April 25, 2002
From the desk of Mindles H. Dreck:Outcomes of the Paulos IPO Exercise
I ran 100 simulations of the Paulos IPO game mentioned below. Each player starts with $10,000 and plays the game for a number of weeks, randomly experiencing an IPO each week that has equal chances of going up 80% or falling 60%.
Because Steve Kuhn asked me whether I would like to be "the house" on this game, I looked at it from that point of view. So in this case, the house wins if the investor ends up with less than his original $10,000. Investor/player loses = house wins.
After 10 weeks, 87 of my 100 players have lost money, but one of the remaining players has a balance of $166,000. After 50 weeks, 97 players are out, but one of the remaining 3 has a balance of $41 million (gulp). After 100 weeks, the only player left had about $218,000. Our sole winner is the same guy who had $41 million at week 50, and $124 million at week 60, so he should have stopped. Everyone else is bust. Only after 100 weeks has the house turned a profit in aggregate ($1 million less the one player's winnings).
Here's a graphical representation showing the house's winning percentage (or the number of bust investors) vs. the largest balance of the remaining investors.
This dovetails perfectly with my earlier discussion about Niederhoffer and Taleb, or being long or short volatility. The house here is Niederhoffer, making good money almost all the time but going out of business every now and then. The players are Talebs, mostly bleeding to death but occasionally hitting it big.
And neither side is particularly interesting to me, although an investor in this theoretical game is doing a hell of a lot better than he could with a lottery ticket.
Posted by Mindles H. Dreck at April 25, 2002 2:13 PM | Technorati inbound linksI will definitely play around with the spreadsheet.
By the way, I hope you don't take my debate as a sign that I do not enjoy your site. I do very much enjoy it and think very highly of your thoughts.
In the spirit of good fun, I continue to argue that you haven't really addressed my arbitrage argument. I still say I could sell off this exposure for more than $10,000.
To say that some game has a positive expectation, and yet is a foolish game to play due to the skewed distribution of results is to implicitly argue (I think) for a diminishing marginal utility of money/risk averse set of beliefs. But, to be somewhat redundant, people empirically are risk seeking when dealing with small sums of money.
We may both be right in a sense. People may be fools to play this game (perhaps you might even convince me of that), but as you concede it would be less foolish than playing the lottery and therefore it is a possible arbitrage opportunity.
Incidentally, it also seems implicit from your argument that if the house has a limit to how large a loss they can sustain, say $10,000,000, it makes more sense for a person to play. An interesting result...
By the way, thought provoking comments on the long term success of options trading strategies vis-a-vis Vranos and Askin. A topic worthy of a discussion over a beer sometime. (I think that was on your site, but possibly Raghu's...)
Thanks for the feedback!
The problems are solved by bankroll management. Don't put all the capital at risk at once. For example, an investor who starts with 70K and risks 10K per IPO has, after 26 IPOs, about a 99% chance of having a non-zero amount, about a 78% chance of being at least break-even, and an expected return of 35%.
These results can be improved upon by dynamicly adjusting the amount risked each time based on current bankroll. (cfr "Kelly Criterion")
A Taleb who can resist the urge to play for the immediate bang will win over time, and the house bleeds to death.
'Mindles' wrote:
>>The house here is Niederhoffer, making good money almost all the time but going out of business every now and then.
The nut of my argument is that "every now and then" is likely in the long run, and that it can work in your favor if you are a buyer of options.
Steve wrote:
>>To say that some game has a positive expectation, and yet is a foolish game to play due to the skewed distribution of results is to implicitly argue (I think) for a diminishing marginal utility of money/risk averse set of beliefs. But, to be somewhat redundant, people empirically are risk seeking when dealing with small sums of money.
Agreed.
Two links on the kelly criterion:
http://www.hquotes.com/kelly.html
http://www.professionalgambler.com/debunking.html
Perhaps we'll run another simulation.
Everyone wins, and everyone must have a prize!
1) Mindles One: You're right - anyone who quits their day job, takes their last $10,000 from the bank, and starts checking the prices of waterfront property in Florida on the basis of this "investment opportunity" is a fool.
2)Steve: You're right - the game does have a positive expected value, so if you can afford to play and losing won't change your life, party on!
3) Chicago Boys, Mark Nau, Steve, and probably others: "Risk management", "Bankroll management", "House limits", the voluntary adoption of limits by the player (aka bankroll management) all change the skewness of outcomes to something that may look a little more "sensible". But if Steve wants to hold out for his slim shot at several hundred billion who are we to say no? Actually, the maximum payout is $10,000 x 1.8 ^ 52. The already tiny probability of earning this outcome is further reduced by the fact that it is a value which far exceeds the capitalization of the world's equity markets.
4) Final Prize - The Mindles Thing again - thanks for an cool illustration of an interesting sidebar to human psychology, and a nice connection to the New Yorker piece, which, shockingly, I had already read on dead tree. And I love that "Parrando's paradox" you have, although the real paradox is why anyone would think that you can change a subtle path-dependent game without changing the outcome. One more discovery that is obvious after the fact.
Regards
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