Bubbles and Scale Invariance

In yesterday’s post I mentioned that bubbles were exponential, scale-invariant and self-similar, making it virtually impossible to time their collapse.

Let’s flesh out this assertion by looking at a particular market index.

For the first 17 years of its existence, this index had a mean of 100 and a standard deviation of 56. (Prices have been scaled to avoid easy recognition). That’s a pretty stable time series.

Then something happened. Over the next 8.5 years, the index went from a starting value of 200 (already near the upper end of its previous range) to a value of 700. What’s more, this rise took on exponential, maybe even super-exponential characteristics, as the graph below makes clear.


Would you sell? If you did, you’d be out of luck. Because over the next 25 months, the index went from 700 to 1100. Once again the rise looked exponential or better:


(Note that this graph has the same start date as the previous one, but different scales on each axis).

Would you sell? If you did, you’d be out of luck again. Because over the next 15 months the index went from 1100 to 1500, with the pace of expansion growing ever higher


(Once again, this graph has the same start date as the previous two, but different scales on each axis).

Now would you sell? How much further and faster can the market rise? The answer is, quite a bit. Over the next 5 months the index rocketed from 1500 to 2800. If you had sold the index at any of the previous junctures – and note that at each of those points, the graph looked convincingly bubbly – you would almost certainly have been carried out at a loss.

2800 was, in fact, the high; over the next 31 months the index dropped all the way back to 600. Here’s the full graph, with dates and true (unscaled) values.


I’ve marked the extrema of each of the previous graphs onto the composite graph, to demonstrate how scale-invariance works. Although zooming in on any sub-graph gives the impression that it’s an exponential curve about to pop, these curves just get lost in the main graph. It’s not easy to time bubbles.

Postscript: The index in question is of course the Nasdaq composite in the days of the dot-com expansion. Interestingly, Alan Greenspan warned about ‘irrational exuberance’ in December 2006, shortly after the first of the graphs above. Three years later he had changed his tune (‘capitulated’?) quite substantially.

Bubbles and the Rational Trader

A few weeks ago, Paul Krugman wrote a lengthy essay on the history of macroeconomic thought for the New York Times Magazine. His article prompted a flood of commentary both pro and con; I do not propose to add to this deluge.

I do however want to take issue with one particular assumption that runs through both the original article, and through many of the responses to it (from both left and right). This assumption has to do with the relationship between rationality and bubbles.

One group of economists argues that traders are rational and markets are efficient; hence bubbles (if they do arise) are likely to be short-lived and self-correcting. Since markets are largely self-regulating, the role of government is to intervene as little as possible¹.

Another group argues that traders are often irrational and markets are often inefficient; hence bubbles may last a long time before eventually (and painfully) bursting. Since markets cannot be trusted 100%, the role of government is to intervene whenever necessary.

Some members of the interventionist crowd go further: they take the (to them, self-evident) existence of bubbles as proof that traders are not rational.

Meanwhile, some members of the non-interventionist crowd invert this logic: they assume the rationality of traders to argue that bubbles cannot in fact exist (“the price is always right”).

Running through all these arguments is the assumption that rational traders will not foster bubbles; indeed, that they will trade against any bubbles that they encounter.

This assumption is wrong. Ask any experienced macro hand what he would do when confronted with an incipient or actual bubble, and the answer comes pat: ride the trend. Contribute to the bubble’s expansion, don’t counter it.

Why is it rational to ride bubbles?

The first reason is the simplest: it is exceedingly difficult – bordering on the impossible – to predict when a given bubble will burst. The canonical financial bubble follows an exponential growth path; such a path is scale-invariant and self-similar, hence there is no way to tell, just from looking at a chart, whether one is closer to its beginning or its end.

Second, the pattern of gains and losses during a bubble’s expansion and subsequent collapse is typically asymmetric. Expansions tend to play out over a scale of years, while collapses often occur within a matter of weeks or months. Expansions involve steady gains gradually accumulating (and eventually exponentiating), while collapses involve sudden massive drops and large amounts of wealth wiped out in very short time spans. From a portfolio point of view, the overall effect is a wash (as indeed it should be, given that bubbles, by definition, do not involve true wealth creation). Hence a portfolio should be agnostic towards bubbles.

But for an individual trader the incentives are quite different. Most professional traders make an annual performance-linked bonus if they’re successful, and face firing if they’re not. Clearly, for a trader it is better to bet on a continuing expansion (and be right 9 years out of 10) than it is to bet on a crash. The payoff matrix is straightforward:

When the crash comes (as eventually it must) the trader’s portfolio will lose far more money than it would have gained in the event of no crash, but the cost to the trader is no more severe than if he had bet against the bubble and been proven wrong.

It’s not just short-term risk-reward considerations that make bubbles more likely; there’s also a long-term selection effect at work. A trader who stays contrarian throughout an expansion is likely to be out of a job by the time the crash finally comes. Rational contrarians recognize that “you have to be in it to win it”; hence they swallow their skepticism and become (or act like) true believers. Bubbles thus tend to create their own boosters, while forcing out all the naysayers. This is selection at its most insidious.

Finally, consider the case of the prescient trader who stays in the game long enough to counter-trade the bubble just before it pops. Does he profit from his acuity? In many cases, the answer is no. Trader bonuses are paid out of firm-wide compensation pools; if the rest of the firm has lost money (and remember, the rest of the firm is full of herd-followers who were riding the bubble, for all the reasons detailed above) then our hypothetical trader would not get paid. One more reason not to counter-trade the bubble (or rather, not to counter-trade your colleagues, which is much the same thing).

Notice that these arguments depend to a large extent on endogenous or even circular reasoning. Bubbles grow exponentially because everyone rides them; but one reason why people ride bubbles is because the growth is exponential. Similarly, traders conform because they fear that contrarianism, even if successful, will go unrewarded; but one reason why contrarianism goes unrewarded is because all the traders are conformists².

This should be no surprise. The defining characteristic of a bubble is positive feedback. Without positive feedback, incipient divergences from ‘fundamental value’ will always be counter-traded, causing reversion to the mean. And what is endogeneity (or circularity) but a positive feedback loop? The triggers may be various and even insignificant, but once a bubble gets under way, it’s very hard to pop. And despite the conventional wisdom, no rational trader would even try.

Addendum: bubbles have many progenitors. This article focuses on the incentives governing one group thereof, namely professional traders. Not everyone has exactly the same payoff profile, or is exposed to exactly the same group dynamics, as traders. Nonetheless it turns out that analogous factors are at play for almost everyone concerned in inflating a bubble. I will return to this topic – how different actors face similar structures leading to similar outcomes – in future posts.

Footnotes:

# ¹ This view, incidentally, provided much of the intellectual ballast for the deregulation policy followed by the Greenspan-era Fed-Treasury-SEC.

# ² This applies to the specific case of multiple traders within a particular firm during a bubble. There are other situations in which being contrarian is profitable and also not inconsistent with trend-following; I will address such situations in future posts.

Implicit Regulatory Arbitrage: The Puts-Payers Trade

Yesterday’s post revealed how (and why) a large portion of the financial industry’s revenues came to depend on explicit regulatory arbitrage. This is fairly common knowledge, and should come as no surprise to industry observers.

What’s not so well known is that many ‘classic’ arbitrages, which appear at first glance to be regulation-independent, also depend implicitly on regulatory asymmetries to work. The textbook example is bond futures arbitrage. While anyone can buy bonds, some market participants are forbidden to sell bonds short. To express a bearish view, this latter group has to sell bond futures. This makes bond futures systematically cheap relative to cash bonds. Arbitrageurs have only to take the opposite side of this transaction to make easy money.

Of course, the classic bond futures arbitrage no longer exists (‘”too many eyeballs”), but other, subtler examples abound. Consider a trade that was very popular with fixed income arbitrageurs earlier this decade: the puts-payers combo. This trade involves selling Treasury puts and using the proceeds to buy payer swaptions, for zero net premium. Both the puts and the payers are struck slightly out of the money.

How does the trade work? If the market rallies or stays rangebound, the options expire worthless. But if the market sells off, the options are exercised, and the trader finds himself long Treasuries and paying fixed in swaps – in other words, long swap spreads. So, the trader is making the bet that ‘swap spreads will widen in a selloff’ – and he’s making this bet for free (remember, there’s zero net premium to enter this trade).

Is this a good bet to make? Let’s look at some history:


That’s a pretty strong relationship between two supposedly independent variables, and hints at some serious inefficiency in the bond market. What’s going on?

The answer is simple. Just as in the bond futures trade example described above, the arbitrageur in the puts-payers trade is taking the other side from entities who are forced by regulations to behave sub-optimally. In this case, these entities are the government sponsored agencies Fannie Mae and Freddie Mac.

Some background may be useful here. In the early years of this decade, Fannie Mae and Freddie Mac were massive players in the bond market. At the time, they had very large mortgage portfolios which were characterized by significant ‘negative convexity’. This characteristic meant that when the market rallied, they needed to buy; and when the market sold off, they needed to sell, in order to keep their portfolios properly hedged.

Now, Fannie and Freddie, being government agencies, faced restrictions on their size and trading activity. Consequently, they decided to do the bulk of their convexity hedging (described above) in swaps rather than in bonds, since swaps are off-balance sheet instruments, while bonds have to be reported. Every time the market sold off, Fannie and Freddie would be out there selling (paying) in swaps, in size. Swaps would therefore underperform bonds in selloffs; hence swap spreads would widen. (Note that the mortgage market is much larger than the government bond market; hence Fannie’s and Freddie’s trading actions, determined by the former, would invariably move prices in the latter.)

This pattern repeated for years and years: it was that rarest of beasts, a persistent and captureable anomaly in the market. Many arbitrageurs took advantage of this, via structures like the puts-payers combo.

Did these arbitrageurs generate alpha? Well, yes and no. Within the context of the bond market, the answer is yes: the agencies behaved sub-optimally, and thus transferred wealth to the arbs. But viewed at a larger scale, the answer is no: the agencies behaved rationally by paying the arbs to move their interest rate exposure off-balance-sheet. The arbs were therefore being compensated for a service they were providing; they were harvesting alternative beta rather than capturing alpha.

(This is just a particular case of the general truth that any alpha is merely a beta within a larger universe. In this case, bond-market alpha turns out to be service beta. I will return to this concept in future posts.)

Of course, even this persistent anomaly couldn’t last forever. The previous scatterplot shows data from April 2000 through March 2006; the following one shows data from April 2006 through August 2008 (Fannie and Freddie went into conservatorship in September 2008):


The inefficiency has all but disappeared. What happened?

The obvious answer is the correct one: over the years, Fannie and Freddie scaled back their interest rate trading activity considerably. Fannie Mae, for instance, shrank its mortgage portfolio (the “owned balance sheet”) from 917 billion in 2004 to 728 billion in 2007. Over roughly the same period, Fannie reduced its duration gap (a measure of the mismatch between assets and liabilities, and a strong proxy for the portfolio’s negative convexity) from over 1 year to less than 1 month, by buying swaptions and issuing callable debt. With a significantly smaller and better-hedged portfolio, Fannie simply didn’t have to trade that actively.

Obvious, yes, but only in hindsight. An arbitrageur who tried to play the puts-payers game after 2006 would not have made any money. Once the regulations changed (and make no mistake, Fannie and Freddie’s portfolio redesign owed a great deal to regulatory pressure), the regulatory arbitrage disappeared.

Why does any of this matter? The case study of Fannie Mae, Freddie Mac and the puts-payers trade highlights a theme that I will return to again and again on this blog: the importance of understanding the source of your returns. It’s not enough to spot an inefficiency (opportunity) in the market; you must also know why the inefficiency exists. Only then can you avoid being blindsided when circumstances change and the opportunity disappears.

Why Is Regulatory Arbitrage So Attractive?

When the histories of today’s very interesting times are finally written, I suspect that the phrase ‘regulatory arbitrage’ will feature prominently. One may point to the housing bubble or the bubble in finance as proximate causes; or to unsustainable global macro imbalances as a more distant cause. But the grease that lubricated the wheels of the runaway train was regulatory arbitrage.

Why was regulatory arbitrage so prevalent during the boom? There are several reasons.

First, regulatory arbitrage is easy. It’s certainly easier than trying to beat the market in ‘legitimate’ ways, as many retired traders can testify. What’s more, this state of affairs is likely to persist. Regulatory agencies in the USA are notoriously understaffed; their few workers are notoriously underpaid. Anyone competent enough to understand the complexities of modern financial instruments (which, incidentally, are often designed specifically to avoid or evade regulatory scrutiny) would waste little time in quitting and joining the very Wall Street firms he is supposed to be monitoring. Add in the phalanxes of lawyers and compliance officers whose job it is to ensure that the shenanigans stay on the right side of the letter of the law, and it’s an unequal battle. The investment banks will always win.

Perversely, this outcome is often reinforced by legislative action. Consider the practice of jurisdiction-shopping, wherein firms migrate their corporate entities to domiciles where the regulators are friendlier, or set up multiple entities in various jurisdictions such that key issues ‘fall through the cracks’. Confronted with this reality, the dominant response on the part of legislators has been to ease regulatory burdens, so as to stanch the corporate exodus. Unchecked, this merely leads to a race-to-the-bottom as countries compete to offer the most lax regimes. The long-term consequences of such a race can be devastating, as recent events make clear.

Second, regulatory arbitrage, unlike say interest rate arbitrage or index arbitrage or cross-border arbitrage, is true arbitrage: the arbitrageur takes no market risk at all. In all other real-world arbitrages, the arbitrageur takes some sort of liquidity or timing or event risk. Even if the final outcome is a guaranteed profit, there may be some path along which the arbitrageur goes bankrupt before he can realize that profit. This is not the case with a ‘pure’ regulatory arbitrage.

It gets even better: the diminished market risk means that the arbitrageur can take much larger positions, and presumably make much larger profits. (Consider the case of SIVs designed to stockpile risky assets off bank balance-sheets. If the assets do well, the bankers get paid. If the assets do badly, well, nothing happens – they weren’t on the bank’s balance sheet, so who cares?) Regulatory arbitrage is thus not only easier than other forms or arbitrage, it is also more lucrative.

But what about non-market risk? Clearly, if regulatory arbitrage is sufficiently widespread, the system as a whole can come crashing down. (Think of the role played by credit ratings abuse in inflating the housing bubble.) Unfortunately, risks to ‘the system as a whole’ are not borne by individual bankers. This brings us to our third contributory factor: incentives. Thanks to the quarterly-earnings / annual-bonus culture on Wall Street, practitioners have almost no incentive to play for the long term. Indeed, anyone who chooses to do so would be quickly forced out or passed over in favor of his more aggressive colleagues. Poorly-structured incentive schemes reinforce the attractiveness of regulatory arbitrage, and ensure that traders will take full advantage of any loopholes they can find.

Will things change? It’s unlikely. The talent mismatch between regulators and Wall Street is not going to diminish. Nor are traders going to be held accountable for non-market risks; indeed, if anything the bailouts have firmed the Street’s expectation that systemic risks will always be backstopped by the government (moral hazard, anyone?). And regulatory arbitrage will continue to be easier as well as more lucrative than other forms of speculation.

The only way to prevent regulator arbitrage is to eliminate the incentive structures that support it. But even if the government took advantage of its post-bailout leverage to impose drastic salary caps or other behavioral restrictions (a scenario improbable in the extreme, given the current condition of de facto state capture), bankers would simply work their way around them. The example of Barclays makes this eminently clear:

Two former Barclays execs are starting a fund called Protium Finance. Protium has two equity investors who are putting in $450 million. Barclays is lending Protium $12.6 billion. Protium is using the cash to buy $12.3 billion in what we used to call toxic assets from Barclays. Protium’s 45 staff members get a management fee of $40 million per year.

Although Barclays is recognizing its exposure to Protium, Protium is a different company, and it’s not a bank. That’s important these days, and this is Tett’s main point. In particular, because it’s not a bank, British regulators can’t do anything to it. In particular, they can’t prevent Protium from paying its managers whatever they want to pay it, and they probably can’t force Protium to even tell them what its managers are making.

So here we have the ultimate form of regulatory arbitrage. If you’re a bank exec worried about public exposure or, even worse, regulation of your compensation, go create a new special-purpose vehicle to manage bank assets, entice the equity investors in with a sweetheart deal, and pay yourself whatever you want.

Brilliant, devious, lucrative, and almost impossible to police. That, I’m afraid, is regulatory arbitrage in a nutshell.

Introduction: About Myself

This may have been true in the early days of the web, but these days people are smarter and more cynical. These days, people assume that you’re a dog unless you can prove otherwise. Much as I would like the ideas on this blog to stand on their own, I fear I will have to provide some shamelessly self-promotional biographical detail. So, a few words about myself:

I joined a hedge fund at the age of 21. By 23 I was a junior trader; by 25 I had my own portfolio; by 27 I was a millionaire; and by 30 I had retired. I closed out the last of my positions on my 30th birthday and walked away with my winnings intact. A large chunk of my success can be put down to simply being in the right place at the right time, but I like to think that skill played a small part too.

This was a few years ago. Since then, I have traveled the world, played a great deal of tennis, and become a father. I still follow the markets constantly, partly so that I can invest my own money productively, but mostly because I’m addicted. To keep myself busy, I write this and two other blogs; I run managed accounts for a few close friends and family; I consult for a variety of industry players; and I’m a principal at a small private-equity fund.

And about my professional expertise:

I cut my teeth in fixed income arbitrage, a field in which I consider myself an expert. I have traded relative value as well as directionally, in rates, currencies and commodities, and I think I am reasonably competent at all of these. My specialty is the design and analysis of quantitative trading strategies, with a strong minor in global macro and thematic investing.

I am not an equity trader and claim no expertise in stock-picking.

Of course, gentle reader, you have no way to tell that the above prose was not, in fact, written by a dog.

Introduction: The Meta Finance Blog

Welcome to the Meta Finance Blog. As the name suggests, this is a blog about what lies beneath the edifice of modern finance. In this blog, instead of addressing the what and how, or even the when and how much, I will focus on the why of financial markets.

The bedrock of any study of finance has to be individual transactions (‘trades’), which suggests the first ‘why’:

Why are certain traders / trades / trading styles more successful than others?

Under this heading I will talk about competing trading philosophies; the design and analysis of trading strategies; various sources of trading returns; the concept of premium capture (especially risk premium); the measurement of trading performance; arbitrage, its implications and its limitations; modeling and meta-modeling; market-making and price-taking; risk management schemes; and so on.

Of course, traders don’t operate in a vacuum; they are typically funded by (and hence beholden to) institutions. This brings us to the second ‘why’:

Why do institutions look the way they do?

Under this heading I will talk about institutional structures and how they have evolved; Red-Queen patterns and races to the bottom; principal-agent issues; incentive schemes and their consequences; regulatory and jurisdictional arbitrage; politics and voting models; and so on.

I will also talk a great deal about institutional relationships: the relationships between Wall Street and Main Street; between regulators and the regulated; between investors and asset managers; between price-takers and market-makers; and so on.

The complex interactions between various institutions (mediated by individual traders, risk managers, brokers, regulators, investors and others) give rise to the glorious mess that we call the market. So, our third ‘why’:

Why do markets behave the way they do?

Under this heading I will talk about the efficient markets hypothesis and its many subtleties; game theory; expectations; positive and negative feedback; stable and unstable equilibria; regime changes and structural breaks; correlations, distributions and extreme events; and so on.

I will also have plenty to say about behavioral finance; the limits of rationality; and the importance of incentives and psychology in determining market behavior.

Markets are the barometer of the economy, hence our fourth ‘why’:

Why do economies behave the way they do?

Under this heading I will talk mainly about the interplay of micro and macro economics: specifically, the micro foundations of macro moves, and the macro currents driving micro behavior. As above, questions of incentives and psychology will dominate.

I will also discuss, but only in passing, some of the usual macro suspects: growth, inflation and unemployment; exchange and interest rates; monetary and fiscal policy; Keynesian, neoclassical and monetarist models; stickiness, rational expectations, time-consistency; positive and negative shocks; and so on.

This introductory post would not be complete without one last ‘why’:

Why are you writing this blog?

I find markets endlessly fascinating. Unfortunately, I cannot say the same for the vast majority of market commentary. Much of the analysis I encounter tends to be superficial, ephemeral or just plain uninteresting; this is because most analysis concerns itself with mere details, without investigating the ‘deep structure’ underlying financial markets. It is this deep structure that dictates why those details should be the way they are, and it is this deep structure that I propose to investigate in this blog.

Happy Reading!