Tuesday, September 27, 2011

Why Ambiguity Aversion is Rational

Kierkegaard noted that 'Life is to be understood backwards, but it is lived forwards,' which is kind of sad--as is much existentialism--because it emphasizes how much time we spend on things we can't affect. Leave it to the government to make this an economic policy.

The SEC gave a Wells notice to S&P for their dealings with a 2007 AAA rated CDO that subsequently went into junk status. The smoking gun is that while the deal was done with an assumed collateral issue that would be investment grade, by early 2007 the market was already tanking, and the issuer had subprime collateral. An email documents S&P was aware of this.

This was a mistake, one that was probably made many times previously but they got away with it because AAA securities tend to have multiple levels of redundancy, belts and suspenders. Securitization became very complicated over the years, with many different tranches and waterfalls, and alas any explicit, complicated process invites its circumvention, so issuers and borrowers eventually figured out the mortgage-CDO game and pushed weaker and weaker collateral into them until they finally imploded. Those screaming warnings while it was happening were ignored (Stan Liebowitz), those who said these effects were innocuous, even morally righteous, were rewarded (eg, Richard Syron, Alicia Munnell). When this house of cards collapsed, everyone points to those with the deepest pockets, though no one seems to be going after Jamie Gorelick.

This was probably the last big mortgage deal to go through as if things were business as usual. As Bernanke noted, the mortgage market shut down in mid 2007 because issuers could not get the ratings needed. Market players make mistakes, but at least they stopped their idiocy 4 years ago, unlike our government, which even today issues mortgages with 3.5% down though private lenders are back to demanding 20% down.

This case highlights the importance of ambiguity aversion, as opposed to risk aversion. If a bad outcome results from a prospect about which an agent had, with the benefit of hindsight, made a mistake, he looks not just unlucky, but incompetent or malicious. In experiments, a lottery ticket is worth a lot less after the drawing for most people even if they don't know what the true number is, and seemingly the seller does not either. People shy away from processes about which they think they have insufficient, as opposed to probabilistic, information, even if framed identically (eg, both with a 50% chance). This is ambiguity aversion.

A bad outcome resulting from a pure risky prospect, on the other hand, cannot be attributed to poor judgment. If all possible information about a risky prospect was known, failure can only be bad luck. The key is, ex post, can you look like a sucker or just unlucky? Investment managers can live with bad luck, but their reputation is essential and they can't be seen a fool.

This aversion to 'incomplete information' games is related to, but different from, classical risk aversion, and probably explains why lenders are now so afraid to lend: if they make a mistake now, it won't be merely a bad investment, but a crime. Life is a lot more like a game of incomplete information than a roulette wheel.

AAA ratings on securities that subsequently suffered generated big losses to investors, the people who ultimately should be monitoring the credit agencies. Their incentives are already aligned. The rating agencies themselves have suffered credibility shocks for this, and so now we have DBRS and Kroll jumping into the previously unpenetrable field. Jumping onto the battlefield and court-marshalling the wounded is a poor tactic for improving morale or future performance, rather, it will just encourage all sorts of tentative, butt-covering behavior that precludes the dynamism a growing economy needs.


John Hall said...

I see ambiguity aversion as more tightly joined with risk aversion than you do. For instance, consider the Ellsberg Paradox (I'm using the 1 urn example from wikipedia). It would be impossible to estimate what the probability distribution is in advance. However, if you assume that the split between black and yellow balls is a uniform random variable (and I believe most people implicitly believe this is the case when they face this game), then it is possible to do the draw 10,000 times and determine the probability distribution of the gambles. The gambles with "ambiguity" are clearly riskier and the paradox melts away.

Eric Falkenstein said...

Well, considering the Ellsberg Paradox is still considered an unsolved paradox, I don't think your solution works.

I don't see what the 10k times does. Once you draw one black or yellow ball, you know the urn distribution with certainty, which would be either 30 red and 60 black, or 30 read and 60 yellow. But the bet is for drawing once.

Anonymous said...

So we should invest in AIG and BAC because if we lose we'd look like fools and thus they are potentially undervalued now because no fund manager wants to deal with this 'career risk'?

John Hall said...

I'm not sure I explained well enough. I'd be happy to send along some code that may make it more clear.

Even in Ellsberg, you never know the urn distribution with certainty. You merely know that if you prefer A to B that implies something about what you think the distribution is and it influences what your bet in C vs D should be.

So 30 red balls, no matter what. Let's say black=floor(70*p) and yellow=70-black. Let's assume p is a random variable (say, uniform between 0 and 1) and you simulate it some 10,000 times. So you have the breakdown of the marbles if you had run this experiment 10,000 times. The person could then determine what the probability distribution is for each gamble. Of course, after they choose the gamble, they will draw from one jar and have one marble and one profit. However, they can still come up with an ex ante distribution of expected profits. For instance, A and D will look like dirac deltas, but B and C will have different distributions depending on how p is simulated.

In this sense, you could compute something like a mean to expected shortfall ratio (assuming you have to pay to play the game) or some utility function like mean-lambda*expected shortfall and I think this would readily explain the way most people behave in these games. They don't like the uncertainty with gambles B and C.

Eric Falkenstein said...

They key is that if you do this 1MM times, they are identical:(same probability of winning in both gambles-1/3 in the first, 2/3 in the second), which is why the preference towards A and D is paradoxical. You don't need to sample to assess the true ex ante probabilities, because the are presented without ambiguity.

John Hall said...

In one sense, what I am doing is assuming that the ambiguity can be converted into a probability distribution that approximates the ambiguity.

Some more points:

1) I'm not disputing that if you only have preferences over expected values than the preference for A and D would be paradoxical.

2) I don't know what you mean by 1MM times is different than 10,000 times. I don't think 1MM is any different than 10,000. I can go and check it, but I doubt I would have any different results. Again, happy to send over some Matlab code to show what I mean.

3) Here's what I don't think I'm explaining well enough. I think we're talking about different things.
You seem to be focusing on the fact that if I think there is some x% probability of a black ball, then I will switch. Indeed, that is what most focus on. I think x is a random variable. For each x, I can compute the expected profit, exactly. No dispute there. However, I need to sample many x's in order to get the actual distribution of profits. This seems to be where I'm not explaining things well enough. I'm implicitly assuming that people make some assumption about how x is chosen. I think in practice that is reasonable. If they think, well the allocation between yellow and black could be anything (and I assume that means they assume it is a uniform random varible), then the black gamble and the red and yellow gambles need to be sampled from to actually get the distribution of profits. The red gamble and the not red gamble are known in advance.

Again, if people only care about expected values, then it doesn't change anything. However, most people care about the possible downside. Hence, most people switch.