1000 Alitalia in one shot: so' forti 'sti Amerikani .... (II)

I apologize for being so verbose, but while writing I am trying to also clear my mind of its many confusions. Because nFA is a blog read by many people, I am also trying to make the argument at least partially understandable to readers not trained in formal economic theory. A machine translation into the Italian language is available (click the flag), which I hope to turn into readable, instead of laughable, Italian tomorrow.

Back to Earth

I ended the first part with a puzzle that seemed unsolvable. This was just to make sure I could keep your attention, because things are not nearly as bad as I made them appear; at least they are not nearly as bad when financial markets function "properly" and "normally". Here's why. As Filippo noted, the notional amounts are seldom if ever paid: they are used only to calculate the actual payments taking place between the two counterparts. Consider the case of a simple interest rate swap on a notional amount of $100 million. Neither party expects to ever have to pay $100 million to the other; instead A will pay to B the difference (0.7%, say) between the fixed and the floating rate in the reference period, time $100 million, that is $700K, which is a lot less than the notional. Also, many derivatives often expire without any payment or only a few payments taking place, other are balanced by the issuing of similar derivatives with the opposite sign, and so on. Further, for derivatives traded in organized markets (e.g. futures) on top of the fact that at settlement one must pay only the net loss (receive the net gain), the organized exchanges ask for margin deposits that are proportional to the open positions and force their closure whenever those margins cannot be reasonably met. In other words, I wanted to scare my readers a bit ... to drive home a point that Warren Buffet has repeated a number of times and to which everyone, including financial economists, have paid little attention.

The OTC derivatives market allows for the establishment of contractual obligations between financial institutions that may be impossible to satisfy, even in principle. In particular, OTC derivatives allow for the creation of a "pyramid" of financial promises that cannot possibly be satisfied because the amount to be paid, in certain states of the world, is larger than the value of total world wealth in those same states of the world. Call this point 1.

In models where individual portfolios are fully observable, beliefs over future states of the world are common (or, at least, they have a common support) and markets are dynamically complete, the situation conjectured in point 1 is impossible. This is because either B, before beginning to tango, will be able to correctly assess A's creditworthiness in all future states of the world and make sure it holds enough net real assets to back its promises to pay, or the rising costs that A faces in financing its portfolio positions will force it to diversify away its risk until the previous condition is in fact met, i.e. A has enough real equities to pay for its derivative commitments in case those come due and X (i.e. shit, for those that just tuned in) happens. Because economic theorists studying financial markets almost always assume these conditions to be satisfied, the fear that point 1 raises in the layman was not shared, until now, by financial economists.

Which begs the next question: along which dimensions did actual US financial markets violate the assumptions above? How about "all, and then some"? While I believe that "some" is the key, let me go through "all" first.

Earth is, indeed, different from the standard model

We teach that financial markets serve two purposes. They allow society to transfer resources from those who did the saving to those that would like to do the investing, which is good. We also teach that financial markets arrange transactions shifting the bearing of risks from those who do not want them to those who want them, in exchange for a fee. The latter function is considered of the utmost importance by financial economists, who spend a large amount of time showing how risk-bearing is reduced as financial markets become more "complete" - i.e. more independent securities are created; derivatives have been shown to be able to play a key role in this beneficial process - and economic allocations more efficient, in the sense of Pareto. An important caveat here is that we assume that there are two kinds of risks: the individual or diversifiable one (I gain, you lose) and the aggregate or undiversifiable one (we lose, or gain, together). While financial markets are magically capable of "dissolving" the first kind of risk, they cannot do the same for the second. The second is just shifted from one person to another in exchange for a fee, but the grand total remains constant independently of how many fancy securities there are out there. Let's keep this in mind.

We never teach that financial markets can be used to take bets, but this is what the second function implies. If A transfers some aggregate risk to B, then A may believe to be safer because B is now bearing its burden. But this is not really true unless B is capable, and willing, to cover the risk by means of actual equities, should the downside event take place. Hence, as before in point 1, risk-shifting is bounded by the total amount of resources available at any given point in time and, specifically, is bounded by the amount of actual equities the seller of insurance owns relative to the insurance it promised through derivative contracts. If you think of it this way, the whole thing becomes quite obvious, no? That's why, traditionally, we (i.e. the regulators and independent overseers that are supposed to act on behalf of citizens) make sure that insurance companies own lots of big and fancy buildings, good land, safe stock, oil fields, and so on ... pretty much like AIG did, right? Let us keep also this in mind.

Now, let me go back to my old example of A, B, C, etc. and make it a bit closer to what we are talking about. In the updated story B is a bank, holding a mortgage of $100 on a house with a market value of $111. B may have purchased that mortgage from someone else, which originated that mortgage by assessing incorrectly the risk that the borrower may default ... or which may have made a small - and for sure unintentional - mistake when typing in the income of the borrower in the loan application form (say, $70 instead of $50, which makes a big difference for the implied probability of defaulting ...). This does not matter at this point: clearly LOTS of things like these happened in the US mortgage market between 2000 and 2006, but our focus here is on the continuation. Hence, B values the mortgage at $100 on the asset side of its books, posting $100 in own capital on the other side, and nothing else. The banker running B feels there is a 50% probability that the borrower will default, in which case, via the foreclosure process, it would end up receiving only $50. B does not like to hold this risk, as it means that its net capital is really only $75 (i.e. $100 - 50x0.5), while the shareholders will approve the banker's hefty bonus of $15 only if net capital is at least $90. Hence B goes to A and buys insurance, say in the form of a CDS, promising to pay $90 no matter what in exchange for the proceedings from the mortgage. You may ask if A is stupid or something, and the short answer is "no". Clearly, something is happening here that is creating a profit, for B, of $15 out of thin air: the mortgage has an expected value of $75, so why should A promise B $90 for sure? There are various explanations for this, all of which I believe apply to the US 2000-2008. Here they are:

1. A assigns only a probability of 20% to the default event. People make random mistakes, we assume, so there are equally as many As assigning a probability of 80% to the default event. But these two groups do not cancel out because the first will sell insurance whereas the second will do nothing. Think of this kind of As as comprising all the "dumb/unlucky guys" that are always around financial markets but become particularly frequent when the market is bully.

2. B intentionally packages the mortgage in some "vehicle" that is confusing enough to lead A to believe it is better than it is. Indeed, this is what private information means, in this world! Think of these As as those guys that said "oops, we did not know what we had purchased", like UBS or SG.

3. A's own capital is only $4, which it will not mind losing should the default occur: 10/2 -4/2 = 3, which means a positive expected profits. Assume A is an investment bank, or an insurer, and pick your name among the now famous ones.

4. A is "betting" by taking up risk that cannot be diversified because it goes always the same way. For example, it may be purchasing very many of these mortgages (at a price of $90) by borrowing on the money market or issuing bonds. A (or should I call it F&F?) pays very low interest rates because markets perceive the Federal Government is backing A's liabilities.

5. The interbank market is flooded with liquidity at a very low nominal rate, say 1.5%. A cannot find any liquid security paying a decent return, while these deals on mortgages are liquid and seem to be paying a hefty return as long as the borrowers do not default. Call A Countriwide.

6. There is another character, called A', from which A plans to buy insurance against the risk of losing $40 in case of default. The character called A' satisfies one or more of the characteristics 1.-5. and charges $8 for this.

7. Repeat 6. as many times as you please, because the OTC derivatives market, which is neither regulated nor centrally organized, allows you to do so. All you need is that S&P, Moodys and friends keep saying you are a great credit. You pay their fees, so chances are they will.

Let me take home my second point.

Actual financial markets are much more imperfect than our theoretical models, whose crucial assumptions are often violated. This is well known, and things have always been like this, hence per se this is not big deal. What the existence of an unregulated OTC derivatives market plagued by private information allows is to leverage these common "frictions" dozens of time, creating, under the appropriate circumstances, a snowball that is, indeed quite big. Call this point 2.

All assumptions are violated, and then some

Let me conclude for today with the "some" that, in my opinion, happens to be the crucial one. That is: if point 3, coming next, had not been true the fact that points 1 and 2 were would have created some problems, but not the disaster we are apparently facing. It would have been, in other words, business as usual on Wall Street.

The key thing is that the probability of default on nominal loans with variable rates (and mortgages are nominal loans with, in recent years, very variable rates) is endogenous. It depends, first and foremost, on the nominal interest rate applied to the loan, which, in turn, depends on the nominal interest rate clearing the short term interbank markets that, in turn, is controlled by the Federal Funds rate. When those rates are low the rates on mortgages are low and liquidity is abundant: very many mortgages are issued and, if one has reasons to believe that the short term rates will stay low for quite a while, it is reasonable to expect the default rates will remain low. When those nominal rates increase, and nominal incomes do not increase likewise, the probability of default on those mortgages increases. This is what happened in the US during the 2001-2007 period due to the Federal Reserve "countercyclical" monetary policy.

Now, this is pretty normal and if those mortgages were held by the banks that had issued them and the latter had not yet "taken profits" on those mortgages, they would have set aside capital reserves to cover those losses. This is what is currently happening in Spain that has also seen a gigantic (in fact, proportionally much bigger than the US one) real estate boom (1997-2006) followed by a bust in the last two years. In Spain default rates on mortgages have tripled and interest rates have increased but, because (a) most mortgages are held by the banks that issued them, and neither (b) have been heavily securitized through derivatives nor, (c) have the "nominal profits" on those derivatives been cashed-in (either in the form of dividends or gigantic bonuses to the investment bankers) the financial system is very far from coming apart. In fact, it posted record profits even during the first semester of 2008, which I find rather surprising. In other words, for reasons that should by now be clear, the "nominal profits from derivatives issuing and trading" were not "taken" but set aside till the end of the life of the underlying mortgages. The opposite happened in the US.

What happened in the US, then? Simple: a derivative is a contract that involves a sequence of payments over a period of time. If you make real profits or not from a given derivative contract can be decided only once the derivative expires and the whole sequence of implied payments has been settled. But the current functioning of the OTC derivative market allows something different to happen. Using our simple example, here's the story. A mortgage is issued that, at current nominal rates, has a low probability of default. Insuring it is cheap and, by securitizing it, profits can be taken right away as the financing of the security is obtained at low nominal rates, insurance is cheap and the mortgage is off our hands in three days. This is quite fine, if the probability of default on that mortgage does not change due to altered (by the Fed's actions) conditions in the borrowing and lending markets. Should conditions remain constant, those initial profits would correspond to actual profits also at expiration. But in the meanwhile interest rates increase and default rates raise accordingly. This means that the derivative security linked to the underlying mortgage is actually loosing value and its prices should drop. But you have it in the book for 100 and writing it down to 80 is a problem, so for a while you borrow on the money market to finance the payments that, for example, the CDS you signed on forces you to. The opacity of the OTC markets allows you to do so, maybe by entering in even more derivative contracts. This goes on as long as you appear to be credit worthy to the counterparts, which is not forever. In the meanwhile pseudo profits are made, dividends are paid (these are peanuts) and bonuses are also paid to you (these are not peanuts). From the point of view of the theory this is money that should "stay in" (in the form of capital reserves of the investment bank or the insurer underwriting the CDS) to cover (via its capitalization at risk-adjusted market rates) for possible future losses. But this is not what happened: the capital reserves to cover future losses did not "stay in", they went out to the mansion in the Hamptons. Call this point 3.

When shit hits the fan, oops X happens, you have no capital reserves, hence you are not credit worthy, hence no one lend to you and you are maybe insolvent and certainly illiquid. Hence you go the way of Bear Sterns or Lehman Brothers ...

To quote, with a small [alteration], Robert Solow:

[...] the hedge-fund operators [read: investment bankers] and others [fill in the name of your preferred banker] may earn perfectly enormous incomes. (Margaret Blair of the Brookings Institution was one of the first to point this out.) If they are clever enough, and they are, they can arrange their compensation packages so that they batten on profits and are shielded from losses.

This is because, in the actual financial environment of USA 2001-2008, (pseudo) profits from derivatives came earlier - when interest rates were low, hence expected default rates were low - and (very real) losses came later - when interest rates increased, hence actual default rates also did - and had to be absorbed by the little capital left in the firm, which was not enough. The actual capital reserves had been taken out by calling them "profits". This is point 3 again, only shortened.

Because it is late, I hope it is now clear why it took the convergence of all three contingencies, summarized as points 1, 2 and 3, for this disaster to happen. Any two of them without the third would have not, I believe, caused the big mess we are currently into.

In this sense this is an "exceptional event", and it needs not imply the "end of capitalism". But, in an another sense, it is and was a perfectly predictable event: various people wiser than myself (e.g. Mr. Warren Buffett) had pretty much predicted it a few years back. We, the academic economists, were blind to the facts and did not see it happening because we assumed the deviations of reality from our "standard model" to be quantitatively small. We were mostly wrong, and a few wiser people were right. More than anything, though, I believe we did not see that the particular nature of derivative contracts (their being "zero sum games, if no one cheats") together with the private information that plagues the OTC derivative markets allowed for gigantic (pseudo) profits-taking of funds that were, according to the theory and should have been in fact, capital reserves that had to be "left in the firm" to serve until the life of the derivative contract. But derivative contracts, these misterious zero net supply securities, allow for redistributing wealth from B to A at points in time that preceed their expiration, and redistributing to oneself very large sums of money (in a perfectly "legal" way) is a temptation no one can easily resist. Investment bankers may not be wizards, as they often portray themselves, but they are certainly humans.

Quite correctly bygones are bygones and, in the unlikely event this analysis will be found convincing, it still does not tell us what to do NOW given the current circumstances. In particular, should we go the way that Bernanke and Paulson are pushing us to go? Is there another and better way? I am not sure, but I believe a narrow but clear other way can be found on the basis of this analysis and similar ones developed by other. To the issue of "WHAT TO DO NOW" I hope to turn soon in the third part of these thoughts.