That’s the question Bob Cringely asks.

Bob points out what might be an embarrassing error in a chart (below) — on the Banks/Financials no less — prepared by a JP Morgan Analyst:

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 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 13.4 times as many little bubbles to fill the big bubble as the chart preparer thought or 179.64 little bubbles.  Pi r squared, remember?  This is because the intended comparison wasn’t two-dimensional but one-dimensional — the chart maker was intending we compare the DIAMETERS of the bubbles, not their areas.

My first read of this is that comparing height (i.e., bars rather than circles) would be accurate. Circles won’t work due to the squaring (π R squared) , where as diameters do not bring in a factorial change. That’s what creates the exponential rather than arithmetic change in the circle’s area.

I don’t have the original data, and I am wondering if this might be a simple Excel charting error [Update: Excel gives you the option of selecting Area or Diameter when choosing the circle chart as an option. I suspect this was a simple spreadsheet graphing error — not a mathematics error — but its embarrassing nonetheless]

If anyone has either the Market cap data handy, or wants to pull the teeny data from the chart onto a spread sheet, please email it to me at Alternatively, if you can design a more informative/accurate graphic, please send that along . . .

UPDATE: 2/15/09 5:52pm

Several corrected versions of the original chart (below) follow . . .


click for ginormous chart


Rene Corda suggested this as the the proper picture:

New & Improved Chart

(looks like JPM fixed their own chart)

QQQ Trader send this chart along (with averages!)

Ironman at Political Calculations gives us these two beauties:

Bar Chart:

Radar Plotting Chart:

And Mark McHugh of Across the Street came up with these two beauties:


Wall Street Can’t Count
Robert X. Cringely
February 12th, 2009

Category: Humor, Markets, Mathematics, Research, Valuation

Please use the comments to demonstrate your own ignorance, unfamiliarity with empirical data and lack of respect for scientific knowledge. Be sure to create straw men and argue against things I have neither said nor implied. If you could repeat previously discredited memes or steer the conversation into irrelevant, off topic discussions, it would be appreciated. Lastly, kindly forgo all civility in your discourse . . . you are, after all, anonymous.

39 Responses to “Can Wall Street Do Basic Math?”

  1. danm says:

    Nearly all don’t know math because they take these introductory course in college which shows them how to apply a formula but not where it came from and why it was discovered in the first place. And most who do know math have troubel with sociology, psychology or history.

  2. Bruce in Tn says:

    SAN FRANCISCO (MarketWatch) – General Motors Corp. will offer the government the choice of giving it billions more in bailout money or seeing it file for bankruptcy when it presents a restructuring plan next week, according to a report published Saturday.

    ..Can the taxpayer do basic math?

    This, as others have stated, is simple theft. Taking from the taxpayer to support this severely badly run company…I vote BK…but I am sure others think they are too big to fail, and would support many more feedings at the trough…

  3. Rajesh says:

    The biggest mistake is that Market Cap doesn’t mean a damn thing for solvency, which is the question that everyone is asking. The low stock price does make it harder to raise capital, but it doesn’t tell you whether the stock is undervalued or if the market knows something that is not reflected in the accounts. My opinion is that the stock price reflects uncertainty about future earning and the fear that the witch-burning party will convince the government to nationalize solvent banks pre-emptively; like Bush invading Iraq to prevent the weapons of mass destruction from being used on us. (Fifteen minutes from launch.)

  4. danm says:

    Anyway, throughout the economy, the sector which has a balance sheet book value best reflecting its market value is probably the banking sector.

    So why would I pay much more than book if it’s marked-to-market? Banks are now trading around book but they still need huge write-offs.

    That’s math­.

  5. danm says:

    reflecting its market value is probably the banking sector.
    I meant market value of its assets.

  6. Bob the unemployed says:

    That is one of the many frequent charting errors cited in Tufte’s first book.

    It is what happens when you make tools so easy to use that no one needs to think or understand in order to use them.

  7. noels says:

    The bubble chart is nice, but also completely wrong in my view.

    The size of the smaller bubble is wrong: it is measured against the width of the bubble, where it should be measured against the size of the bubble area .
    In that way, it does not give a true refelction of the shrinking marketcaps.
    That being said, I am convinced that one day the smaller bubbles will become reality, even when measured against the bubble area of 2 years ago.

    Geert Noels

  8. Greg0658 says:

    Rajesh – I agree with you on market cap (stock price) being a inconsequential number.

    An excellent posted market number of a businesses stock worth would need to include current debt (increased by proposed interest), current property value (reduced by wear and tear losses), position of business in the creation of a widget spectrum, value of that widget spectrum, and employee liabilities. Thats a good start.

    I guess thats why we have analysist today. Mechanism shortcomings. Sorta like the Republic Voting Mechanism vs the Democracy Vote’g for itself.

  9. Baille Beag says:

    Bubble Charts in Excel have an Option for “Area” or “Diameter”. Whoops!

  10. try2bamused says:

    Here is some basic math for you:

    US policy makers and elites = incapable of doing the right thing

    SPX = 150

  11. tranchefoot says:

    The pedant in me has to make a small correction. The growth in the area of a circle is not exponential, it is polynomial: r^2 not 2^r. sorry…

  12. constantnormal says:

    And here I thought all the opportunities to short the banks had passed me by … if the smaller circles are really 13.4 times larger, then the potential for declines in the bank stocks is still significant.

    It’s really just a question of whether they are allowed to sink themselves, or take the government/taxpayer with them.

    Bernanke has come to represent a banking Capt Ahab in my eyes, sacrificing all in order to nail the Great White Whale. The man has completely forgotten about the greater economy in his quest to preserve the dead financial industry of yesteryear.

  13. constantnormal says:

    Ok — never mind — I see (typing instead of thinking), it’s the proportion of areas that should be constant, the 13.4X only applies to Citi. Staggered bar charts would be a lot clearer. Obfuscation by charting — marketing 101.

  14. Andy Tabbo says:

    funny stuff that. Publishing an erroneous chart to the general public from a banker who “should” no more…He probably made lots of charts like that at Wharton B-School, but nobody there knew any better.

    contantnormal: I like you’re comment about sacrificing all in order to nail the Great White Whale. At this point the morbid fixation “with getting toxic assets off the balance sheet” is becoming a real sideshow. As is customary, legislators are fighting the last battle. That was early 2008 problems….getting banks to quickly clean up there balance sheets.

    Sure the blowhard congress people can cite examples of people/firms losing credit, but that’s what happens in depressions. People don’t feel like borrowing and banks don’t feel like lending. It’s an easy psychological problem to understand.

    The only battle for 2009 is figuring out ways to turn the economy around. The government should be:

    1) providing increased safety nets to the recently unemployed;
    2) providing massive incentives for businesses, or potential business, of all sizes to “invest” right now;
    3) relaxing the standards for bank holding companies. Let new private money come in and recapitalize. It’s actually a great time to be a bank….private money wants to enter this space.

  15. Mike in Nola says:

    Boy, learned something new about excel. Don’t use it that often and didn’t know it had bubble charts. Assumed that was Visio.

  16. Bruce in Tn says:

    Stock slaughter
    For equities, a sustained period of deflation is widely seen as a disaster

    Another math question: Will we have a worldwide deflation? Is the synchronous global decline in imports and exports a harbinger of continuing deflation?

    ‘It’s not a question of if. Deflation is upon us. It’s a question of how bad it will get.’
    — John Brynjolfsson, hedge fund investor

  17. constantnormal says:

    Back in the day, in a prior life in a galaxy far, far away, I was a sales support droid for a time, and we learned such valuable presentation skilz as creating charts with dual Y-axes with different scales, so as to flatten the appearance of choice A vs choice B. The trick is to not leave them on-screen for too long, lest the prey/customer get beyond the curves to examining the fine print and tumbling to the misrepresentation. Small/sparse printing also helps.

    This sort of deceptive charting is standard practice, the corporation I worked for at the time hired away the guy who taught us how to lie like this, from the industry leader, one of the larger corporations in America (a S&P 100 company) that is widely respected for its ethical practices.

    The lesson here, at least regarding sales pitches, is to get copies of all the charts used in the presentations — arrange for this ahead of time, and if you get stiffed with the “proprietary” block, tell them you’ll sign a NDA (you probably already did, and if not, ask why not if it is proprietary), and if they won’t leave you with copies to study, they can’t present it.

    Of course, these sort of presentations are usually restricted to the most senior management (and thus most easily fooled by technical or detailed financial stuff), and lesser mortals do not get to apply constraints to the pitches.

    Everyone should spend one career in a sales organization, it gives respect for the salespeople who are gifted and for how hard they work, and also develops a healthy skepticism for presentations.

  18. Its_Science says:

    I’m glad someone called attention to this. I’ve seen this type of error in other places.

  19. Greg0658 says:

    constantnormal – fyi I noticed in my picture editor via zoom-in

    Citigroup has a ratio presented 255:19
    Goldman Sachs seems to be the initial compare to entity at 100:35

    it took me 4 miserable years to pass 2nd semester Algebra. I am just pointing that out … with the wonder if the base compare entiy slants the charts anywhichway

  20. Jeff L says:

    Executive Summary: No. If Wall Street could do (and understand) math, they could never come up with AAA rated CDOs from crap debt, they would never pay more than retail (i.e. BAC/MER) and a host of other stupid things they’ve done over the past umpteen years. People in Washington and Wall St. who continue to claim that these are the smartest/best people available (so don’t cut those bonuses, nobody but Geithner is capable etc) don’t get around much and hang out with too many stupid people. In short, they are too insular. Cemeteries are full of indispensable stupid people.

  21. dead hobo says:

    Mike in Nola Said:
    February 15th, 2009 at 12:17 pm

    Boy, learned something new about excel. Don’t use it that often and didn’t know it had bubble charts. Assumed that was Visio

    reply: I converted to OpenOffice a couple of years ago and completely removed all Microsoft Office programs. OpenOffice rocks. It’s free. It does everything I need. I don’t need to download security fixes for it ever, unlike MS Office which required them with regularity. The menus are a little different, that’s about it. I haven’t needed MS-Access / VBA in almost a decade so that isn’t a handicap and OpenOffice includes a database program that works with a multitude of databases.

  22. dead hobo says:

    Re the above charts:

    Is this how your basic quant does numbers?

    If a caption on a computer chart says it, then it must be true? (The AP news model)

    Do these graphs come from the mark to model objects?… the calculations look about right.

    I think the captions are wrong. They are really the secret management plans that illustrates what the cash for trash TARP properties are actually worth and what the banks tell Uncle Stupid they are worth.

    A graphical illustration of the gozintas. (As senior quant Jethro Bodine liked to illustrate .. 2 gozinta 4 twice, 3 gozinta 6 twice ..etc)

  23. dead hobo says:

    mark mchugh Said:
    February 15th, 2009 at 1:56 pm

    I took the assignment to heart, you can find it here:


    Great job. You win a GOZINTA award for being the first to graph the obvious in an easy to understand manner.

    Unfortunately you are not a quant.

    If you were a true quant, you would have added a third graph that illustrates a complicate regression technique that does nothing more than calculate rise over run. Then you would have assumed it to be a prefect predictor of the future because it fits the past so well. Then, by inference, you would accurately be able to predict the End of Times for these banks. Cable news would pick up your discovery and it would be the news of the day.

  24. mark mchugh says:


    I think the Mayans already did that.

  25. dps says:

    Maybe a stupid question. What are all those MBA and /or graduate business schools good for, connections?

  26. tranchefoot says:



  27. Marcus says:

    Microsoft Excel can plot decreases in market cap over the past year as a bubble chart. If you assume that market cap is a total amount represented by the volume of a sphere, then the volume’s diameter is the plot parameter to compare spheres.

    The set of numbers below represent Citi’s legacy market cap based on 5.5 billion shares at the share price on the 15th of each month, and data are listed in the order needed to plot an excel chart; the date, the assumed market cap on that date, and the diameter of a sphere volume with that market cap value.

    Just put this set of numbers in an excel spread sheet, highlight them, and click the 3D bubble chart. This gives a proper proportionality to Citi’s bubbles. The Big Picture posting format would not let me insert a chart, but it is a neat plot. Try it.

    2/15/08 $140 11.6
    4/15/08 $125 10.9
    6/15/08 $113 10.4
    8/15/08 $102 9.9
    10/15/08 $89 9.2
    12/15/08 $41 6.2
    2/15/09 $19 4.3

    This is charting at its best. It shows a clear trend, down and crash. And begs the question: Why is anyone in Citi senior management during this period still employed?

  28. Mike in Nola says:

    dead hobo: While I didn’t expect it, Office 2007 is surprisingly new feeling. The customizable ribbon is really nice. Also now will create pdf’s from whatever doc you are doing, which it should have had before. There are always 30 day trials available.

  29. Mike in Nola says:

    Forgot to mention that MS got real on the prices and you can now get the Office Home and student edition for a a bit over $100. It gives you a license for 3 computers.

    I think they are going after the open source market, too. Windows 7 will have a version that is very basic and somewhat limited for emerging markets. Will be very low cost or possibly free. Like the heroin dealer giving out the free samples.

  30. A reply to one of Cringely’s Microsoft threads had this link:

    Under accepted accounting rules, IBM’s corporate pension fund is not included in its balance sheet – although the company is liable to pay the pensions of its past and present employees and, to do so, it must invest their pension savings in financial and other assets. However, in line with most American (and British, Dutch and Irish) pension funds, IBM’s is heavily invested in equities and therefore suffered massive losses last year, to the tune of 21 percent of its assets. The resulting huge hole in the company’s pension liability had to be made good – by IBM, with its own money. That’s why its equity halved in one quarter.

    All this generated a sense of déjà vu for Doron Tsur, because he had written a piece two years earlier, noting a sudden 25% drop in IBM’s equity. Worse still, six years ago, in January 2003, he had written how General Motors had lost two-thirds of its equity in the last quarter of 2002, when the previous bear market punched an abyss in its pension assets. It turns out that most veteran American companies are carrying pension assets and liabilities that exceed, and sometimes dwarf, their “official” balance sheets – but these are not included in the company’s published accounts.

    Gotta wonder if non-Americans bring more objectivity to their observations..

  31. Bruce in Tn says:

    Japan’s GDP Shrinks 12.7%, Most Since 1974 Oil Shock

    Oops…Japan shrinks even more than the most pessimistic economists thought…

  32. usphoenix says:

    Au contraire. Wall Street is very focused on the most important math and very good at it. The other stuff’s a waste of time when your bonus equal $1M/hr.

    Your money = My cut off the top(both fixed and variable, one time and continuing) +x( Same)(quant speak for simplified geometric progression- for as many people,x, as I can pass your money through) + Your true remaining actually invested equity basis (just enough to keep you from finding your fellow investors and filing a class action law suit before we liquidate).

    Actually Madoff may have been better at the math than most. Maybe a little too good.

    @Bruce in Tn: Thanks for the link to the Bill Moyer interview with Simon Johnson. Yes. He captures the essence and frames the situation quite nicely. Bank Oligarchy.

    My sense is everyone is about to pull a “Slick Willie”: Wall Street fakes contrition, Washington talks tough, telling taxpayers what they want to hear, and then does what Wall Street wants, but only after extorting cover and campaign funding.

    Actually contrition may have given way to continued arrogance. I just saw a clip of a banker stating “Retention Bonuses” would be given out.

    For those that prefer a no holds barred discussion:


  33. Bruce in Tn says:

    Aso’s Approval Rating Slumps to 9.7 Percent

    ..Aso in Japanese means “Bush”…

  34. Bruce in Tn says:

    39 pubs shut a week
    A record number of pubs are closing every week in Britain, highlighting the “extreme” economic pressures facing the industry, new figures have shown.

    ..Yes, fellow bloggers, it has finally happened..people in the UK are too depressed and broke to drink…ah, the economy….

    last one for the night…maybe better news in the morning..

  35. DL says:

    usphoenix @ 8:58

    “My sense is everyone is about to pull a ‘Slick Willie’: Wall Street fakes contrition, Washington talks tough, telling taxpayers what they want to hear, and then does what Wall Street wants…”

    Yeah, all this hullabaloo over CEO pay is just a smokescreen. I think that Obama is ultimately going to shaft the taxpayers for the benefit of the banks. If credit isn’t flowing by the end of 2011, Obama’s going to have a difficult time getting re-elected. Reelection is going to be his top priority, no matter what he has to do to make it happen.

  36. CJ says:

    I like QQQ Trader’s chart with the cylindical columns best. It’s really a very good visual representation. Just one suggestion — change the cylindrical columns to poker chips.

    Maybe poker chips with the name of a defunct casino.