## A Puzzle From the World of Quant Finance

Here is a little puzzle that may stymie many a professional trader. Sup- pose a certain stock exhibits a true (geometric) random walk, by which I mean there is a 50â€“50 chance that the stock is going up 1 percent or down 1 percent every minute. If you buy this stock, are you most likelyâ€”in the long run and ignoring financing costsâ€”to make money, lose money, or be flat?

I am interested to see what you guys think the answer is?

### jmao87 posted on March 11, 2010 at 15:52 PM

In the long run you lose all your money.

### bellatrix posted on March 11, 2010 at 16:51 PM

if you are talking about eons of years and a limited bankroll to invest you'll lose your money. Kelly criterion tells you that if you overbet your edge constantly, you'll lose your money. Well, the edge here is zero, so you'll lose your money.

However, within a certain amount of years and a fairly large bankroll, you'll most likely break even.

### fnupple posted on March 11, 2010 at 17:55 PM

lol u will never lose ALL your money since you can never lose more than 1 percent at any given step. but yeah, you're gonna go broke almost certainly.

### ninjagnu posted on March 23, 2010 at 21:42 PM

Given an even amount of 1% additions and subtractions the total amount will decrease.

100 + 1% = 101 - 1% = 99.99
100 - 1% = 99 + 1% = 99.9

So in the long run you will lose money over on said stock.

### ninjagnu posted on March 23, 2010 at 21:42 PM

sorry for the poor formatting, apparently line breaks are ignored in this blog comment system.

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