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http://www.foxnews.com/story/0,2933,477686,00.html

George Edw. Seymour http://www.npr.org/templates/story/story.php?storyId=9979 2155

http://www.npr.org/templates/story/story.php?storyId=99792155 P.S. Would appreciate more actual

applications and explanations of counter-intuitive probability events.

2D:4D

If you put 2D:4D into a Google search, you will obtain 11,700,000 hits so you know that something is missing in your life if 2D:4D doesn’t ring a bell. From Wikipedia we are informed that “It has been suggested by some scientists that the ratio of two digits in particular, the 2nd (index finger) and 4th (ring finger) is affected by exposure to androgens such as testosterone while in the uterus and that this 2D:4D ratio can be used as a crude measure for prenatal androgen exposure, with lower 2D:4D ratios pointing to higher androgen exposure.” Because “Some authors suggest that digit ratio [is] correlated to health, behavior, and even sexuality,” there is a great deal of finger measurements all over the globe. For a previous Chance News wiki on the subject, see here; in that wiki, according to those who subscribe to the relevance of 2D:4D, “the 2D:4D ratio is able to explain such disparate entities as sex and population difference, assertiveness, status, aggression, attractiveness, the wearing of rings, reproductive success, hand preference, verbal fluency, autism, depression, birth weight, breast cancer, sex dependent diseases, mate choice, sporting ability, running speed, spatial perception, homosexuality and more.”

One of the latest extensions of the importance of 2D:4D phenomenon is to financial trading and may be unearthed here. The startling conclusion is “We found that 2D:4D predicted the traders' long-term profitability as well as the number of years they remained in the business.” More specifically, “traders with a lower 2D:4D would make greater long-term profits and would remain in the business for a longer period of time.” Numerically, “a trader in the lowest tertile of the 2D:4D range makes 11 times the P&L of a trader in the highest tertile.” With regard to experienced traders only, “low 2D:4D traders make, on average 5.4 times the P&L of high 2D:4D traders.”

Discussion

1. The article looked at 44 traders over a 20 month period who “specialize in noise or high-frequency trading: they buy and sell securities, specifically futures contracts, sometimes in sizes of up to £1 billion, but hold their positions for only a few minutes, sometimes mere seconds.” Comment upon (a) the sample size, (b) whether the traders represent a random sample, (c) what population the traders might represent and (d) whether this is an experiment or an observational study.

2. Compare high-frequency trading with outright gambling.

3. The article looked at the performance of traders several years ago before the economic downturn. Speculate on how performance might be different in 2008-2009.

4. The 2D:4D ratio of the 44 traders ranged from about .9 to 1.02. If you are a male, look at your right hand—somehow, the left hand is irrelevant--and comment on the difficulty of accurately measuring the ratio over that small range.

5. The approximate annual P&L for the 44 traders ranged from -£2000 to +£4,200,000 and was heavily skewed to the right.

	Age (years)	Trading experience (years)	Aproximation Annual Income (£1-£2)
Mean	28.99	2.77	£285,000
Std	4.14	1.9	£259,000
Range	19 to 38	1 to 12	£2,000 to £4,200,000

http://www.dartmouth.edu/~chance/forwiki/figure 2d-4da.gif

That is, a very small number of the 44 traders made a great deal more money than the others. The graph below is for the average P&L.

How would this affect regression assumptions of P&L vs. 2D:4D.

6. Naturally, this 2D:4D investigation catches the eye of the media. Typical is Are You a Moneymaker? Look at Your Hands. This article quotes Tim Harford, a columnist for the Financial Times and author of The Logic of Life: The Rational Economics of an Irrational World, who calls the study "fascinating." Harford “says he's glad to see that economists have started looking at financial markets in terms of natural selection instead of looking at them in terms of rational people making rational decisions.” Why would Harford be glad?

7. Because P&L of these traders is far from being normally distributed, the investigators did a Box-Cox transformation (cube root of P&L) in order to induce normality. As can be seen from below with this transformation, p-value is very low and the magnitude of the correlation coefficient is far from zero indicating that this model has some validity.

http://www.dartmouth.edu/~chance/forwiki/2d-4d.gif

However, what is the physical meaning of the units of this y variable?

8. The investigators note that high-frequency trading is different from ordinary trading where the emphasis is on the “long-term approach to the markets. For example, arbitrage traders at the investment banks and hedge funds are increasingly hired from the math and science departments of universities, and one study, which looked at average digit ratios in university departments found that faculty from math, science, and engineering exhibited higher, more feminine digit ratios. A similar result may well be found among traders with a long-term holding period.” As a possible statistics project, verify that the 2D:4D ratio for your math, science and engineering faculty is higher and thus, more feminine.

9. Bearing in mind that statistical research can be costly and time consuming, what is the special appeal of 2D:4D?

Submitted by Paul Alper