Mechanism design and the bailout

Introduction

Since the explosion of the banking crisis we have seen many analyses and many proposals for solution; hardly a day seems to pass by without the appearance of a new plan to save the banks. So, you may ask, why do we need plan n+1? Well, I am not going to propose a full-fledged plan. Rather, I would like to make a partial proposal related to one aspect of the problem, the evaluation of the so-called ''toxic assets''. The theoretical underpinnings of many of the existing proposals are often quite opaque: I would like to do the opposite, so I will try to explain in some detail the theoretical basis of my proposal.

To clarify, there seem to be two big and somewhat separate problems we have to deal with. The first is what we can call ''the mispricing problem'', or maybe more accurately ''the lack of pricing'' problem. It refers to the fact that an hefty amount of the assets currently in the portfolios of the banks is, at the moment, very difficult to price. The second is what we can call the ''how to deal with bankrupt banks'' problem or, to be more technical, ''how to avoid deadweight losses from bankruptcies in the banking sector'' problem. In many proposals the two aspects have been conflated, but I believe that they should be considered separately. More than that, there is a hierarchical order in which we should proceed. The ''mispricing problem'' has to be taken care of before we start reasoning about the efficient way to reorganize bankrupt banks, for the somewhat trivial reason that unless we put a sensible and credible value on the banks' assets it is impossible to say who is actually insolvent and who is not. The point has been made very well by Larry Ausubel and Pete Cramton, so it doesn't need to be repeated here.

I will concentrate my attention on the mispricing problem, but before I go there I want to make a point about the bankruptcy problem which is frequently overlooked. In every bankruptcy there are two issues: who gets the assets and how to avoid deadweight losses. There have been many calls to inject public funds in insolvent banks, through ''nationalization'' or whatever is the politically acceptable name of the process. Even if this implies reducing to zero the value for current shareholders (and it is not clear, in many proposals, that this would be the case), in many cases the idea is to help the creditors of the failing institutions (I'm referring to creditors other than depositors, who are covered by FDIC insurance). This is the way, for example, in which the billions given to AIG have been used. Helping the creditors of failing banks, or insurance companies, should not be per se a goal of public policy. If it is believed that some disastrous systemic effects would follow if such creditors end up losing their money then it is the duty of the policy maker to provide clear evidence of the existence of such effects. Not only that, creditors should be helped only to the minimum extent necessary to prevent such systemic effects. Policy proposals in this area should concentrate on eliminating deadweight losses, i.e. making sure that the assets of bankrupt banks are put back to work as soon as possible, not on saving the creditors.

Private vs. public information.

The mispricing problem originates in the many Mortgage Backed Assets that the banks have in their balance sheets and, at the moment, are very hard to price. What is creating problems is the uncertainty on the size of the losses these assets will face. It is important, however, to understand exactly what is the type of uncertainty that creates problems. At least from the theoretical point of view, uncertainty which is symmetric, meaning that there is no single party who has better information, does not create special problems. It is surely true, for example, that in the last year the expected payoffs of many mortgages have decreased. This reflects, on the one hand, the increased probability that borrowers will be unable to meet their obligations and, on the other hand, the decrease in value of collateral, due to the decrease in the price of houses. But, at least in the case of symmetric information, this merely implies that the price of the assets goes down. Risky assets will find their equilibrium price in the capital markets, prices which reflect their expected payments, their risk and the risk aversion of investors. Given the decrease of the expected payoffs, prices have to fall. It is also probably true that the payments on many mortage backed assets have become riskier and that investors have become more risk averse. These two additional factors have contributed to the loss of value of the MBAs. But, again, these losses reflect true changes in fundamental factors, preferences and probability of repayment, and there is really no reason to believe that they cannot be properly priced in the capital markets.

Asymmetric information, however, is an entirely different matter. If the market starts to suspect that some of those MBAs are more toxic than others and that the managers of the banks know the ones that are more dangerous, then the markets can easily collapse. This is the standard ''market for lemons'' problem, which is by now well understood: investors don't want to buy MBAs at a price equal to their average value, because they are afraid that what they get is not the average but the worse, i.e. they suspect that the banks will first try to unload the most toxic securities. Lowering the price in this case does not work, since it only convinces even more the investors that the securities are truly toxic. The market essentially freezes. Investors will only buy at very low prices, the ones corresponding to the most pessimistic expectations on the assets. But this must mean that on average the MBAs are worth more than the market prices and therefore the sellers will be unwilling to sell.

Willem Buiter has called toxic the assets ''whose fair value cannot be determined with any degree of accuracy'', as opposed to clean assets, whose fair value can easily be determined. As pointed out by Buiter

 

Clean assets can be good assets (assets whose fair value equal their notional or face value) or bad assets (assets whose fair value is below their notional or face value).

 

In other words, clean assets are the ones subject to symmetric uncertainty, while toxic assets are the one subject to asymmetric information. This point seems to be quite clear from the theoretical point of view, but many observers seem to believe that the cause of the low prices lies not in the asymmetry of information but in some form of irrationality that is right now pervasive in the capital markets or in some form of uncertainty regarding the availability of capital on the part of the buyers. An important example of this kind of confused reasoning was provided in a recent interview by Treasury Secretary Tim Geithner.

While factors linked to forms of irrationality or financial constraints cannot be entirely ruled out, I find it difficult to believe that they are an important part of the story. The existence of asymmetric information is more than sufficient to explain the freezing of the markets for MBAs. To give an idea of how large the uncertainty may be, the Financial Times on Feb. 26 reported:

 

JPMorgan estimates that $102bn of CDOs has already been liquidated. The average recovery rate for super-senior tranches of debt – or the stuff that was supposed to be so ultra safe that it always carried a triple A tag – has been 32 per cent for the high grade CDOs. With mezzanine CDO’s, though, recovery rates on those AAA assets have been a mere 5 per cent.

I dare say this might be an extreme case. The subprime loans extended in 2006 and 2007 have suffered particularly high default rates and the CDOs that have already been liquidated are presumably the very worst of the pack.

 

Clearly, with such numbers there is no need of irrationality to stay away from these assets. Even if the standard deviation surrounding this sample estimates is small (and chances that it is instead big), the distance between 100 (face value), 32 and 5 is large enough to scare anyone. And, again, while we may all be convinced that the actual average value is higher, how can we know that the seller is not trying to unload on us ''the very worst of the pack''? Even with perfectly rational agents, in these circumstances the markets collapse.

Since toxic assets are an important component of many banks' balance sheets, the uncertainty on their value implies uncertainty on the value of the banks, in particular bank equity. Hall and Woodward, in discussing a mechanism for efficient bankruptcy attributed to Jeremy Bulow, report a stylized balance sheet for Citicorp in which toxic assets account for $610 bn out of $1935 bn of assets. Given that the value of equity is just $11 bn, it is easy to see how even marginal changes in the value of the toxic assets may lead to bankruptcy (or, if you prefer to be an optimist, to a large increase in the value of equity). Buiter has performed similar calculations looking at the balance sheet of the Royal Bank of Scotland, and he credibly claims that the situation is similar for many big banks.

Thus, pricing toxic assets is crucial to determine properly which institutions are bankrupt and which are not. Notice that the existence of asymmetric information implies that the arguments claiming that the toxic assets are currently underpriced do have some merit. Presumably, absent asymmetric information, a careful analysis of the cash flows likely to be generated by these assets would produce higher values than what we would observe in the market. The question therefore becomes: how can we eliminate or at least alleviate the asymmetry of information, so that the capital markets will be able to price properly these assets?

The market vs. the government

Markets tend to underperform in situations of asymmetric information, but there are things that can be done. Remedies fall under two broad categories. First, direct action can be taken to reduce the asymmetric information, e.g. when you buy a used car you may ask a mechanic you trust to inspect the car before the purchase. Second, the seller can try to credibly signal the information. Of course every seller will claim that the car he is trying to sell is in perfect conditions. But only the seller of a car which is truly good may be willing to offer a warranty on the car, covering all mechanical problems that will appear in the next two years. This kind of ''signaling mechanism'' have been widely studied in the literature and we can apply the same insights to the pricing of toxic assets.

In principle these are remedies which do not require any government intervention, as rational agents should be willing to implement them in their self interest. But this has not happened, and the markets for toxic assets have remained frozen. Why?

The most sensible explanation I can come up with is that the management of the banks seems to lack the incentives to get the assets properly priced. Their strategy, although rarely spelled out in detail in the official debate, [has been on this site] and seems well described in this post by John Hempton: sit tight on your assets, wait for extra revenue to cover the losses, and then go back to normal. In the meantime, pretend you are solvent by claiming unverifiable values for your assets (Tyler Cowen in the New York Times also has an interesting post on the matter and the matter has been discussed by Michele Boldrin in this blog) and avoid taking new risks, i.e. avod doing the things that banks are supposed to do. This, it should be made clear, is a terrifying scenario. We really can't afford many years (three? five? ten?) without a functioning banking system.

Exactly why the managers are so reluctant to get the assets priced is hard to tell. Regulatory uncertainty, in particular the hope of getting additional bailout funds, is surely part of the problem. More in general I believe it is by now uncontroversial that bank managers have been earning huge rents in the past few years. They clearly hope to maintain at least part of these rents, and keeping their jobs is a crucial part of the strategy. Be it as it may be, at the end of the day what really matters is the empirical observation that markets are not self-correcting. Thus, it makes sense to look at what the government can do.

Differently from markets, governments can make offers that cannot be refused. Or, to put it more technically, governments can violate the individual rationality constraint of the parties involved in the transaction. Given the overwhelming public interest in having a well capitalized and well functioning banking sector, I think that the time is ripe for government intervention. But it is important to get the details right. Direct intervention to reduce asymmetry of information is being tried, partially and awkwardly, with the ''stress test'', but the potential for gains of financial assets is not something as easily checkable as the engine of a car. Providing incentives to managers to get them to disclose their private information therefore becomes important. Providing incentives may be costly for the market, but much less so for the government which can use the stick as well as the carrot. What we need to do is to set up a mechanism which elicits the information while avoiding paying excessive incentive rents to the bankers. In general the amount of incentive rents can be made small if we can violate the individual rationality constraints.

What is to be done

I simply propose that, when it comes to evaluating toxic assets, bank managers be forced to put their money where their mouth is. The initial idea of using TARP money to buy toxic assets failed over disagreement about the proper price to pay. Ausubel and Cramton have proposed using a reverse auction for finding the prices, while Lucian Bebchuk is now proposing setting up competing buying funds with on a mix of public and private captal (here is a synthesis of his proposal).

Whatever buying mechanism for toxic assets is used, I propose to supplement it with a collateral to be provided by the bank managers. The mechanism should work as follows.

First, the government decides how much money it wants to spend buying toxic assets. Auctions (or some other mechanism) are held, and the prices at which the government buys the toxic assets are determined. Once the prices are determined, we can assess the solvency of the banks. If, at the equilibrium price, the bank is not solvent then the transaction does not take place. At that point we should proceed to liquidate bankrupt banks in the most efficient way. As previously said, what to do with bankrupt banks is not the topic of this post.

If the bank is in fact solvent, at the prices determined by the auctions, then the Treasury pays the price. The toxic assets are removed from the bank's balance sheet in exchange of hard cash and put into a government-owned investment fund. On top of this, the managers of the bank selling the toxic assets are required to put some of their money as collateral or, which is the same, put some of their own money in the capital of the investment fund owning the toxic assets.

I will illustrate with an example; the numbers are very tentative, and should be carefully analyzed before implementing the plan.

Suppose that the Treasury buys from Bank A assets for a total value of $100 million. The assets are held by a government-run fund. The bank managers are required to pay a certain amount of their wealth (for example, a total of $5 million) and then to deposit into the fund all their earnings in excess of a certain amount, say $200K. The money is deposited in an escrow account and is remunerated at the risk free interest rate. The fund lasts ten years and the Treasury requires a return of 7% per year. This means that after 10 years the Treasury should get 100×(1.07)¹⁰=196.72 million dollars. In the meantime let's say that the money in the escrow account is remunerated at 4% and that the manager deposit an additional 300K every year. After 10 years the amount is 5(1.04)¹⁰+0.3(∑_i=1⁹(1.04)ⁱ)=10.70.

Let X be the value of the fund at the end of the 10 years. We can distinguish 3 cases:

1.The rate of returns has been more than 7%, i.e. X≥196.72. In this case the Treasury receives X and the bank managers get $10.70 million.

2.The rate of return has been less than 7%, but adding the money paid by the bank managers we get more than 7%, i.e. 196.72≥X≥186.02. In this case the Treasury receives 196.72. This is obtained from X plus 196.72-X from the escrow account. What remains in the escrow account (i.e. X-186.02) is given back to the bank managers.

3.The rate of return has been less than 7%, even when adding the money paid by the bank's manager, i.e. X<186.02. In this case the Treasury receives X+10.70 and the bank manager receives nothing.

This is the basic structure of the proposal. The central idea is to provide the bank managers with incentives to price realistically the toxic assets. Such incentives are best provided when the managers' wealth (rather than the wealth of the banks' shareholders) is at stake.
In all the schemes provided up to now these incentives were absent, so the bank managers always had an incentive to overstate the true value of the toxic assets. In order to counter this incentive the mechanism asks the bank manager to put their money where their mouth is. If the price claimed by the bank manager is unreasonably high then the risk of losing the deposit and all the extra compensations becomes very real.

One potential problem with the scheme is that now the bank managers may have an incentive to understate the true value of the assets, in order to make it easier to earn the annual rate of 7%. In order to counter this incentive, the mechanism stipulates that the toxic assets are purchased only if, at the resulting price, the bank is solvent. Thus, bank managers will be reluctant to lower too much the prices because that would mean losing their jobs and the rents that go with them.

In the ideal mechanism the incentives to understate the value of the assets are exactly matched by the incentives to overstate the value, resulting in truthful disclosure. The strength of the incentives in one direction or the other depend on the exact parameters of the mechanism: what is the required rate of returm, how much the managers are asked to put in the escrow account, and so on. But, I believe, even an imperfect mechanism would do much better than the current situation in which bank managers can claim wild values for their assets without having to pay any consequence.

Improving the mechanism

The basic mechanism described above can be enriched and modified in a number of ways. I will describe a few.

A) Flexible horizon. The investment funds holding the toxic assets should have a limited duration, say 10 years. However, the goal should be to close them down as soon as possible, with the constraint that the investment yields the required return over the period of life of the fund. For example, suppose that after one year the assets bought by the Treasury for $100 million can be sold at $107 million. In this case the assets are sold, the Treasury gets the money and the bank manager receives back 5(1.04)=5.2; from this point on the manager is free from the obligation to deposit the excess salary in the escrow account. The government is out of the picture and the (formerly) toxic assets are now less toxic and freely exchanged in the capital markets.

Similarly, suppose that after one year some of the assets appreciate more than 7%, while others do not. For the sake of the example, let's say that assets which have been paid $50 million are now worth $55 million. The assets can be sold and 50(1.07)=53.5 should be paid back to the Treasury. The remaining 1.5 million goes back into the fund. The new goal is to make sure that the remaining 50 million earn 7% over the 10 years, with the extra gain coming from the sale of the assets going toward that objective. In general the assets can be sold at any time at which they can produce a return of 7%. The bank manager will have the money back and will be able to stop depositing the excess salary only when the fund is liquidated.

B) Managing the escrow account. I have assumed that the money deposited by the bank managers is remunerated with a fixed rate. This is really not necessary. There would be no problem in, for example, letting the bank managers actively manage their account. In fact, if they have provided truthful values for the toxic assets they should attach a high probability to getting their money back. It should therefore be in their interest to maximize the value of such funds. Of course, some provisions against fraud (e.g. using the money to give loans to family members) would be necessary if active management is allowed.

C) Reducing the risks for the government. Realistically, the amount of money that bank managers can put in the escrow account will be only a tiny fraction of the value of the toxic assets. The role of those deposits is to provide managers with a strong incentive to tell the truth about the value of the toxic assets, rather than to provide valuable collateral. The scheme however can be supplemented by using the bank assets as collateral. For example, it can be stipulated that banks are not allowed to distribute dividends as long as the fund exists, and that in case the return on the toxic assets is inferior to the required return the banks have to make up for at least part of the difference putting money in the fund. The detail may vary, but this would give an additional incentive for bank managers to provide realistic valuations for the assets. The sooner the fund is liquidated, the sooner the managers will be freed by constraints in the management of the banks.

Conclusion

The main point that I tried to make is that the mechanisms proposed up to now for pricing toxic assets ignore one important way in which asymmetric information problems may be dealt with, namely making the prices of the transactions contingent on the future values of the assets. No information can remain private forever. The value of the toxic assets will be revealed over time and we can set up mechanisms making payments contingent on the future values. My proposal is equivalent to making the wealth and future incomes of bank managers, the ones having the private information on the assets, contingent on the future values of the toxic assets. If, as it is often claimed, a strategy of ''buy and hold'' for these assets can produce very high returns at the current prices then the managers should have no problem accepting the scheme here proposed. On the other hand, if the managers oppose the proposal we will have obtained valuable information anyway: that their claims on the high value of the toxic assets are not to be trusted.