Broken Symmetry

Paul Samuelson the Investor

From Economic Principals:

It turns out that the great MIT economist was influential in the creation of one of the earliest and most influential hedge funds. Launched in 1970, Commodities Corp. blazed a trail of extremely high returns throughout the 1970s and early ’80s, before disappearing in various pieces into Bermuda mailboxes and Goldman Sachs. Many of its star traders – Bruce Kovner of Caxton and Paul Tudor Jones, chief among them—formed successful hedge funds of their own. Samuelson thus had a ringside seat at the birth of an influential industry that is still only poorly understood.

About the same time, he invested a substantial amount in shares of Warren Buffet’s Berkshire Hathaway Inc. It was in 1970, too, that he won the Nobel prize in economics, the second to be awarded. Long famous for the fortune that his pioneering textbook earned him after 1948, it turns out that Samuelson may have made more money as an investor than as an author. He was both smarter and richer than is generally understood: as an investor, a bigger winner, perhaps, than the more volatile John Maynard Keynes.

Via Tyler Cowen at MR. More evidence for the Paul-Samuelson-as-Isaac-Newton theory?

Move Bankrupty-Remote Entities Back on the Balance Sheet?

Fascinating interview of Gary Gorton re: the gory details of the credit crisis in late 2008, which continues to present:

Securitization basically allows the traditional banks to finance their loans by selling them rather than holding them on balance sheet, and the source of value here is avoidance of bankruptcy costs. A firm that originates loans does so by lending money to any number of borrowers—both corporate and consumer—and it then selects a large portfolio of its loans to sell, in a very specific legal sense, to a “special purpose vehicle,” an entity it creates for that very precise reason. The main advantage of doing so—of establishing the SPV and legally selling the loans to it—is that this arrangement circumvents the costs associated with bankruptcy.

Via Alex Tabarrok at MR.

I understand why Gorton is in favor of innovation in revenue generation, and I even understand why he considers shadow banking an inevitable next step given the amount of institutional money moving around now. I even understand why there need to be bankruptcy remote entities -- there should be a spread of higher and lower-risk vehicles.

What I don't understand is how or why these special purpose vehicles get to stay off the balance sheet.

The Coase Theorem Does Not Apply to Multilateral Agreements

In The Problem of Social Cost (available here), Ronald Coase presented the case for what became his eponymous Theorem. In short, Coase argued that in the absence of transactions costs, parties would contract around default legal rules to achieve an economically efficient allocation of resources. As a result, in the absence of transactions costs, lawmakers should only need to ensure a clear definition of property rights and the enforcement of contracts, without worrying too much about who starts off with the property rights. The Coase Theorem has been on my mind a bit lately thanks, in part, to the Supreme Court grant of certiorari in the Stanford v. Roche case. If transactions costs could be ignored, then (according to Coase) none of the stakeholders in the tech transfer system should worry too much about a reallocation of ownership rights by the Supreme Court. An economically efficient bargain would always be reachable under a new allocation of rights -- assuming the transactions costs can be ignored.

But can they? Of course not. The uncertainty associated with tech transfer investments is often so great as to swamp the costs of negotiating these agreements. In this post, however, I want to abstract away from the specific economics of tech transfer, mortgage finance, corporate chartering, insurance, derivatives, or any other economically multilateral agreement in order to emphasize just how limited the Coase Theorem is in its general applicability to the analysis of large-scale social costs.

The Problem of Social Costs makes its case using a hypothetical example of a negotiation between a rancher and a farmer over who should have to pay for a fence and/or crop damage. That archetypical case comes in the first main section of the paper, titled "The Reciprocal Nature of the Problem." Coase's hypothetical is explicitly a bilateral agreement. Coase's emphasis of the "reciprocal" nature of the problem is implicitly bilateral in its symmetry.

So what? Consider the graph below, which compares how the transactions costs of bilateral contracts and the transactions costs of trilateral contracts add up as a population of parties increases. The calculation of both is based on the assumption that each party to an agreement (whether bilateral or trilateral) will pay the same fee for entering into an agreement. The calculation of both is made assuming every party in the population will enter into a single agreement with every unique combination of counter-parties. (In detail, these are total unique combinations of two and three picks from a population of n graphed as a function of n.) The graph shows how the relative difference in transactions costs diverges dramatically even for a population of 15 parties.

The difference is even more dramatic for a population of 100 parties.

What does this mean? At the very least it means that in policy debates about the allocation or reallocation of resources whose use involve three or more distinct economic interests (i.e., stakeholders), the Coase Theorem should not be invoked, or at the very least invoked only after everybody is satisfied that the transactions costs are completely overwhelmed by the economic benefits of a bargain.

But nearly every policy question involves more than two stakeholders. Even consumer transactions -- which seem like the quintessential bilateral agreement -- have indirect effects, compensated for through indemnifications and warranties. In other words, the Coase Theorem simply doesn't apply to any practical policy problem of interest.

At the same time, the Coase Theorem was very useful because it focusses our attention on transactions costs. In many cases, it may be easier to lower transactions costs than to decide how rights should be allocated. My point in this post is not to say that The Problem of Social Cost was fundamentally wrong, or even useless. Rather, I want to point out that we can usefully analyze transactions costs by breaking them out according to the number of parties necessary to an agreement.

This point gains strength as the number and variety of multilateral agreements increases. Nothing much at all seems to happen in our economy without getting buy-in from a host of stakeholders, either formally or informally. And the biggest economic issues of our day -- from Fed policy, to mortgage financing, to tech transfer models -- are all examples of vast, multilateral negotiations. Our world is no longer Coasean.

Positional goods present an especially interesting application of this analysis of transactions by number of parties. A positional good, by definition, is a good whose value depends both on the supply available and on the demand for the good by other consumers. Every transaction involving a positional good is at least a trilateral agreement, and arguably much more multilateral than that since the other consumer might not be based on the activity of a particular person, but rather on a general perception of the activity of an entire group of other consumers. The Coase Theorem simply doesn't apply to positional goods.

Geanakoplos and Farmer on the Nonequilibrium Statistical Mechanics of Markets

The WSJ leads with Geanakoplos today and Marginal Revolution picks the story up. Skimming through SSRN publications by Geanakoplos, I find this chestnut:

An alternative point of view is that, due to a lack of a perfect rational ity, the market is not in perfect equilibrium and thus prices do not simply passively reflect new information. Under this view the market acts as a non-linear dynamical system: agents process information via decision-making rules that respond to prices and other inputs, and prices are formed as a result of agent decisions. Since this information processing is imperfect, the resulting feedback loop amplies noise. As a result a signicant component of volatility is generated by the market itself.

From a paper co-authored with J. Doyne Farmer.

Leverage Causes Fat Tails and Clustered Volatility

From Stefan Thurner, J. Doyne Farmer, John Geanakoplos:

When funds use leverage, price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on 'irrational behavior', such as trend following. We show that the immediate cause of the increase in extreme risks in our model is the risk control policy of the banks: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy by individual banks makes these extreme fluctuations even worse. Thus it is the very effort to control risk at the local level that creates excessive risk at the aggregate level, which shows up as fat tails and clustered volatility.

A Systems Theory of Financial Regulation

From Geithner and Summers:

First, existing regulation focuses on the safety and soundness of individual institutions but not the stability of the system as a whole. As a result, institutions were not required to maintain sufficient capital or liquidity to keep them safe in times of system-wide stress. In a world in which the troubles of a few large firms can put the entire system at risk, that approach is insufficient.

Perfectly consistent with Summers's column on "Regulatory Systems Design" almost a year ago today.

For a systems theory of patent law, see Question 9 here.

More on the Application of Non-equilibrium Statistical Mechanics to Economics

Edge.org recently published a manifesto on how science can help economists and politicians improve forecasts and regulations:

Instead of being in equilibrium, markets can be understood as self-organized critical systems. This is a theoretical construct that can be usefully applied to real markets. It leads one to expect that in steady states markets are approximately scale invariant. This implies a prediction for how certain quantities will be distributed in an economy, which includes wealth, income, sizes of firms, populations of cities, and total values of currencies. The prediction is that these distributions are power laws and the prediction is observed in the real economy.

Note that the theory is that the entire market displays self-organized criticality, not individual firms within the market.

Time scales matter. Different functional cash to cash cycles have very different time scales. Instabilities can be easily introduced by too strongly coupling processes on different time scales.

What this means is that if in a population of 300 million people, only 3 million or so are going to be eligible to borrow under subprime terms in a given year, then you're going to create a bubble by coupling enough money to fund 30 million a year into the market through things like CDOs and CDO^2s.

Read the whole thing. There's also mention of periodicity in cycles of economic activity.

Nitty Gritty Details on Subprime Securities

For those interested in doing a deep dive into the details of how and why subprime mortgages were securitized into the various tiers of of MBS, CDO, and CDO^2, I recommend this paper by Gary Gorton, who did this work at AIG. Thanks to Tyler Cowen for the link.

Rational Price Bubbles

Via Tyler Cowen I got my hands on this paper by some folks at Harvard about how price bubbles can exist without irrational exuberance under the right circumstances.

The assumptions made in the paper are not "physical" in the sense that the exogenous shock they model in is not observable.  But it appears that you might get their same results by modeling individual utility functions with poisson distributions in frequency.  The notion of poisson distributions in production and consumption is familiar to regular readers of Broken Symmetry.

With that caveat aside, I really like the approach in this paper.  It demonstrates the benefits of thinking about supply and demand as flows and it demonstrates how price bubbles can result even without relaxing the requirement of rationality.  It's a definite step forward toward a dynamic model of supply and demand.

My main response to the paper for now is that it doesn't address the other variables that seem to contribute to rational price bubbles.  In a post about the subprime mortgage market a few months ago, I looked at liquidity constraints and external money supply as independent variables that could be used to model rational price bubbles.  Liquidity, money supply, and cross-elasticities with other markets all contribute to elasticity in supply and demand, but at different characteristic time scales and magnitudes.  I understand that you have to make simplifying assumptions to understand each.  But it would have been nice if they'd mentioned these other influences somewhere.  Maybe they did and I didn't catch it.

Are Fannie Mae and Freddie Mac evidence that Creative Capitalism cannot Work?

Not quite.

Over at the Creative Capitalism blog, Lawrence Summers points to the failure of privatization of government home mortgage lending as evidence of the limits to Creative Capitalism.

But the problem with these institutions, as Summers seems at least implicitly aware, was not with the existence of public/private partnerships, but with the bundling of incentives effectively implemented by these partnerships.  Specifically, with the government put on F&F mortgages, the banks buying them could afford to ignore low probability, large-scale catastrophes.  The ability to ignore this contingency, ironically, is part of what led to its more rapid development.  Markets are cyclical.  A clump of clothes in your washing machine can throw the whole machine out of whack.  How much more so a clump of poorly priced assets in a market?

The way forward, as I blogged a few months ago, is to focus on how assets are bundled.  Within any market, the smallest unit of demand must both receive benefits and pay costs of social consequences to a transaction.  In the mortgage market, this means that home buyers should also have been paying for insurance premiums for the risk of price declines due to offsite factors.

If we give up on creative capitalism now, we'll only be back where we started with marxism vs. laissez-faire.  We shouldn't give up just because it's hard.

Applying Control Theory to the Subprime Mortgage Supply Cycle

In an earlier post, I explained how transactions costs, liquidity, money supply, and scarcity can be modeled as the resistance, inductance, capacitance, and voltage of an RLC circuit.  When Schumpeterian creative destruction causes a demand voltage to spike, the coupled supply circuit will damp the spike at the "resonance frequency."  Oscillation will still be observed if the demand spike is large enough, but the resonance or bubble effect will decay to zero over longer time periods unless an active element is included in the supply circuit.

To show how the resonant frequency for this RLC filter can be calculated, let's apply some actual numbers to the supply cycle for subprime mortgages.

Because of MBS, CDOs, and CDO^2s, the liquidity in the subprime market was actually much larger than ever before.  How many orders of magnitude is hard to say.  I'll estimate that the rebundling and sale of mortgages increased the scale of supply by a few orders of magnitude, and also increased the number of days / sale as the bundling, rebundling, etc. takes longer to accomplish than a simple mortgage.  If it takes 100 days to do the bundling, but by doing so you get up to $10,000,000 scale, the measure of liquidity becomes:

L = (100 day / sale) / ($10,000,000 sale) = 1 x 10^(-5) days / $

Money supply (capacitance) should be measured in units of days / $ -- i.e., the number of days that each $ loaned from an external supply spends in the market before being paid back.  I'm going to estimate that about $1,000,000,000 of the entire money supply (on average) was locked up in mortgages, MBSs, CDOs, or CDO^2s.  And banks were probably holding onto these funds for about 100 days before going back to the Fed.  Of course the government kept messing with money supply by increasing and decreasing the cost of lending, but I'm ignoring that.  I'll repeat, however, that if the money supply obeyed something like Taylor's rules, we'd have a more determinate system.

C = ($1,000,000,000 * 100 days) = 1x10^11 $-days

Solving the differential equations for the frequency of the resonant peak for this cycle, we find that:

Resonant frequency = 1 / square root (L * C) = 1 / sqr ( 1x10^-5 days / $ * 1x10^11 $-days ) = 0.001 cycles / day.

In other words, according to these estimates of liquidity and money supply, we can predict a peak in the subprime mortgage market to occur about once every three years.  And that's roughly how long it seems to have taken for us to reach a peak once bundling of mortgages started.  In general, when you hit a damped harmonic oscillator (like an RLC circuit) with a signal spike, it will ring at a particular resonant frequency.  The resonant frequency is like the "sweet spot" on a baseball bat, whereby  an incoming spike at that exact frequency will be damped to zero at exactly the length of one period of oscillation.  If the demand spike has a longer or shorter frequency, then the damping will either occur in less than the period of the resonant frequency (overdamping) or the spike will continue to oscillate but at lower amplitude (underdamping).

When the liquidity and money supply effectively underdamp the incoming demand spike, the RLC supply circuit will continue to oscillate at the resonant frequency, but at successively lower amplitudes.

Modeling the Subprime Mortgage Market as a Closed Loop Oscillator with only Positive Feedback

Electrical engineers who design analog circuits learn an important rule of thumb: closed loop systems that provide only positive feedback to their inputs can become unstable.  In the diagram at right, when A and B are relatively good amplifiers, the multiplication of their amplifying effect at the input Vin can cause the system to blow up.

The closed loop oscillator with only positive feedback is actually also a useful way to understand what caused the subprime mortgage market bubble, and what could have been done to prevent it.

According to the newspaper accounts, something like this was happening: home buyers were bidding for price (Vin), which was being approved by assessors. Banks were then offering loans based on the assessments to the buyers, and selling the loans to loan-buyers.  Loan-buyers were then bundling the loans into CDOs (amplifier A), and then selling them to bigger loan-buyers, who were then bundling CDOs into CDO^2s (amplifier B).  The bundling permitted for larger-scale buyers of loans to get into the market, which has a multiplying effect on demand for loans, which in turn gave the banks and assessors an incentive to offer loans at higher assessed values regardless of the underlying value of the property.  There was no mechanism for negative feedback on price to enter the closed loop that buyers, assessors, banks, and institutional investors formed.  And when A*B approaches 1, as it will eventually in a system with powerful amplifiers and no negative feedback, the system blows up.

Electrical engineers avoid these kinds of instabilities (usually!) by building negative feedback into the loop -- i.e., by introducing some circuit element that inverts or phase shifts the signal fed back into the input of the circuit so that the signal doesn't just keep growing and growing until it blows up the circuit.

Lee Fennell at the University of Chicago law school has a great suggestion for how we could have built negative feedback into the system: bifurcate on-site and off-site risks associated with homeownership, and make buyers pay separately for these two types of risk.  So for example, a home buyer might be required to buy an insurance contract at the same time they purchase their home, the premium for which is large enough to permit the insurer to pay the home buyer off for a loss in home value should the value of her home later decrease precipitously because of off-site problems in her community (such as factory closings, pollution, or crime).

Now imagine how the same cycle would have worked: the home buyer makes a bid on both the home and the insurance for off-site risk -- the law has to require her to buy both, otherwise this doesn't work.  The home assessor approves an inflated price.  That's still the assessor's incentive because of the demand for mortgages.  But the insurer then raises insurance prices in response to the assessment to offset the larger risk associated with the inflated price.  If the home buyer can pay the increased premium, it's a deal.  If not, the deal falls through, and prices tend to fall back to a level that more accurately reflects the underlying value of the property.

UPDATE: Upon reflection, I realize that the government actually does not have to require homebuyers to buy both the home and the insurance.  In fact, only the insurance-provider and mortgage-provider would have to agree.  This raises other complications (what happens when they're owned by the same entity, e.g.?), but it's useful to see at least that new legislation might not be required.

The credit market debacle

Major financial scandals seem to transpire once every three to five years.  The cycle seems to go in four phases: (1) price crash; (2) journalist frenzy, usually ending with the revelation of scheme to "defraud" investors; (3) government investigation and prosecution; (4) private lawsuits and reorganization.  The quotes are there, of course, because for most people, most of the time what looks culpable in one context (e.g., when indictments are being handed down) looks merely aggressive in another (e.g., when everyone else is doing it and you're afraid of being at a competitive disadvantage if you don't).

We seem to be nearing the tail end of the cycle for options backdating scandals.  I'm thinking we're just now getting into phase 2 with the credit markets.  My prediction is that some major fraud in how collateralized debt obligations (CDOs) were packaged and repackaged into securities is going to be "discovered," and one of the major investment banks is going to be left holding the bag.  Like the risk profile for LTCM assets, the risk profile for CDOs was determined based on market data from the past.  And if there is one place where Shakespeare's dictum ("what is past is prologue") fails, it's the publicly traded markets.

Things may not end as badly as they did for Arthur Andersen.  Almost nobody's retirement is going up in smoke this time around.  But nobody's pension disappeared because of options backdating either, and there was nonetheless plenty of of public political activity in response.

UPDATE: looks like the SEC is ready to skip to phase 3, and the law firms to phase 4!

UPDATE 2: We're now definitively in phase 3.  Check out this photo.