I was listening to this excellent audio presentation that ugly posted about, and it got me thinking yet again about expectancy. The audio was about how people have trouble with probability. One example characterizes lotteries as a stupidity tax, because the odds of winning are so remote. But, what is the expectancy of playing the lottery?
The odds of winning the Texas lottery (according to this site) are 1 in 15,890,700. So, simplifying away all the small cash prizes you can hit, the expectancy of a lottery ticket is:
(1/15890700)*jackpot - (15890699/15890700)*ticket_price
So, knowing the ticket price is $1, you can ask yourself “how big does the jackpot need to be before the lottery has a positive expectancy for me?” And, of course, the answer is: $15,890,701.
But does that mean it’s a good idea to play the lottery any time the jackpot gets that high (and it does get that high with some regularity)? What about a jackpot of $28mil? In that case, the expectancy is that you will make 76 cents of profit per ticket you buy! You should buy as many as you can, then, right? WRONG! Of course wrong. Because, like many statistical measures, expectancy only tends to “come true” as the number of times you play tends towards infinity.
In other words, if you had the funds and time to buy ticket after ticket, then after playing a few hundred million times, you would expect your winnings to converge on that 76 cents of profit per ticket figure. Do you have the time or money to do that? If so, what the heck are you doing playing the lottery?!?
Apply that to the Stock Market
This is just another way to point out that, yes, expectancy tells us we can be profitable stock traders while winning less than 50% of the time. But, you can’t stop there. A system with an expectancy of 76 cents profit for every dollar traded could be just as bad a deal as the lottery above. You should strongly prefer to win as much as possible, and not because it’s psychologically pleasant. Winning more is less risky–it will lessen the probability of financial ruin when strings of bad luck happen (and you must assume they WILL happen–see my previous post about this). I feel so strongly about this that I would prefer a system with a slightly lower expectancy, if it had a significantly better winning percentage. Trust me, the dull ache of slightly lower returns as the number of trades approaches infinity means little compared to the sharp pain of applying for a day job to rebuild your trading stake.
(note: I just keep hitting this point because I don’t ever see anyone else do it, and I think everyone should keep these facts in mind. Measures like expectancy live in an abstract world where you can trade with a negative account balance until your losing streak is over. In the real world, you are job hunting and eating ramen noodles long before that. All that said, I still like, use, and recommend expectancy as the first measure of a trading system’s viability. You just can’t stop there.)
