Good Math, Bad Math

Perverse Incentives

A lot of people, reading the reporting on the current financial
disaster, have been writing me to ask what people mean when they talk
about incentives. The traders, the bankers, the fund managers, and all
of the other folks involved in this giant cluster-fuck aren’t
stupid. So naturaly, the question keeps coming up, why would they go
along with it? And the answer that we keep hearing is something along
the lines of “perverse incentives”.

The basic idea is that the way that the people in the industry got paid,
it was actually in their interest do do things that they knew would
eventually cause a disaster. How could that work?

The easy way to understand this is to just walk through a simple
scenario, looking at it from a game-theoretic approach.

Imagine that you’re a fund manager at an investment bank, and
you’ve got one million dollars to invest. You want to invest in a way
that maximizes your bonus at the end of the year. Your bonus is
going to be computed based on your performance relative to your
coworkers.

Your coworkers are all investing in mortgage-backed
securities. They’re bringing in 20% a year, but you know that
eventually they’re going to collapse; for the purposes of simplicity,
assume that there’s a 20% chance each year that they’ll fail. What
should you do?

You could invest in the MBSs. Then, if the MBSs do well, you’ve
performed just as well as your coworkers. If they fail, then
all of you fail; you’re no worse off than they are.

You could invest in something else. The problem is, there are very
few other investments that are earning 20% like the MBSs. So if you
put your money into something else, odds are, you’re going to be
bringing in less than you coworkers. So your bonus is going
to suck.

You could split things. But if things go well for the MBSs, that
doesn’t help. By dividing your investment between the MBSs and
something else, you’ll be closer to what you coworkers are making,
but still less. And so you bonus is gonig to suck.

So – if the MBSs follow the 80% pat and do well, and you didn’t
invest in them, you’re screwed. But what if the MBSs follow the 20%
path, and they crash?

Well, if that happens, everyone is screwed. Your firm is so deeply
invested in them that if they crash, there’s not going to be bonus
money for anyone. So even if you didn’t invest in them, if they crash,
you’re going to be screwed.

Look at it as a game table:

Invest in MBS Invest in something
else
MBSs do well Hurrah! Big bonus You’re
screwed
MBSs crash Firm bankrupt: you’re screwed Firm bankrupt: you’re screwed

Given your incentives, what’s the smartest thing to do? Invest
in the MBSs, even though you know that they’re going to crash.

Of course, to make matters worse, you can fill in that bottom
row a bit differently. Based on how things are going now, the table
should look like the following:

Invest in MBS Invest in something
else
MBSs do well Hurrah! Big bonus You’re
screwed
MBSs crash Gov’t Bailout: big bonus! You’re screwed

Comments

  1. #1 The Science Pundit
    March 16, 2009

    Oversight is supposed to prevent this sort of situation from manifesting itself. Of course that would require that there actually be oversight.

    A similar analysis could be done for financial advisors and analysts. If they tell people to buy MBS’s and they do well, they keep their jobs. If the MBS’s fail, then “nobody could have predicted it” and they keep their jobs. If they say don’t buy MBS’s and they do well, they lose their jobs. If the MBS’s fail, they’ll be painted–by all their collegues with a vested interest in perpetuating the “nobody could have predicted it” myth–as a doomsday prophet who, like a broken clock, only coincidentally got it right.

  2. #2 tony
    March 16, 2009

    It’s even simpler than that, Mark.

    I know a lot of sales guys, who live by commission. They simply push that which gives them the biggest net. period. No need to look for other, deeper motivation. There is none.

    I did like your post hoc ‘game theoretic’ analysis. I just don’t think it is at all relevant.

    When you say they knew their investments were ultimately a house of cards – you invest them with more knowledge than many actually have. They can sell. They can trade. But they really aren’t the smartest guys in the room – not by a long shot.

  3. #3 Blake Stacey
    March 16, 2009

    One might say, with tongue protruding somewhat into cheek, that the evolutionary stable strategy was to invest in MBSes. Once all the players have adopted that strategy, any other strategy trying to invade the population will fail; no player can benefit from a mutation.

    Sadly, fitness landscapes are notoriously dynamic things, and what looks like an ESS in the short- or medium-term can be releasing toxins into the environment. . . .

  4. #4 natural cynic
    March 16, 2009

    With the somewhat likely outcome of a crash, another allocation strategy is to short a part of the investment. Maybe gamble 1/3 of the money by shorting the market, or financials, or whatever. If the market drops, you can still make money and look golden when compared to everybody else. I’m sure someone has used this strategy to make a killing recently, although they would keep their heads down and out of the line of fire.

  5. #5 William Wallace
    March 16, 2009

    I think we both agree that the mixture of bailouts and corporate regulation that we have is bad.

    I suspect you want more regulation. If so, what do you think is a fair amount of compensation for corporate employees?

    Who was it that signed the deregulation bill you think caused this mess?

    Regarding your analysis, something similar could be said about the current quarterly corporate reporting system, that incentives corporations to worry more about the next quarterly earnings report than long term steady growth.

    And, have you considered the effect of mark-to-market requirements? Where if corporation A owned a financial instrument and had no intention of selling, they still had to discount its value if the current market rate when down?

  6. #6 Jud
    March 17, 2009

    And, have you considered the effect of mark-to-market requirements? Where if corporation A owned a financial instrument and had no intention of selling, they still had to discount its value if the current market rate when down?

    Hmm, and what about Corporation B, that bought credit default swaps from Corporation A, which are backed by the capital of Corporation A? Shouldn’t Corporation B know when that capital is reduced?

    Mark, I think a combination of what you’ve outlined and Tony’s comment covers a lot of what went on.

  7. #7 Mark C. Chu-Carroll
    March 17, 2009

    Re #5:

    compensation: I don’t know what the right answer is. I do think that the current system, the incentives are fouled up. Unfortunately, it’s very hard to design incentive systems that don’t have unintended consequences. I think that only incentivizing the short-term is definitely a problem.

    As one example of a different model: at Google, we get a base salary which is somewhat smaller than average for the industry. In addition, we get a yearly bonus, based on a combination of company performance and individual performance. Finally, we get stock options in the company. But the options don’t vest immediately. In fact, they don’t *necessarily* vest at all. Each year, during our performance reviews, they decide how much should vest.

    So, to make up some numbers: I was given an option grant when I joined the company. Imagine that it was 100 shares. They vest over a period of five years. At the end of the first year, if I performed well, 20 would vest. If the following year, I didn’t do so well, I might only get another 10 vested.

    That system gives me both a short-term performance incentive (my bonus and my vesting schedule) and a longer term incentive (a significant part of my pay is tied into the options, which I can’t cash in until they’re vested, and that will happen over a fairly long period of time.

    Models like that make a lot of sense. For traders, something that spreads things out would make more sense. So – for example, one plan that I’ve seen proposed would base a traders yearly bonus on the performance of their trades over a long period of time. So, for example, there bonus could be computed 40% based on the performance of their trades this year; 20% based on the performance of any assets the company holds based on their trades last year, 20% based on the performance of assets the year before, etc. And the percentage applies whether it’s positive or negative. So if the trader bought stuff which did great last year, but totally crashed this year, then that would mean that the 20% based on last year is negative, and would be subtracted from this year.

    Would that work? I don’t know. Like I said, incentives are complicated. and almost always have counter-intuitive effects. You’d need a game theorist with a lot more skill than me to work out the expected effects of that scheme.

  8. #8 Mark C. Chu-Carroll
    March 17, 2009

    More re #5:

    As far as mark-to-market goes… I’m not an accountant, so I don’t fully understand the implications of different valuation systems. In other words, I’m talking out my ass here based on incomplete knowledge.

    When it comes to computing the value of a company’s assets, I don’t think that the fact that they don’t plan on selling a given asset means that they should be allowed to assign it more value than it currently has.

    In terms of corporate regulation, the point of valuation of assets is to ensure that a company has sufficient resources to cover its liabilities. Regulations limit how much a given asset can be leveraged, based on its assessed value.

    If a company is using an asset to secure a loan, and the value of that asset is set artificially high, then when things go bad, you get a cascading effect: the loan gets called in, they can’t pay it because the value of the asset was artificially high, which means they need to sell other assets to cover it, which means that other loans lose their security, and so on. That’s a huge part of what’s going on right now.

    No one thought that AIG would be selling many of the assets that it’s now trying to dump onto the federal government. But when problems came up, they needed to. But the valuations of those assets were based on some bullshit rosey picture, which was justified by the fact that they weren’t planning on selling them.

    Whether you plan or selling an asset doesn’t matter – because circumstances can force you to change your plans. So it sure seems to make sense to require the company to compute its assets, in terms of whether it can cover its obligations, based on what both the assets and obligations are worth today.

    Right now, you’ve got a very strange system, where for the purposes of regulation, a company can claim that things have some value for securing various debts which is entirely differerent from what the assets are worth to the company whose debt is being secured. Effectively, it’s like I take out a mortgage from my bank. The bank assesses the house at $100,000. Then I go and take out a million dollar loan against my house, because I’m not going to sell it for 50 years, and in fifty years, I project that it’ll be worth a million. Maybe it will. But if the lender calls in the million dollar loan, the fact that 50 years from now, it’ll be worth a million bucks is completely irrelevant. It’s only worth $100,000 now.

  9. #9 Ras
    March 17, 2009

    I think Tony (2) has it. I worked in the back office managing compensation payouts for a sales office at a multi-national corporation for a few years. The consistently highest paid salespeople were the ones who most quickly figured out how to work that year’s compensation program to their own advantage. We consistently had “star performers” who did extremely badly by their customers, but maximized their compensations. “Good” salespeople aren’t thinking about the big picture, they’re thinking about their paycheck. Ideally the people putting together the compensation plan would be thinking about the big picture, but I suspect more often they’re think about maximizing profit and off-loading outdated inventory.

  10. #10 Mark C. Chu-Carroll
    March 17, 2009

    Re #9:

    I agree that salespeople are generally working to maximize their own compensation. I think that’s natural – the people who go into sales tend to be pretty smart, very aggressive, and very competitive. They’re going to work out what maximizes their benefits, and they’re going to stick with that.

    On the other hand, I think that the people who put together the compensation plans are trying to think about the big picture. The problem is that it’s really difficult. Even if you use mathematical tools like game theory, it’s really tricky to work out all of the angles, and figure out how someone can play the system. And in general, the people who work out those plans aren’t game theorists. They’re usually MBAs – people with a background in management and business, not game theory.

    It’s important to remember that this isn’t simple. It’s not just evil people trying to manipulate things to screw everyone over. Any time you build an incentive structure,
    there are probably going to be unintended consequences, because you didn’t foresee some bizzare way that someone could game it.

  11. #11 lukas
    March 17, 2009

    When it comes to computing the value of a company’s assets, I don’t think that the fact that they don’t plan on selling a given asset means that they should be allowed to assign it more value than it currently has.

    In terms of corporate regulation, the point of valuation of assets is to ensure that a company has sufficient resources to cover its liabilities. Regulations limit how much a given asset can be leveraged, based on its assessed value.

    Well, how do we determine “value”? Usually, market prices are taken a reasonably close approximation to value, but when markets break down (“freeze”, meaning virtually no one is buying or selling anything) prices fluctuate widely and become meaningless.

    Coming back to your original point, I wonder why the incentive structure has been so uniform across the industry… why, say, a Google-style model hasn’t been tried with any of the big players out there. Is it because the system is run primarily for the benefit of their executive level (and lower-tier?) employees and not the stockholders? When I look at who calls the shots at the SEC, FTC, Fed, Treasury and the like, regulatory capture seems unavoidable… but then I don’t know enough about the details of the regulatory structure and how it would be able to limit stockholders’ influence.

  12. #12 Mark C. Chu-Carroll
    March 17, 2009

    Re #11:

    Market prices are, I think, the right way to compute value. A I said, the point of the valuation is to determine if the business has enough assets to cover its obligations. If they’ve got assets whose current market value is essentially zero, then their ability to use those assets to cover their debts is zero. So why should those assets count as having non-zero value? In their corporate reports, they’re free to say “current market value of asset X is effectively zero, but we believe that this is a temporary fluctuation due to adverse market conditions, and we believe it’s true value to be $y, which will be realizable in 24 months”. But when it comes to determining whether or not the firm is over-leveraged, they need to be able to show that if they take on additional debt X, they’ve got the ability to cover it, without needing the government to come bail them out.

    The current situation is ridiculous. We’ve got firms who claim to have hundreds of billions of dollars of assets, and yet, they need to take hundreds of billions of dollars from the government to prevent them from collapsing. Because their assets, which they continue to claim are worth hundreds of billions of dollars, aren’t worth anything close to that.

  13. #13 lukas
    March 17, 2009

    But when it comes to determining whether or not the firm is over-leveraged, they need to be able to show that if they take on additional debt X, they’ve got the ability to cover it, without needing the government to come bail them out.

    But this is not what is happening. We’re beyond that. The government is recapitalizing those firms (some of whom, remember, insist that they are standing on firm financial ground) so they can meet the capital requirements set out by — the government! In this instance, easing/modifying the capital requirements seems much more sensible than what is going on now. If the firms are not really unsustainably over-leveraged, that will be enough for them to weather the crisis. But if they are, the bailout money goes right down the drain anyway.