How Wall Street Lied to Its Computers

Traders and bankers knew, philosophically, that the risk in these products was much higher than the models would admit. "25 sigma", to use Goldman's excuse, means nothing when the distribution is not normal. For a 20-year-old to die (death being a 0/1 event) within a year is "30 sigma", and yet it is not uncommon for a college student to die.

My lay explanation of the risk-management failure is as follows. Let's say that you're of average means, with a net worth of $25,500. You've decided that "fuck you" money is $10 million, and you want to get there by (wait for it) betting on coin flips, pursuing the Martingale betting strategy. You'll stop flipping when either (1) you lose everything, or (2) you get to the fuck-you mark of $10m.

Martingale works as follows: start with a small bet (say, $100). If you win, bet again at the small size. If you lose, bet again, doubling your size. You'll win almost all of the time, losing only on an improbable string of losses. When you win, you'll be up exactly $100.

Obviously, this is an extremely stupid strategy. On the first go, you lose everything on a string of 8 failures (1/256). You win $100, 255/256 of the time. Expectancy is still zero, and although a blow-out loss is unlikely on a single round, you're going to progress to $10m so slowly that you'll almost certainly fail out beforehand. You have, roughly, a 0.255% chance of getting the "win" outcome of $10m. This doesn't improve if you change the size of the bet.

If you're able to borrow $1 billion, in addition to your meager $25.5k, this strategy makes perfect sense. Let's assume that the coin-flips are instantaneous, and interest is agreed-upon to be a flat 1%/$10m, meaning that you need to win $20 million to have your "fuck you" money. Now your blow-out probability is extremely low. The probability of getting to +20m before -1000m is about 98%. So, you have a very high chance of reaching your goal, and a low chance of losing your few-months'-salary bankroll (plus a lot of someone else's money). Of course, the billionaire is getting screwed.

This is a toy example, but it's not far off from what actually happens. Much of the money made in finance has been obtained by borrowing others' money to bet against "black swan" events, so infrequent that no one can accurately model their likelihood and impact. This is what "rock star traders" try to do their banks, and what banks try to do to their customers, and we've now seen the resulting clusterfuck.

Shorting is generally a bad idea because even if you're right, if your timing is wrong, you can still lose everything. Say that you call "overvalued" and short the market. You're right, but the market gets more overvalued before it corrects. You can get short-squeezed out of your positions because with the new, bubble-inflated prices, you don't meet margin requirements. Then the market corrects, you're vindicated, but you've lost everything already.

Same goes for buying on margin when the market undershoots. You can be right, but if the price continues to drop past rationality (as it often does), you can lose everything.

And I did make a pretty good return, both in 2001 and 2007, simply by holding money in cash when people were greedy and investing when they were fearful. Not a fortune (I was a poor college student in 01/02, and only had 2 years of accumulated work savings in 07), but enough to fund my year-long startup adventure, and to fund a few more years of it if I had a decent idea.