Posts filed under “Mathematics”
“I keep saying the sexy job in the next ten years will be statisticians. People think I’m joking, but who would’ve guessed that computer engineers would’ve been the sexy job of the 1990s?” -Hal Varian, The McKinsey Quarterly, January 2009 > Well, not quite sex symbols. But as Google’s chief economist (and former NYT columnist)…Read More
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