Value at Risk and the Failure of Self Interest in Real Life Economics

An interesting article at the NY Times delves into the concept of Value at Risk and analyzes its role in the current economic disaster. It's an interesting read, and you should definitely go through it if you've got the patience.

If you don't want to read the article, here's the brutally inaccurate summary:

1. Value at Risk (VaR) is a way of measuring with a 99% certainty how much money you're possibly going to lose based on your portfolio
   
2. What if you hit that 1% "jackpot" and lose more than your VaR? Who knows...you could lose twice your VaR, or a thousand times it. VaR doesn't distinguish, and it tells you nothing about the expectation value, either - your VaR could be $1, but your expected loss might be $1000. And you'll lose more than your VaR eventually - 1% ain't that small a chance!
   
3. Regulators allowed companies to use internally calculated VaRs to set cash reserve levels. Stupidly.
   
4. Managers paid more attention to 1) than 2). Stupidly.
   
5. Traders took on as much risk as they could find while staying within the bounds of the VaR requirements. Stupidly? Ha - don't be so quick to judge!
   
6. ...
   
7. We all know the rest, and it has nothing to do with profit!
   

This has all been discussed to death elsewhere, so we'll leave most of it alone.

Ah, the traders, though. Arguably the only people that haven't done anything stupid here. 'What?', you say, 'they're the ones that started this whole thing, without them it couldn't have happened at all!'

True enough.

But from an economic point of view, the traders were acting rationally, thanks to the way they get paid. You know, that thing where they get reviewed every year, and either get a hefty bonus based on their profit, or get canned if they've been losing?

That's what we call an asymmetric risk profile. The upside is limited only by the maximum gain that the trader achieves over the year, which is a pretty astronomical number if they're either very good or very lucky. But the downside is just a lost job. Boo hoo. On to the next bank, I suppose, unless you've already got enough money to sit on it and retire. Or maybe you just start your own fund - hey, John Meriwether ran Long Term Capital Management into the ground to the tune of $4.6 billion, and after that massive failure he went on to...surprise!...start up a brand new billion dollar Greenwich hedge fund! That's what I call punishment for failure!

I digress. The point is, traders have a significant self interest in taking on as much risk as possible. After all, if I told you I would give you a 50% chance of making $N along with another chance to play my game vs. a 50% chance of getting nothing, and the only choice you had was what number to pick for N, what would you do? You'd set N as high as I'm willing to let you, since your expected payout is .5*N.

Now, there's a peculiar thing about financial markets. If you were trading plain old stocks for a company, you'd be in exactly the situation I've outlined. And it would still have a pretty massive expected payoff, as long as you're allowed to set N high enough. But then people invented wonderful things called derivatives, which let you shuffle risk around pretty much at will.

You want a sure thing? No problem - write a boatload of deep out-of-the-money options, millions of them (writing an option is the inverse of buying one - you take an up-front fee and offer someone the right to purchase a share of a stock at a given price from you). They'll probably never be exercised, so you're almost sure to make a lot of money. It's like a money printing machine! Seriously, you're almost guaranteed to make money - the only reason more people don't do it is that you generally need to get special permission from your broker to write naked options.

The catch? That one-in-a-million shot that the option you've written pays out has to balance the odds, so you'll lose a lot of money if it hits. Like, a million times more than you made by selling them.

You're now allowed to change the odds however you'd like, but the payout profile changes, too.

Balance is restored...unless you're a derivatives trader playing with someone else's money, that is!

Because now you can play my game differently. Instead of playing a 50/50 game, you can make it a 99/1 game, so you're almost definitely going to end the year with a bunch of cash. And the 1% chance that you lose means that whoever fronted the money is really screwed now, but what do you care? You're an economically rational agent in search of maximized utility, and that 1% option only reduces someone else's payout, not your own. Yay rationality!

Extra bonus: if the riskiness of your bet sneaks by with under 1% uncertainty, it doesn't affect your VaR measurement, so you can push N ever higher and further increase your payout! Why isn't everyone in this business? Thank the Lord for financial derivatives!

When the house of cards comes toppling down, the only loser is...well, everybody, that is, everybody except the traders, assuming they stashed away enough cash to last them while things were going well.

Now do you see why Warren Buffet famously (and presciently!) called complex derivatives "financial weapons of mass destruction"?

The Failure of the Free Market...?

But wait. In Econ 101 didn't we learn that the best thing for an economy is for each player to act in his own self interest, remaining as unregulated as possible while still preserving competition? Damn straight we did. And if we're even somewhat libertarian-leaning, we treat this as gospel. And let's be honest - who's not at least a little libertarian these days?

There's an implicit claim there, which we might call the...

Zeroth Law Of Free Market Economics: a collection of self interested entities united under a single banner functions as a larger self interested entity.

I urge you to reflect deeply on this if you haven't already. It's an extremely non-trivial assumption, but if it doesn't hold, almost all of the economic theory that you learned in college literally falls apart.

Without it, you can't consider a company to be acting in its own best interests, which means you can't even think about applying standard game theory to company-company interactions. You can't even bring up supply-demand curves when you're trying to price products, since they might be perverted by internal quotas and incentives. And if you tried to analyze things more accurately, the complexity would go through the roof, since the only way to consider the economy would be as a collection of loosely grouped individual people under a whole bunch of (possibly confidential and unknown) incentive systems, which is a lot more difficult to do than considering the groups of people as purely self-interested companies.

When laws like the Zeroth Law fail to hold, the bogeyman to blame is usually Government Regulation. Government Regulation is when an external influence changes people's individual payoffs, and in the process, changes the way they interact (in unpredictable ways, with many unexpected consequences), so that now, a collection of self-interested individuals does not necessarily do what is in the best interest of the collection. We see this all the time in practice, and it's part of what makes economics so difficult a subject. Once you start paying out unemployment benefits, and giving tax breaks to people in certain industries, it makes it all but impossible to predict anything.

So now, lest you think that I'm going to repeat the tired old Proper Libertarian Mantra and blame the financial meltdown on government meddling in the private affairs of business, let me come clean and get to the point. Meddling with payoff structures is at fault here, but this meddling had nothing to do with the government. It's entirely the result of the free market.

The fundamental problem with libertarian economics: a free, unregulated market allows private entities to meddle with payoff structures in ways that are just as disastrous as when the government does it. These payoff structures will arise completely organically, just because of the fact that when people organize, they tend to do these things. I have yet to hear the most radical right winger suggest that the way traders are paid had anything to do with direct government interference, and that's because it didn't. It emerged in the purest of senses from free market negotiations, and caused a group of self interested people to act against the collective self interest of their organization. Period.

Put more simply, if we want to talk reasonably about free market economics, we need to be more liberal in our definition of "government." Governments and government meddling are natural consequences of a free market - any time people organize, they start to form rules that govern their organizations. And these rules disrupt the assumptions of a free market, whether the "government" in question is a small research group, a startup company, a Fortune 500 company, or an entire country.

The extent to which meddling affects the economy overall may depend on the size of the "government" in question, of course - nobody will suggest that the way Bob handles things at his furniture store (yup, that Bob!) has nearly the same impact as when the President revamps the way investment inside the country is rewarded or punished. Maybe it is generally better to prefer small scale regulations as opposed to large, top-down ones.

But as the current crisis demonstrates, the internal affairs of a handful of companies in one sector have more than enough power to cause the entire economy to collapse, and perhaps it's worth considering the idea that maybe, just maybe, the real solution would have been for the Government (the real one) to step in and break up what has always been a predictably problematic compensation and management structure in the smaller "government" known as the financial sector. Pay traders ridiculous salaries, fine, and fire them if they don't perform - but don't tie their upside potential to the amount of exposure they take on while letting them take on fantastic amounts of exposure! The combination of asymmetric risk coupled with the scam whereby the traders can increase exposure almost without limit was a time bomb waiting to explode, and that had nothing to do with housing, credit, or anything of the sort.

So the next time a Libertarian (big-L) tells you that the current mess we're in is the result of governmental meddling, and the only way to avoid this mess would have been to have zero regulation, feel free to agree with them. As long as they accept the fact that the term "regulation" must necessarily include the formation of companies, which are, after all, mini-governments that can invalidate the Zeroth Law of Free Market Economics just as easily as the real government unless they are exceedinly careful.

A truly free market is a beautiful theoretical entity. But unfortunately in practice, it is very hard to come by, since humans acting freely always group and regulate their groups. Which brings us to...

The First Law Of Free Market Economics: a market will become non-free if the participants are allowed to organize into groups.

Since a free market must allow people to organize into groups, we prove:

Corollary: there can be no free market. Deal with it and let's try to find a realistic balance.