View Full Version : Applying Game-Theory to Investing

4-26-11, 11:37pm

I’m posting snippets from this article with you in mind, since you expressed an interest in game-theory. The article is by Van Tharp, a trading coach, whose books on stock-trading got into me into bond-investing, because I could see how his ideas of risk-management and profit-capture could be extended to fixed-income investing.

Imagine playing a game for money in which marbles are drawn out of
a bag and then replaced. 60% of the marbles are white. If one of the
white marbles is drawn out, you win whatever you risked. The other
40% are blue. If one of the blue marbles is drawn, then you lose whatever
you risked. This game has an expectancy of 20¢. That is, over a large
number of trials, you’ll make 20 cents for every dollar you risk. That
means it’s much better than any game you’ll ever play in Las Vegas. But
what percentage of the people who play it make money?

I have introduced this game numerous times in talks that I’ve given at
seminars and conferences. Typically, we don’t play for real money, but
the winner (i.e., the person who ends up with the most “money” after 50
trials) is given a prize. The results at a typical talk are that one third of
the audience ends up broke, another third of the audience loses money,
and only a third of the audience makes money. And these results are not

Ralph Vince, author of three books on money management, allowed
50 Ph.D.s who knew nothing about money management or statistics to
play a game similar to the one described for 100 trials. They were not
given any incentive for winning (which can induce stupid behavior).
They were merely instructed to make as much money as they could playing
the game. Guess how many of them made money? Only two of them,
or four percent, made money!

Typically, except for going broke, there are as many different ending
equities as there are people in the audience. Yet they all start out with
the same amount of money and they all get the same trades (i.e., marbles).
But in the end, there are so many different results. Why? Poor position
sizing™ and an undisciplined psychology. If people have trouble making
money with a 60% marble system, what are their chances of making
money in the markets? Very slim!

And the article continues on, laying out the implications for investors/traders. http://www.indicatorwarehouse.com/blog/wp-content/uploads/2011/04/Van-Tharp.pdf

In the bruhaha in another thread of over what constitutes sensible investing (as opposed to fear-driven choices), one of the points I did make is that currently (and typically never) do CDs have a positive expectancy after taxes and inflation. Thus, to buy them is to choose to lose money which is the very antithesis of investing, as Joe Dominguez clearly implies with his definition of what an investment is “…the conversion of capital into some form of wealth other than cash with the expectation of driving income”. (YMOTL, p. 262)

The caveat that does need to be made about applying game-theory to investing is that it works superbly well in the 1st Quadrant (closed systems such as casino games e.g., card-counting in Black Jack), but it becomes dangerous when extended to the 3rd and 4th quadrants (e.g., securities markets as the Modern Portfolio Theorists attempt to do), and especially so when they over-leverage their bets, as Long Term Capital Management did under the guidance of the two Nobel-Prize idiots, Merton and Scholes, who were advising them and blew up. (“Ah, that wasn‘t supposed to happen according to our models.”) But as Taleb implies in his technical papers, if proper respect for the data and the limitations of what can be known is taken, and if left-hand tails can be chopped, then an investor/trader might be able to keep himself out of trouble.



4-27-11, 12:12am
The caveat that does need to be made about applying game-theory to investing is that it works superbly well in the 1st Quadrant (closed systems such as casino games e.g., card-counting in Black Jack),

Indeed. I was one of the Princeton Statistics Department crew that put ourselves through school on blackjack at Atlantic City :-) Understanding expected values, the law of large numbers, how runs work, how that relates to position sizing and capitalization, was crucial. You also had to pick the casino with the best rules, and not get caught. Easier in the early days of Atlantic City, and even then you only barely had an edge. But a little edge is sufficient if you take care, which is why it is insane to me that people can lose a 60% game, but yes, they do.

The key is, as you correctly point out, to understand which magisteria your tools and understanding are suited for, and not try to press them into service where they mislead or damage you. Or where large men will break your legs :-)