathaway Inc Class A,"116,950","120,755","104,701","107,600","14,100",1.206926,
11/30/2011,Berkshire Hathaway Inc Class A,"118,500","118,500","110,092","114,329.99","13,586",1.222922,
12/30/2011,Berkshire Hathaway Inc Class A,"114,755","118,373","110,741","116,900","10,479",,
01/31/2012,Berkshire Hathaway Inc Class A,"117,925","120,000","113,855","115,000","10,335",1.1809,
02/29/2012,Berkshire Hathaway Inc Class A,"117,934","120,627","116,850","118,251","12,119",1.181053,
03/30/2012,Berkshire Hathaway Inc Class A,"121,900","123,578","117,301","118,400","12,863",,
04/30/2012,Berkshire Hathaway Inc Class A,"120,800","123,000","117,551.11","121,950","10,683",1.133373,
05/31/2012,Berkshire Hathaway Inc Class A,"118,850","123,868","118,252","120,800","13,390",1.115078,
06/29/2012,Berkshire Hathaway Inc Class A,"124,945","124,950","118,000","118,000","11,620",,
07/31/2012,Berkshire Hathaway Inc Class A,"127,445","128,109","123,226.95","124,895","11,066",1.187018,
08/31/2012,Berkshire Hathaway Inc Class A,"126,559.9","129,040","123,418","127,500","9,061",1.178775,
09/28/2012,Berkshire Hathaway Inc Class A,"132,700","134,891.98","126,021.01","126,515","11,104",,
10/31/2012,Berkshire Hathaway Inc Class A,"129,505","136,344.98","129,264","132,630","12,084",1.159284,
11/30/2012,Berkshire Hathaway Inc Class A,"131,916","132,955.83","125,950","130,053","13,315",1.180866,
12/31/2012,Berkshire Hathaway Inc Class A,"134,060","136,208","130,432","132,373","23,816",1.173764,
01/31/2013,Berkshire Hathaway Inc Class A,"145,875","147,475","132,400","132,500","14,364",1.27721,
02/28/2013,Berkshire Hathaway Inc Class A,"152,600","153,738.88","145,010","146,759","9,788",1.336287,
03/29/2013,Berkshire Hathaway Inc Class A,"156,280","156,634","150,800","152,363.88","11,301",,
04/30/2013,Berkshire Hathaway Inc Class A,"159,000","161,969","154,144.81","155,800","9,763",1.392578,
05/31/2013,Berkshire Hathaway Inc Class A,"171,300","172,450","159,100","159,360","12,325",1.421348,
06/28/2013,Berkshire Hathaway Inc Class A,"168,600","173,809.5","164,548","171,900","10,099",,
07/31/2013,Berkshire Hathaway Inc Class A,"173,900","178,900","167,520","169,200","7,548",1.443174,
08/30/2013,Berkshire Hathaway Inc Class A,"167,050","178,547.91","166,367.3","175,600","8,296",,
09/30/2013,Berkshire Hathaway Inc Class A,"170,410","176,783","166,168","168,226","9,339",1.386654,
10/31/2013,Berkshire Hathaway Inc Class A,"172,994.8","176,465","166,510.05","170,438","10,501",1.407708,
11/29/2013,Berkshire Hathaway Inc Class A,"174,750","175,908","170,180","173,220","8,673",,
12/31/2013,Berkshire Hathaway Inc Class A,"177,900","177,950","170,375","174,500","9,378",1.403477,
01/31/2014,Berkshire Hathaway Inc Class A,"169,511.9","177,950","167,632.77","177,000","11,526",1.337302,
02/28/2014,Berkshire Hathaway Inc Class A,"173,708","173,833.87","163,038.88","169,599.9","7,736",1.370449,
03/31/2014,Berkshire Hathaway Inc Class A,"187,350.05","188,852.99","172,759.99","174,100","8,582",1.388334,
04/30/2014,Berkshire Hathaway Inc Class A,"193,275","193,789","181,785","187,500","7,555",1.432303,
05/30/2014,Berkshire Hathaway Inc Class A,"192,000","194,670","186,250","193,295","4,670",,
06/30/2014,Berkshire Hathaway Inc Class A,"189,900.5","192,908","188,220","192,300","6,355",1.370227,
07/31/2014,Berkshire Hathaway Inc Class A,"188,124","193,860","188,124","190,100","4,282",1.357432,
08/29/2014,Berkshire Hathaway Inc Class A,"205,880","205,880","185,005","187,152","8,015",,
09/30/2014,Berkshire Hathaway Inc Class A,"206,900","213,612","204,050","204,050","6,504",1.452525,
10/31/2014,Berkshire Hathaway Inc Class A,"210,000","212,300","198,000","207,310","10,886",1.474309,
11/28/2014,Berkshire Hathaway Inc Class A,"223,065","224,070.7","209,000","210,835","4,549",,
12/31/2014,Berkshire Hathaway Inc Class A,"226,000","229,374","215,500","223,100","10,102",1.563647,
01/30/2015,Berkshire Hathaway Inc Class A,"215,865","228,870","215,865","228,180","7,573",,
02/27/2015,Berkshire Hathaway Inc Class A,"221,180","227,450","215,151.21","216,001.1","4,888",,
03/31/2015,Berkshire Hathaway Inc Class A,"217,500","221,899.99","215,464.05","221,899.99","7,962",1.487899,
04/30/2015,Berkshire Hathaway Inc Class A,"213,400","217,980","211,960.05","217,900","6,026",1.459894,
05/29/2015,Berkshire Hathaway Inc Class A,"214,800","223,011.49","213,650","214,665.89","4,982",,
06/30/2015,Berkshire Hathaway Inc Class A,"204,850","216,420","204,800","215,260","4,738",1.394062,
07/31/2015,Berkshire Hathaway Inc Class A,"214,000","217,100","204,340","206,740","6,003",1.456456,
08/31/2015,Berkshire Hathaway Inc Class A,"202,531","215,999.95","190,007","214,400","7,248",1.352713,
09/30/2015,Berkshire Hathaway Inc Class A,"195,240","202,699.99","192,000","199,995","7,454",1.304035,
10/30/2015,Berkshire Hathaway Inc Class A,"204,596","207,776","192,200","196,299.76","5,219",,
11/30/2015,Berkshire Hathaway Inc Class A,"201,360","207,780","197,280.01","205,200","4,970",1.332788,
12/31/2015,Berkshire Hathaway Inc Class A,"197,800","205,015","194,500","201,850","7,880",1.309244,
01/29/2016,Berkshire Hathaway Inc Class A,"194,360.05","200,000","186,900","199,220","9,110",,
02/29/2016,Berkshire Hathaway Inc Class A,"202,555","203,192","186,921","194,000","8,310",1.302649,
03/31/2016,Berkshire Hathaway Inc Class A,"213,450","215,130","202,600","203,899","9,015",1.372878,
04/29/2016,Berkshire Hathaway Inc Class A,"219,000","221,985","209,641","211,850","4,769",,
05/31/2016,Berkshire Hathaway Inc Class A,"211,695","220,640","209,600","219,180","4,905",1.345267,
06/30/2016,Berkshire Hathaway Inc Class A,"216,975","218,850","205,074","211,100","6,720",1.378895,
07/29/2016,Berkshire Hathaway Inc Class A,"216,000","220,360","211,500","216,421","4,502",,
08/31/2016,Berkshire Hathaway Inc Class A,"225,760","226,145","214,400","216,540","7,495",1.410957,
09/30/2016,Berkshire Hathaway Inc Class A,"216,220","226,490","215,208.19","225,680","6,228",1.351478,
10/31/2016,Berkshire Hathaway Inc Class A,"215,700","218,500","213,030","216,000","5,304",1.348234,
11/30/2016,Berkshire Hathaway Inc Class A,"237,000","238,589.99","213,680","216,798","11,500",1.447045,
12/30/2016,Berkshire Hathaway Inc Class A,"244,121","250,786","236,340","236,361","6,975",,
01/31/2017,Berkshire Hathaway Inc Class A,"245,980.35","247,737.5","237,983.82","244,850","5,549",1.502134,
02/28/2017,Berkshire Hathaway Inc Class A,"257,100","258,270","243,370","247,700","8,389",1.493907,
03/31/2017,Berkshire Hathaway Inc Class A,"249,850","266,445","248,810","261,815","8,407",1.451914,
04/28/2017,Berkshire Hathaway Inc Class A,"247,780","253,390","243,600","250,121","4,826",,
05/31/2017,Berkshire Hathaway Inc Class A,"248,440","252,000","242,180","248,460","7,318",1.395177,
06/30/2017,Berkshire Hathaway Inc Class A,"254,700","257,944.64","247,610","248,530","8,093",1.430353,
07/31/2017,Berkshire Hathaway Inc Class A,"262,786","263,441","252,254.15","254,990","6,562",1.475776,
08/31/2017,Berkshire Hathaway Inc Class A,"271,450","272,857","262,700","263,929","6,281",1.484843,
09/29/2017,Berkshire Hathaway Inc Class A,"274,740","275,945","259,040","272,800","5,916",,
10/31/2017,Berkshire Hathaway Inc Class A,"280,470","285,950","274,500","274,999","4,886",1.534343,
11/30/2017,Berkshire Hathaway Inc Class A,"291,500","291,500","270,250","282,199.99","6,430",1.555272,
12/29/2017,Berkshire Hathaway Inc Class A,"297,600.01","301,000","284,750","290,634","6,204",,
01/31/2018,Berkshire Hathaway Inc Class A,"323,375.05","326,350","294,000","300,000","9,582",1.725398,
02/28/2018,Berkshire Hathaway Inc Class A,"310,250","326,110","285,250","322,300.01","10,176",1.465279,
03/30/2018,Berkshire Hathaway Inc Class A,"299,100","320,000","288,450","311,000","7,169",,
04/30/2018,Berkshire Hathaway Inc Class A,"290,650","304,200","288,739.99","298,620","5,167",1.37279,
05/31/2018,Berkshire Hathaway Inc Class A,"287,200","303,530","280,427.97","291,150","7,118",1.35999,
06/29/2018,Berkshire Hathaway Inc Class A,"282,040.01","295,302.5","281,600","290,080","6,763",,
07/31/2018,Berkshire Hathaway Inc Class A,"301,550","304,399.5","281,600","282,050","6,812",1.427964,
08/31/2018,Berkshire Hathaway Inc Class A,"315,800","317,850","299,000","302,500","5,460",1.450788,
09/28/2018,Berkshire Hathaway Inc Class A,"320,000.05","334,560","315,000","316,900","6,261",,
10/31/2018,Berkshire Hathaway Inc Class A,"307,705","335,900","296,002.5","323,165","8,598",1.410673,
11/30/2018,Berkshire Hathaway Inc Class A,"326,000","335,109.08","305,250","308,007","5,756",1.424865,
12/31/2018,Berkshire Hathaway Inc Class A,"306,000","335,041","279,410","331,500","10,505",1.336838,
01/31/2019,Berkshire Hathaway Inc Class A,"311,500","311,890","286,650","306,000","9,117",1.360866,
02/28/2019,Berkshire Hathaway Inc Class A,"302,200","313,960","297,381","310,005","5,031",1.422135,
03/29/2019,Berkshire Hathaway Inc Class A,"301,215","311,299","295,900","304,520","5,255",,
04/30/2019,Berkshire Hathaway Inc Class A,"325,080.01","325,844.93","302,800","302,800","4,615",1.524494,
05/31/2019,Berkshire Hathaway Inc Class A,"297,060","328,555","296,800","325,700","6,730",1.316903,
06/28/2019,Berkshire Hathaway Inc Class A,"318,350","319,960","296,622.75","297,000","4,742",,
07/31/2019,Berkshire Hathaway Inc Class A,"308,666","324,711","306,623","321,032.25","5,590",1.367323,
08/30/2019,Berkshire Hathaway Inc Class A,"303,078","316,000","294,510.58","310,250","5,448",,
09/30/2019,Berkshire Hathaway Inc Class A,"311,832","321,833","300,731.42","306,750","4,993",1.3301,
10/31/2019,Berkshire Hathaway Inc Class A,"318,939","320,500","302,260.01","313,099.99","7,219",1.359009,
11/29/2019,Berkshire Hathaway Inc Class A,"330,495.11","335,000","320,000","320,250","6,063",,
12/31/2019,Berkshire Hathaway Inc Class A,"339,590","342,250","324,900","330,802.15","5,698",1.387845,
01/31/2020,Berkshire Hathaway Inc Class A,"335,996.01","347,400","332,000","338,750","5,520",1.373157,
02/28/2020,Berkshire Hathaway Inc Class A,"309,096","345,000","300,750.02","338,160","6,046",,
03/31/2020,Berkshire Hathaway Inc Class A,"272,000","327,937","239,440","314,000","18,913",1.037325,
04/30/2020,Berkshire Hathaway Inc Class A,"281,700","295,764.67","261,180","265,900","14,104",1.074318,
05/29/2020,Berkshire Hathaway Inc Class A,"278,640","280,899","250,926.02","278,121","8,574",,
06/30/2020,Berkshire Hathaway Inc Class A,"267,300","304,990.01","262,700","278,167","13,834",1.151483,
07/31/2020,Berkshire Hathaway Inc Class A,"293,631","294,869.99","266,356.59","267,600","8,122",1.258199,
08/31/2020,Berkshire Hathaway Inc Class A,"327,560","329,299.19","294,510.01","295,000","8,064",1.32536,
09/30/2020,Berkshire Hathaway Inc Class A,"320,001","334,960","310,591.03","325,500","9,825",1.277285,
10/30/2020,Berkshire Hathaway Inc Class A,"302,500.01","326,150","297,817","321,219.01","5,612",,
11/30/2020,Berkshire Hathaway Inc Class A,"343,688","352,500","305,242.01","307,499.9","7,520",1.294063,
12/31/2020,Berkshire Hathaway Inc Class A,"347,815","348,500","333,150","346,480","9,220",1.293523,
01/29/2021,Berkshire Hathaway Inc Class A,"344,100","354,837","340,816.06","344,302.25","7,044",,
02/26/2021,Berkshire Hathaway Inc Class A,"364,580.01","377,356.95","344,250","345,000","18,995",,
03/31/2021,Berkshire Hathaway Inc Class A,"385,702","407,750","368,430.01","372,555","56,239",1.327834,
04/30/2021,Berkshire Hathaway Inc Class A,"412,500","417,905","385,702","387,979","37,493",1.417033,
05/31/2021,Berkshire Hathaway Inc Class A,"435,999.99","445,000","410,850","418,961.98","42,395",1.481636,
06/30/2021,Berkshire Hathaway Inc Class A,"418,601","441,063","409,701.02","438,717.56","32,818",1.412099,
07/30/2021,Berkshire Hathaway Inc Class A,"418,900","424,304.08","407,773.23","418,708","24,523",,
08/31/2021,Berkshire Hathaway Inc Class A,"429,900","439,800","416,964.875","420,985.27","23,669",1.377269,
09/30/2021,Berkshire Hathaway Inc Class A,"411,378.99","433,720","409,000","431,180.5","25,618",1.305733,
10/29/2021,Berkshire Hathaway Inc Class A,"432,902","439,849.99","410,099.5","412,915.5","32,109",,
11/30/2021,Berkshire Hathaway Inc Class A,"416,876","445,000","416,545.61","434,513.0078125","39,405",1.313698,
12/31/2021,Berkshire Hathaway Inc Class A,"450,662","455,910","415,000","421,535.48","39,045",1.409205,
01/31/2022,Berkshire Hathaway Inc Class A,"469,805","487,255","443,401.7","452,005.14","46,323",1.469064,
02/28/2022,Berkshire Hathaway Inc Class A,"476,205","488,399.85","450,000","469,465.13","37,165",1.388675,
03/31/2022,Berkshire Hathaway Inc Class A,"528,921","544,389.26","470,644.87","482,000","58,141",1.536898,
04/29/2022,Berkshire Hathaway Inc Class A,"484,340","533,139.26","484,340","530,026","59,632",,
05/31/2022,Berkshire Hathaway Inc Class A,"474,050","494,343","448,108.34","485,921.01","54,295",1.372194,
06/30/2022,Berkshire Hathaway Inc Class A,"408,950","476,594.26","396,500","476,594.26","48,580",1.181812,
07/29/2022,Berkshire Hathaway Inc Class A,"451,700","453,985","407,700","407,700","44,200",,
08/31/2022,Berkshire Hathaway Inc Class A,"421,308","463,000","421,308","451,989.26","59,192",1.340338,
09/30/2022,Berkshire Hathaway Inc Class A,"406,470","434,576.75","395,202.25","421,000","59,666",1.293133,
10/18/2022,Berkshire Hathaway Inc Class A,"428,465","431,340","393,012.25","409,434.625","33,347",,
1 Like
Hopefully the main point didn’t get lost in the other interesting tidbits:
Suppose we want to do something like Jim’s analysis, but use IV and not Book, in the hopes of maybe even getting a tighter relation.
That’s in a different thread, so to rephrase the issue in terms of @rrr12345 graph of "Price/Trendline Oct 1964-Jun2022):
when you’re way below 1 (undervalued) do you tend to get higher forward average returns and when you’re way above do you tend to get lower?
My understanding of @rrr12345 work is that IV on a date would be the TrendlinePrice for that date in a plot of log(Price ) vs log(Book).
Is the relation between IV and future return tighter than Book and forward return?
But for the analysis suggested above, you can’t take IV from the trend line determined from all the data i.e.including data in the future of the date for which you’re determining IV, because that requires a crystal ball. You need to calculate the trendline using all data to the past of each date of interest. There’d be a ‘burn-in’ period to establish a gross trend, and then you start calculating trendlines and hence IV for each date after the burn-in period in a walk-forward process (lots of trendlines).
Having had my attention drawn to trend lines by the above thought, I then started noticing these breaks I referenced in the trendlines, even before doing much of any walkforward analysis. And things would get even more complicated when you start determining trendlines in a walk forward manner.
So I thought I’d post it and see what people might think.
I agree, it’s probably no co-incidence that BRK and the SP500 share a similar break.
2 Likes
Using trend price as a proxy for IV is risky if there is a genuine deterioration in the business. It assumes that IV growth continues at a constant rate. Even if IV continues to grow but at a lower rate, you could get caught out by this plan. While a multiple of BV is not a perfect substitute for IV, I think it is safer than trend price.
Actually it doesn’t assume that either IV or BV grow at a constant rate, or at the same rate. It just assumes that IV/share more or less tracks BV/share, which is borne out in John Kish’s IV estimates over a period of 33 years. John’s IV estimates, using both DCF and two-column calculations, have almost perfect fits (r^2 = 0.99) when plotted against BV. The question is which of his set of IV estimates, conservative, more conservative, etc, is right. Price/share plotted against BV/share also has an excellent fit (r^2 = 0.97), and it seems to me that over the long term, say 30+ years, the trendline of P/share versus BV/share provides a reasonable estimate of IV. That’s the hypothesis anyway.
4 Likes