Jan 29th 2009 05:04 pm Wall Street Can’t Count
Take a look at this chart that someone sent to me a couple days ago. I’m making it big so you can see as much detail as possible. Have a look and then come back, okay?
Pretty scary, eh? It’s a chart showing the deterioration of major bank market caps since 2007. Prepared by someone at JP Morgan based on data from Bloomberg, this chart flashed across Wall Street and the financial world a few days ago, filling thousands of e-mail in boxes. Putting a face on the current banking crisis it really brought home to many people on Wall Street the critical position the financial industry finds itself in.
Too bad the chart is wrong.
It’s a simple error, really. The bubbles are two-dimensional so they imply that the way to see measure change is by comparing AREAS of the bubbles. But if you look at the numbers themselves you can see that’s not the case.
Take CitiGroup, for example. The CITI market cap dropped from $255 billion to $19 billion — a difference of 13.4X. If we’re really comparing the areas of the bubbles, that means 13.4 of those tiny CitiGroup-of-today bubbles should precisely fill the big CitiGroup-of-the-good-old-days bubble. Only they won’t. As a matter of fact it would take about 3.1415928 times as many little bubbles to fill the big bubble as the chart preparer thought. That’s because the comparison isn’t two-dimensional but one-dimensional — the true comparison is the DIAMETERS of the bubbles, not their areas.
So it’s a typo: no big deal, right? Yeah, but what a typo! It got past Bloomberg and JP Morgan and pretty much all of Wall Street before someone said, “Hey, this makes no sense!”
How could this be? It’s because Wall Street doesn’t work the way we think it does — the way we are led to believe it does. Wall Street is a marketplace, a selling ground where everything from ideas to stocks and bonds are on sale every day. And there is nobody easier to sell to than a salesman. Come up with a good chart that’s within an order of magnitude of reality, put a disclaimer on the bottom, and let ‘er rip.
No wonder we’re in a global financial crisis.
The people we count on to understand what’s going on can’t even read a chart.
Tags: banks, cringely, market cap, Wall StreetPosted by APIyuIRrClENtBtCk / Other People's Ideas
PaulProgrammer on 29 Jan 2009 at 5:16 pm #
Bob,
Your incredulity is not totally misplaced, but I take issue with the statement that the same “journalists” and PR agents responsible for this chart are the guys behind the “financial engineering” of the last decade that has made our life so miserable this year. Without a doubt the chart is misleading (nearly all published charts are skewed to make a point — see “how to lie using statistics”), but only in a yellow journalism sense, not in a savvy financier manipulation sense.
Ian on 29 Jan 2009 at 5:36 pm #
I’m pretty sure your math is incorrect, too. The bubbles are incorrectly sized by a factor of the squares of their respective radii, not by a factor of pi.
brian on 29 Jan 2009 at 8:03 pm #
Man that’s dirty. I’ve never seen someone use circles for a bar chart type representation. Blegh.
Ed on 29 Jan 2009 at 8:23 pm #
Ian is right. The ratio of the areas of the circles mentioned is out by a factor of 13.4, not Pi.
Oh, Bob. Not only are you attacking people for not being able to do maths, but you can’t do maths yourself. And apparently you also didn’t understand the critiques that people posted either.
Still, who expects either maths or reading comprehension from journalists?
trent on 30 Jan 2009 at 3:33 am #
Picking nits with Bob eh?
The Anatomy of a Misleading graph with color commentary:
Area of circle = radius squared x Pi (~3.14 etc…)
These figures are most understandable when graphed linearly. Typically, $ valuation would be reflected on the Y (Vertical) axis while the comparision time periods (2007 & 2009) would be labeled on the X (horizontal) axis. A single variable ( $ market cap) is being measured.
It is an assumption on the reader’s part that the $valuations given are meant to indicate the area of the circles. It is also reasonable on Bob’s part to assume that these numbers would best reflect the diameter if one was silly enough to use circles to compare these values. I should note that financial statements and home finance software love to use pie charts to breakdown categories of assets for graphing comparisons. (My 401K Pi has been shrinking.)
If one was to use circles to compare $ market caps these numbers could represent the area, diameter or radius of the circle. It does not matter if $valuation is represented by the radius, diameter or area of a circle as long as the same component is used consistently.
The actual size scaling of the circles would depend on which component was used as the comparison. Differences in circle size would be magnified the most by assigning the $valuation to the radius and magnified the least using area.
(see formula for area of a circle and plug in the numbers).
Lets use the Citigroup numbers:
Example A: If Area(2007) = 255; radius~9, diameter ~18
Area (2009)= 19; radius~2.46
area 2007 is ~13.4 times greater than 2009
Example B: If Diameter 2007= 255 and Diameter 2009= 19;
Area 2007~ 51070 and Area 2009 ~ 284
Area 2007 ~180 x greater than 2009
Example C: If Radius 2007=255 and Radius 2009=19;
Area 2007 way way greater than Area 2009.
I think you get the point.
Apples to Apples, Oranges to Oranges
Maybe the marketing guys are not clueless but understand how to get their message across. Keep us impressed but confused.
Thanks again to Bob for pointing out something I would not have noticed and to other readers for pointing out minor glitches. This lead to some stimulating mental exercise in math and logic when I should have been in bed sleeping. I should not to read Bob just before going to bed.
P.S- Any chance of getting a grammar checker for this reply box (I’m lazy). It would be of help to me as well as some of your other readers.
Best Wishes
trent on 30 Jan 2009 at 4:11 am #
A correction to my last post before some catches it.
I should have done the full math for previous post using example C. Proportional differences in area are the same for two different sized circles whether radius or diameter are used.
Example C: If Radius 2007=255 and Radius 2009=19;
Area 2007 = 204282 area 2009~ 1134
Area 2007~180 X greater than 2009
I was actually losing sleep over this and got up out of bed to fix it.
Brent Williams on 30 Jan 2009 at 8:10 am #
Typical lying with statistics, Bob. This was covered in the 1954 classic by Darrell Huff “How to Lie with Statistics” and is available for less than $5 on Amazon, used. New, of course, is twice that. It’s not so much that the Wall Street types can’t read a chart as the person that put this chart together intentionally chose a graphing method that is intentionally misleading. It’s a psychological trick that is used in advertising all the time. Look around and you’ll find other examples in high-pressure sales. In this case, who ever was the author was probably had a vested interest in killing the banking industry even more.
Mark Hewis on 30 Jan 2009 at 7:18 pm #
http://en.wikipedia.org/wiki/Fractional_reserve_banking
Works perfectly until the assets decrease by more than than the fractional reserve.
Sadly all the financial instruments break if all the assets break together. At that point you might as well ask Kermit the Frog what the value of the above really is.
The good news is that if you provide any value that is respected by the market to these assets the recovery can start.
Just don’t expect anyone to trust these ‘instruments’ again. Which is a lot of jobs and revenue.
The second good news is a lot of top notch brains are on the market for cheap and guess what - from environment to health to social we have a lot of problems to solve.
Picking itself up, learning from mistakes and going for the big one is what US folk I have met are great at. Good luck - hope here in UK we can do likewise.
Robert X. Cringely on 31 Jan 2009 at 3:07 pm #
Damn! And here I’ve had Huff’s masterpiece sitting on my bedside table all this time.
I’m sorry if I got the math wrong, though where these nasty attacks on journalists come from I don’t understand. Feel free to stop reading at any time.
All the best,
Bob
Mario Sikorski on 31 Jan 2009 at 7:08 pm #
Welcome to the perfect world of economics where the interest don’t exist. Only debt that must by payed off. Damn this is a masterpiece that you gentleman must visit.
this is the latest news quest for perfect economy interest-free-monetary-system, but not debt free, as was originally intended by the founding fathers of our republic.
http://perfecteconomy.com/wp/2009/01/25/how-mathematically-perfected-economy-shakes-out-for-gold/
Great conversation.
It is re posted on mpe forum.
http://www.perfecteconomy.com/f/viewtopic.php?f=80&t=340&p=890#p890
Perfect Economy is about eliminating any financial vulnerabilities of the free market.
Mario Sikorski on 01 Feb 2009 at 2:12 am #
Perfect Economy is a world wide quest to eliminate any financial vulnerabilities by providing solution leading to full sustainability for all the monetary systems for all governments in the global free market economy.
Jonovitch on 03 Feb 2009 at 2:53 pm #
Bob, the first thing I thought — before I even started reading — was, “those charts are distorted.” (Thanks Stats 201!) It’s one of my pet peeves, and I see it all the time.
I thought I was going to have to write to you how your chart was screwed up and blown way out of propotion, but then you did it for me in the third paragraph! Woohoo!
If only all journalists (and financial analysts?) were required to take stats. *sigh*
Jon
William Cross on 03 Feb 2009 at 5:59 pm #
Hi Bob,
Yeah, it hurts to correct you when you’re (correctly) pointing out someone else is wrong, but Ian is correct: you made a mistake in your algebra.
For two circles with a given ratio of their diameters, d1=2*r1 and d2=2*r2, the ratio is Rd d1/d2= (2*r1)/(2*r2) = r1/r2. The ratio of their areas will be Ra = A1/A2 = (PI*r1^2)/(PI*r2^2) = (r1^2)/(r2^2).
Notice that, when doing ratios, the factor of PI drops out, so if a financial whiz is confusing areas and diameters of circles, he will be off not by a factor of PI, but by a factor of Rd/Ra = r2/r1 = d2 / d1, although the ratio of the diameter d1 to the area A2 would be 2*r1/ (PI*r2^2) = (r1/r2)* 2/(PI*r2), but that’s neither here nor there.
-Wil
jp on 04 Feb 2009 at 10:54 am #
To trent… use the latest Firefox for built-in spell-check. Grammar check though? I haven’t seen that in a web site yet (please, no referrals necessary)
trent on 05 Feb 2009 at 1:59 pm #
Thanks JP,
Sorry for the confusion; I was too subtle with my satirical request for “grammar” checker. Comment intended as a DBHBS (double back handed bitch slap) at “Ed” for inelegantly playing rough with Bob and journalists.
ED: “Oh, Bob. Not only are you attacking people for not being able to do maths, but you can’t do maths yourself. And apparently you also didn’t understand the critiques that people posted either. Still, who expects either maths or reading comprehension from journalists?”
TRENT: OUCH!!
Ed on 05 Feb 2009 at 6:37 pm #
Trent,
Seems your DBHBS missed. Better luck next time…
What have we done? | Software as Services | ZDNet.com on 07 Feb 2009 at 6:38 pm #
[...] yes. Even Wall St can’t count, as Robert Cringely revealed last week. (An analyst at JP Morgan came up with a graphic to [...]
Tim McGuire (Sr.) on 09 Feb 2009 at 11:53 am #
I believe that a problem perhaps even more serious than math(s) incompetency is the pervasiveness of innumeracy, which is also illustrated by the original example. Far too large a proportion of the US population has no sensitivity for order of magnitude.
Andy on 09 Feb 2009 at 12:33 pm #
OK. So here’s my bias:
http://www-personal.umich.edu/~jpboyd/eng403_chap2_tuftegospel.pdf
What I see in the JPM graph:
“Banks: Market Cap”
MS RBS DB …etc (yes! mea culpa)
07Q2 49 120 76
09Q1 16 4.6 10.3
CS … etc (yes! mea culpa)
07Q2 75
09Q1 27
“WE CANNOT GUARANTEE THE ACCURACY …”
Message - JPM has the biggest green circle at 85: “we win”
Take Away: The graph is a political statement intended for a political audience.
The area selections and arrangement are puffery used to make them look even bigger relative to the competition. Edward Tufte would be dancing all over this mess (with perhaps a few kicks at my write-up here!)
This chart is not about statistics or economics. I certainly wouldn’t use it (or its inconsistent data) as a source for “the deterioration of major bank market caps since 2007.”
fmo on 09 Feb 2009 at 3:00 pm #
Please don’t assume that the author of the chart did not know the error. Have you worked with Wall Street types? I have.
Bill Strickland on 09 Feb 2009 at 3:56 pm #
As was pointed out by one correspondent, when calculating the ratios of the areas of each circle in a pair, the factor pi no longer matters. This should be apparent because the figures could be squares, triangles or silhouettes of Kermit the Frog and, as long as they’re the same figure at different magnifications, the area ratios will always be between the squares of [pick a dimension]. As pi has nothing to do with the area of a square, it must have nothing to do with any area ratio between geometrically similar two-dimensional figures.
(That paragraph may not have been as interesting as I thought it would be.)
Norm Cimon on 09 Feb 2009 at 5:39 pm #
Reducing the diameters by the proportion of the reduced valuation means that r2 = (v2/v1)*r1. The area ratio of the two circles as a function of the radii is (r2/r1)^2. so the distortion is ((v2/v1)r1/r1)^2, or just (v2/v1)^2, the square of the original valuation ratios. So if the new valuation is half the old, the reduced circle is 1/4 the area. But if the valuation is 1/10, the reduced size is 1/100! That has its uses I guess, but bringing a sense of reality to this particular effort is not one of them. The name that the irascible Edward Tufte uses for this sort of useless exercise is chart junk. No one should consider themselves visually numerical until they’ve read his classic, The Visual Display of Quantitative Information.
Ed on 09 Feb 2009 at 8:09 pm #
@Norm Cimon
“So if the new valuation is half the old, the reduced circle is 1/4 the area. But if the valuation is 1/10, the reduced size is 1/100!”
You have said that the distortion is equal to the ratio of values, squared ((v2/v1)^2). However, this is wrong. Since the CORRECT ratio of values is (v2/v1), and the displayed ratio is ((v2/v1)^2), then the DISTORTION is only (v2/v1).
This has already been explained above a couple of times, both with and without algebra. This article may be of some assistance.
Norm Cimon on 09 Feb 2009 at 9:44 pm #
No I meant what I said. The original is distorted - has its shape changed - by what should have been a straight ratio but is, instead, that ratio squared. But that’s a quibble over the word definition isn’t it?
There’s a larger point here. The ability to use anything for a presentation often leads people to use everything. When presentation software was new I had to sit down with otherwise rational scientists and beg them to step back and look at what they were doing to their basic goal of delivering information. In fact there’s a larger argument to be made about whether and what “is our children learning”. And Tufte makes it, whacking the ruler on the table the entire way:
http://www.wired.com/wired/archive/11.09/ppt2.html
Ed on 09 Feb 2009 at 11:46 pm #
Norm,
So don’t use the word “distort” when you mean “change”, or maybe “scale“. It heavily implies a change that’s bad, or in this case wrong. Unless you’re saying it’s a mathematical term.
There is also a larger argument to be made about accurate use of language. And possibly about admitting when one errs rather than simply accusing others of quibbling. Unlike certain recently-evicted senior US politicians.
The culture of free money: What have we done? « Notes to me on 10 Feb 2009 at 8:40 pm #
[...] yes. Even Wall St can’t count, as Robert Cringely revealed last week. (An analyst at JP Morgan came up with a graphic to [...]
Norm Cimon on 10 Feb 2009 at 9:27 pm #
Dude, a change in a shape is a distortion. As for words are ambiguous by design. It is the beauty of language, and what distinguishes it from math. Try this one on for size, a headline that reads “Shipping Sinks”… Explain please.
Ed on 10 Feb 2009 at 11:38 pm #
Dude,
Learn to either use language well, or do math well. Either would be good here.
Tom on 11 Feb 2009 at 9:51 am #
This string of comments illustrates what is wrong with the typical waste of our intellectual resources. Rather than spend energy in analyzing how we as an economy should address the collapse of these companies and the corruption that led to the disappearance of billions of investor and now tax payer dollars; we debate the grammer and mathmatical skills used to illustrate the discrepancies in the values of these businesses.
Ed on 11 Feb 2009 at 6:21 pm #
Tom,
a) If one’s analyses are flawed, then one’s prescriptions for action will be wrong. We need to get our analysis right. Otherwise we will not just fail to improve things, but certainly make things worse.
b) You’re right, the commenters on a blog should turn their energies to fixing the economic problems!
Any suggestions?
p.s. It’s “grammAr” and “mathEmatical”. Live by the nitpicking, DIE by the nitpicking!
Nicolas Thiery on 05 Apr 2009 at 11:31 am #
By the way, pi is not approx 3.1415928, it is approx 3.1415927 (3.1415926535…). Isn’t anyone paying attention
How to Get Six Pack Fast on 15 Apr 2009 at 11:15 am #
After reading this article, I just feel that I need more information on the topic. Can you share some more resources please?
Overcharting at This is the Green Room on 02 Jun 2009 at 6:24 pm #
[...] may remember last year a JP Morgan chart was circulated which showed the deterioration of bank’s market values. The old and new market values were [...]
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