Posts filed under “Mathematics”
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 thebigpicture-at-optonline.net. 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
> What could be a more appropriate thing to do on Friday the 13th than have lunch with Fooled by Randomness and The Black Swan author Nassim Taleb? I am looking forward to an interesting meal . . . (apologies for the shameless name dropping) > UPDATE: February (Friday the) 13th, 2009 Fascinating lunch —…Read More
Yesterday, we discussed an ongoing Marketwatch chart on historical trend regressions (Is the Market Bottom in Sight (Again?)). Peter Brimelow and Edwin S. Rubenstein have argued that markets bottom when they fall to 40-42% below trend. Doug Short disagrees. As he shows in the chart below, markets have dropped as much as 67% below trend,…Read More
Interesting take over the weekend in Marketwatch on stock market bottoms relative to historic trendlines.In past bear markets, whenever equities as a group fall into the range of 40-42% below trend, at bottom was not far off. HFN editor Peter Brimelow, along with ESR Research’s Edwin S. Rubenstein observe: “We have looked at stocks relative…Read More
The NYT has this nice interactive graphic that calculates how long it will take to return to breakeven: > Source: Calculate Your Financial Comeback NYT, January 6, 2009 http://www.nytimes.com/interactive/2009/01/06/business/20090106-comeback-graphic.html
> > One of the things we like to do with Fusion IQ is review the full universe of stock scores and the new Buy & Sell ratings. From time to time we can glean information from our overall statistics to get a handle on what is going on under the surface of the market….Read More
Terrific l o n g article in the Sunday Times Magazine by Joe Nocera, titled Risk Mismanagement. Its all about how Wall Street developed and still uses VaR — Value at Risk.
The application of VaR remains hotly debated today. Did it contribute to the credit crisis — or was it ignored/misapplied/distorted, and THATS what was a key factor.
Risk managers use VaR to quantify their firm’s risk positions to their board. In the late 1990s, as the use of derivatives was exploding, the Securities and Exchange Commission ruled that firms had to include a quantitative disclosure of market risks in their financial statements for the convenience of investors, and VaR became the main tool for doing so. Around the same time, an important international rule-making body, the Basel Committee on Banking Supervision, went even further to validate VaR by saying that firms and banks could rely on their own internal VaR calculations to set their capital requirements. So long as their VaR was reasonably low, the amount of money they had to set aside to cover risks that might go bad could also be low.
Given the calamity that has since occurred, there has been a great deal of talk, even in quant circles, that this widespread institutional reliance on VaR was a terrible mistake. At the very least, the risks that VaR measured did not include the biggest risk of all: the possibility of a financial meltdown. “Risk modeling didn’t help as much as it should have,” says Aaron Brown, a former risk manager at Morgan Stanley who now works at AQR, a big quant-oriented hedge fund. A risk consultant named Marc Groz says, “VaR is a very limited tool.” David Einhorn, who founded Greenlight Capital, a prominent hedge fund, wrote not long ago that VaR was “relatively useless as a risk-management tool and potentially catastrophic when its use creates a false sense of security among senior managers and watchdogs. This is like an air bag that works all the time, except when you have a car accident.” Nassim Nicholas Taleb, the best-selling author of “The Black Swan,” has crusaded against VaR for more than a decade. He calls it, flatly, “a fraud.” . . .
What will cause you to lose billions instead of millions? Something rare, something you’ve never considered a possibility. Taleb calls these events “fat tails” or “black swans,” and he is convinced that they take place far more frequently than most human beings are willing to contemplate. Groz has his own way of illustrating the problem: he showed me a slide he made of a curve with the letters “T.B.D.” at the extreme ends of the curve. I thought the letters stood for “To Be Determined,” but that wasn’t what Groz meant. “T.B.D. stands for ‘There Be Dragons,’ ” he told me.
Best line in the article: “When Wall Street stopped looking for dragons, nothing was going to save it.”
I particularly loved the graphics and illustrations that were part of it:
MIT’s Andrew Lo: The key concept here, developed by MIT professor and noted hedge-fund theorist Andrew Lo, is “serial correlation.” Simply put, serial correlation is the degree to which each month’s returns in a fund mirror the results of the month before. A fund that returns the exact same amount every month is perfectly serially…Read More