Analyzing performance of a stock picker

[musicgold]

Hi,

I was trying to analyze the performance of a so called expert stock picker. Can you please check my argument? Are there any holes in my argument?

According to the stock picker, out of 15 stocks he picked over his career 10 turned out to be big winners.

I made the following argument. Assume that the performance of a stock is as random as a fair coin flip; half the time the stock can become a winner and the rest of the time a loser. If we select 15 such stocks, the chance of getting at least 10 winner stocks in that group is 15.09% (using the binomial theorem). In fact, the 10 winners case falls in the 95% confidence interval of the binomial distribution of this experiment. As such, having 10 winners out of 15 picks is not so impressive an achievement.

Thanks,

MG.

[HallsofIvy]

Could you show how you did the calculation?
I get _{15}C_{10}(1/2)^{15}= 3003/2^{15} equals about 9%.

[CRGreathouse]

Could you show how you did the calculation?
I get _{15}C_{10}(1/2)^{15}= 3003/2^{15} equals about 9%.

9.2% chance of picking exactly 10; 15.1% chance of picking 10 or more.

[statdad]

Musicgold's analysis is on the correct track for this type of problem. Stock prices are, in general, nothing more than a random walk, and whether a "picker" bases picks on graphical analysis or other items, their choices turn out to be no better than random selection.
A group of 20 choices is a rather small sample, but still the result he sees is not surprising.

[musicgold]

HallsofIvy, CRGreathouse, and statdad,

Thanks a lot for your comments.