(Dis)continuous Time Finance

I grew up in a time when markets were considered to be "continuous." Portfolio insurance. Robert Merton's 1987 treatise Continuous-Time Finance. Liquidity was presumed to be available. And while markets could and did gap due to an event, new information, etc., it could and would clear with transactions taking place at the new level. The financial markets, through price discovery in the presence of liquidity, conveyed valuable information that could be used for both security selection and asset allocation. The field of financial economics, as such, was predicated upon the existence of bids and offers and, therefore, liquidity. And this phenomenon was assumed to persist across time. 

But this is not the world I observe today; quite the contrary. Price movements are not only discontinuous, but the notion of liquidity across time as traditionally assumed simply does not exist. Something has happened to rock the prevailing academic paradigm. Have the experiences of the past six months essentially blown a hole through the heart of modern financial theory?

This line of thought was spurred by my friend and mentor Bill Janeway. He is working on a project with colleagues at Cambridge that delve deeply into the issue I am going to tangentially speak of. I personally can't wait for their study to be released. But in the meantime, consider what Merton said back in 1957 as it relates to capital markets:

The conscious motivation for creating a capital market is to provide the means for financial transactions. However, an objective consequence of this action is to produce a flow of information that is essential for all agents' decision-making, including that of those agents who only rarely transact in the market.

You see, the problem is that without transactions it is hard to get information, and without information it is hard for people to transact. We are caught in this Catch-22, the Fed's prescription for which is injecting hundreds of billions of dollars into the financial system. And while this creates money, it does not necessarily create liquidity in the instruments for which no bids are available. Why? Because potential investors are sorely lacking information, either intrinsic to the securities or extrinsic in the form of observable market prices. This is partly due to the complexity of the instruments in question, the structured asset-backed market and related derivatives. And while this problem is not intractable, it is easy to imagine that getting sufficient information to make educated bids will take quite some time.

Another problem is that an element of liquidity was predicated upon the faith and belief in the ratings system. A AAA-rated security was available for purchase by trillions of investment dollars, AA-rated fewer trillions, A-rated hundreds of billions, and so on. But now that we've seen tens of billions of AAA-rated securities marked like junk, the very foundations of the institutional investment model have been shaken. Trust has been shattered. No trust, no liquidity. This partly explains the strength of the rally in U.S. Treasuries, even in the face of a sharply declining dollar. Most investors aren't looking to a rating agency for comfort that the U.S. Treasury will make good (no chuckles, please), ergo, the trust issue is moot and liquidity in Treasuries is plentiful. But we can't and don't live in a riskless world. The problem is that too many investors and market intermediaries thought we did. This was telegraphed by the historically low levels of volatility during the latter part of 2006 and into early 2007.

Today we live in a world fraught with risks that we barely understand, risks that modern financial theory doesn't have great answers for. A new model is needed that incorporates the effects of discontinuity as an outgrowth of, among other things:

• Complexity - structured securities, derivative instruments;

• Interdependency - widely disseminated holdings that can pollute portfolios globally, hundreds of trillions in counterparty exposures;

• Intermediary errors  - ratings that don't reflect the risks, financial institutions with weak control environments and poor risk management practices; and

• Bad actors - originators, underwriters, traders and managers with mis-aligned motives.

We have seen examples of each of these in the past six months, seeming "black swans" that don't appear so unusual any more. It's not that these risks didn't exist before. It is that their confluence when experienced over a short period of time yielded results that were unforeseen to many. Our models and academic frameworks needs to be robust enough to handle these occurrences and to provide a model for maintaining liquidity, price discovery and information dissemination. Based upon today's market action we've got a long way to go.

Comments

[Bernard]

The big systemic problem is that financial intermediaries have combined three elements together:

1) High leverage
2) Duration mismatch of liabilities and assets
3) Illiquid assets

These are the three ingredients for a crash.

Maybe this is a stupid rhetorical question, but why are financial intermediaries even allowed by law to mismatch the duration of liabilities and assets? Intermediaries are incurring duration risk in order to make more profit (putting their very solvency at risk). This is seems to be "accepted business practice", but I just don't see why this should be allowed at all.

[Morgy]

Roger.. always nice to cruise to your blog every now and again and catch up on your insightful posts. It has always amazed me that given the collective wisdom of Wall Street & the money they pay to smart people, why does this happen so often whereby they get caught with their pants down. I would have thought a market cycle chart would be positioned on everyones desk, if not then at least the board or managing group would understand that at some point the down cycle will come and it almost always comes to the new "gee whizz, this time its different" money making products, the same as it it does for your average consumer product introduction. Yet time and time again we see the smart guys caught like this. Is the thinking on Wall Street just such absolute greed that they don't care if it will take them down?. I am interested if you would kindly comment on this aspect.

[victor s]

Thanks for an interesting blog.

I am sorry to say, that what is happening now is not contradicting modern financial economics, everything that has always happened in markets, has contradicted modern financial economics.

Volatility and jumps always cluster, the last couple of years have just been low vol, but things have been different (going back 10, 15, 20, … , 2000 years).

People in trading environments going way back, before monetary standards, in barter societies, have time and time again reported the problems surrounding mistrust and fear, the problem that arises when liquidity dries up and there's no information to be found in prices.

All of us are very dependent that there remains confidence, a driving force in liquidity.

Cheers,

V

[Roger]

Bill, I don't think so. My thesis (read my last paragraph) is not that the risks didn't exist, but there have been some structural changes in the way risk is manufactured and managed that has upped the ante and made the markets increasingly discontinuous. This I do believe, and it certainly didn't happen in six months. It happened over 30 years. Believe me, I understand recency bias and all the other pitfalls. As always, thanks for commenting.

[Paul Denlinger]

My gut tells me that we are heading to a new world where there are islands of information, and deals are done among small groups who know and, to some extent, trust each other. This is because the system of openness which was supposed to be introduced thru globalization really has not been able to deliver the goods, so things just break up and fragment along the older traditional lines which really have not entirely gone away.

In this respect, the 21st century will appear a lot like the 18th and 19th centuries, with the rise of the nation states, the growing gap between rich and poor and haves and have-nots. Eventually this will lead to another shot at globalization. Hopefully future generations will get it right the second time.

I found the book Making Globalization Work by Joseph Stiglitz very helpful in understanding the present problems with globalization, and particularly where US administrations, by placing the interests of large corporate donors first, have largely failed the promise of globalization for Americans and everybody else.

[Bill aka NO DooDahs!]

I think your perspective is skewed.

The markets never were continuous. It's not that the last six months blew a hole in the theory, the theory was flawed to begin with.

Black Swans (and Golden Swans, extremely positive return events) aren't happening any more frequently in this decade than they did in previous decades. They cluster; we're in a cluster; there's a recency bias in us that makes us think previous travails weren't as bad as we thought they were when they were happening, and it's hard for most of us to look at historical data and "feel" it the way we would if THEN were NOW.