Berkshire Historical IV data

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21

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))
PriceOverBookOverTime
Blow up period 1998-1999
Book1998_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
logPrice
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
logPriceYahoo

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
Book

Zooming in on that big blip towards end of 1998 shows a big rise in Boook:
Book1998_1999

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):
Book

and here it is again with log(Book)
logBook

One sees this in a plot of log(Price) vs log(Book)
LogPriceVsLogBook
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:
LogPriceVsLogBookPost1998
slope=0.88036

Here’s pre-1998
LogPriceVsLogBookPreDec1998
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.

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22

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?

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23

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.

1 Like
24

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.

Picture5
Picture52630×1801 364 KB

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25

O

Oops. I meant semi-log plots, with exponential trendlines.

With a power law trendline.

26

Sorry for messing up the cut and paste of the quotes.

27

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.

28

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 :slight_smile:
Good luck with your analysis,
rrr12345

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29

@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
30

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
31

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
32

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.

33

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
34

That’s true if one is making a real time IV estimate, but there’s no reason why one can’t go back later and revise an IV estimate using data before and after the given point in time.

It’s hard to say without making the two forward return plots. For the period Dec 1999 to Jun 2022 it may not make much difference. The scatter results more from changes in P/BV and P/IV than it does from changes in BV/share and IV/share growth rates.

3 Likes
35

Thanks, I copied it. I was visualizing just a quarterly series that had BV on the day it was released. Do we know if Morningside makes any adjustments to BV? Or would this just be pulled from the statements. I’m assuming the later.

36

@johnIII I don’t know the answer to your question. Also recall that M* data was a bit different between what I had and what @cwags02 had (not by much, but what the heck M*?). You’ll also see that the data I posted isn’t always just quarterly, although all quarters are represented. What’s up with that? Mysteries remain, but it’s probably about as good off-the-shelf data that one can get.

1 Like
37

For those not following every detail, it may be worth clarifying that we’re talking about two very different types of ‘trend’:
(1) trend of e.g. log(BRK) price or log(BRKbook) over time, also log(SP500) price over time
(2) trend of log(BRKprice) plotted against log(BRKbook). The trendline price is suggested by @rrr12345 to be strongly related to IV

It’s the plots over time that look piecewise linear, i.e. linear for a long stretch with one slope, then linear for a long stretch with a different slope.
I hadn’t expected it and don’t know how to explain it.

For those liking the idea of using BRK book as a proxy for IV – that’s probably generally good (and Jim had remarked in his posts in sort of a bemused way that despite all his very careful hand adjustments for getting IV, that it looked pretty much like a multiple of Book). But WEB himself noted in his 1998 annual report how the GenRe acquisition made an artifactual bump in book that has nothing to do with IV. Also, ordinary least squares, which is usually used to find trend lines, can be thrown off by bumps i.e. outliers. So some care may be needed.

I’m still interested in Jim’s style of analysis of BRK that relates some measure of present value such as Book (not from a trendline), to some measure of forward return. @cwags02 has started similar analysis for KMX using Sales and not Book.

Jim used peak Book. I’m still agnostic on that:
Is it peak book forever? Over the past X years? What about things like the GenRe acquisition artifactually bumping up book, is that accounted for? FWIW, Hussman has used Price/PeakEarnings for S&P analysis, where peak was over last 10 years, so there’s some other thinking along similar lines (I’m not at all endorsing Hussman’s approach, just mentioning it):

Hussman Funds - Price to Peak Earnings

I generally don’t like single point statistics such as min or max (peak) for messy data, so I might try median P/B over past X-years or something. I also don’t like using averages for messy data (Jim used average forward one year return) so I may play with some median ideas on future price.

My intellectual interest in all this is that Jim showed a strong relation between P/B for Berkshire and forward returns. This is a demonstration that at least for one ‘good’ company that the thesis of value investing, i.e. buy ‘good’ companies ‘cheap’, actually works. Many have failed at value investing.
My lizard brain interest is that I followed up on Jim’s suggestion a few times and bought DITM calls on BRK when it was ‘undervalued’. Worked like a charm, so I want to do this with a small portfolio of companies.

3 Likes
38

Well, I think the idea was that if BV ever dropped it was transient, or temporary. I suspect it’s never taken more than a year or so for BV to recover. Is that true?

I’d also be inclined to not worry about fitting the older data. It was essentially a different company then, so it’s like piecing together data points from two different companies. Based on Jim’s suggestion that since 2012 P/BV changed, I’d maybe stick to data from 2012-present. Or at least start with that model and then see about the intricacies of adding older data, perhaps with some kind of adjustments. I think Jim made an adjustment for new tax laws that took place around 2017(?). I think he speculated that the company was worth 3-4% more due to the tax laws. I’m not sure if he boosted the price series for prices prior to the tax law to account for this or what, but I think he made an adjustment. But probably not necessary, especially for a first order model.

I think Jim had several models he used independently, even averaging them at times. I think one of the variables in his models was how far back the data went.

4 Likes
39

@johniii
I see nothing special in P/BV in 2012, if you do let me know?

PerformanceAnalytics package in R has charts.PerformanceSummary() as well as other tools which answers your question about Book drawdown, look at last chart:
BookDrawdowns
Ignore the center chart, I simply treated Book as a price so it wants to create a plot of ‘return’, first chart is basically Book. We know what happened around 1998.

2 Likes