## Saturday, January 9, 2016

### The Gambler’s Fallacy and the Chinese Stock Market Crash of 2015

Innumeracy is pretty common.

One example of this is commonly called the gambler’s fallacy. It goes like this: if you make one bet and go up by 60%, bet it all on a second bet and lose 40%, most people think you’re actually ahead. The fallacy is that you’re not.

Think about it: suppose you start with \$100. Your first bet wins you \$60, so you now have \$160. On the second bet you lose 40% of that, or \$64. Subtract that out, and you have \$96. You’re down 4% over the two bets.

What goofs people up is the inclination to take an arithmetic average of net growth rates, rather than a geometric average of gross growth rates. In this case, the net growth rates are +60% and –40%. Average them together and you get +10%. The arithmetic is correct, but it’s the wrong method to use for growth rates. Instead you should multiply the gross growth rates. These are +160%, and 60%. Multiply them and you get 96%.

A ton of what we’re going to do for the rest of the semester has to do with dealing with growth rates properly, so this is an excellent and easy example.

AND, it showed up in graphical form in that chart of stock prices from the front page of Friday’s issue of The New York Times. Check it out:

If you’d put 100 into the Shanghai exchange in January 2015, you’d have had about 160 by June, and you’d be back down to a little below 100 by January 2016.