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Infinite Liquidity,
Infinite Capital,
Infinite Jest


Ross M. Miller
Miller Risk Advisors
June 28, 2004

Alas and alack, astronomical summer is here. With each day that the black swan or raven fails to come a-tapping at my chamber door, the market trends lazily upward and the VIX trends lazily downward. Even the occasional videotaped beheading serves only to reinforce this trend, making the misdeeds on the allied troops appear little more than a frat hazing gone awry.

Still, it warms my heart to see the VIX trading in its own futures market. Who could have ever imagined that the numerical solution to a nontrivial partial differential equation would become a marketable commodity? Whatever will they think of next?

To my second question, I proffer a general suggestion; however, I must insist on keeping the details to myself.

It's summer. Think of ice cream. Think of ice cream melting down the side of a sugar cone. Think LIX. Liquidity index. Now hold that thought while I take you on a journey.

Somewhere there is a world of infinite liquidity and infinite capital at fixed interest rates. Need to sell some stock? Need to sell all the stock on the world's exchanges? It's done. In a flash. Don't worry about the market impact. The bid always equals the ask. For a hundred shares. For a billion shares. It makes no difference. And no more margin calls, all the capital in the universe is available at one low fixed rate. And not just while supply lasts, because supply is infinite. What a deal!

(The squeamish should skip this paragraph. It is not necessary for supply and demand to be infinite in a strict sense in order for theories that assume perfectly competitive markets to work. It is sufficient that individual supply and demand, though nonzero, be infinitesimally small, where "infinitesimal" is a mathematical term with a precise definition that no real-world object satisfies.)

Where is this world? In the finance textbooks, of course. It was there when I picked up the first edition of Brealey and Myers hot off the presses and it's still there today. CAPM, APT, Black-Scholes-Merton, NPV, you name it--all of them only work as advertised in this wondrous fantasy land.

Do the names Scholes and Merton ring a bell? Of course, they do. The hedge fund they were partners in, Long-Term Capital Management (LTCM), died on the cross of infinite liquidity and infinite capital. Guess what? Both liquidity and capital are, indeed, finite. That means, according to basic economics, that both of them should have a nonzero price.

In the case of capital, it turns out that it really was finite all along only there was so much of it around that any demand that one of us might make on the capital market would seem small by comparison. That is, unless we were LTCM.

Liquidity is different, though. All the textbook theories (though not some newer theories that will require a new generation of textbook writers to explain properly) assume that price is what mathematicians refer to as a well-defined number, preferably rational. When I ask the question "What is the price of GE?" the textbooks implicitly do not accept "It depends," "Are you buying or selling?" or "What do you mean by 'price'?" as acceptable answers. They live in a world where the answer is something like $31.23 per share and that applies to one share and one billion shares equally.

I remember reading soon after the LTCM collapse that Myron Scholes pithily explained the fund's predicament as being "long liquidity." I don't know if Myron then went on to conclude the obvious, which was that LTCM needed to hedge its position with a contract that would be short liquidity. That's where LIX, the liquidity index, comes in.

Just like bond prices and interest rates, LIX moves in inverse proportion to the amount of liquidity in the market. In the oh-so-pleasant dream world of infinite liquidity, liquidity has an implicit price of 0, and so the LIX is 0. The less liquidity there is the benchmark market, the higher LIX goes. During the Russian debt-induced crisis of 1998, LIX would have gone sky-high and if it had existed back then and had LTCM held LIX in sufficient quantity to hedge its long liquidity position, everything would have been hunky-dory.

Please note that while CNBC, the Wall Street Journal, and the rest of the financial press have some unnatural fascination with the notion of Alan Greenspan "pumping up liquidity" as measured by M1, M2, M3, or Mwhatever, that is not what I am writing about here, at least not directly. The "true" LIX indicates the ease with which one can buy or sell a suitably chosen portfolio of securities in volume. More problems mean a higher LIX.

There are some technical issues involved in how one would construct LIX, but the details are left, as the textbooks say, as an exercise for the reader. There is also a peculiar paradox involving the LIX, but then it is hard to find a financial theory that is not, when inspected closely enough, paradoxical if not outright self-contradictory.

If you haven't figured it out already, everything written about in these commentaries on in the past few weeks is linked in some way to what is going on at, where Chapter 6, with the alluring title of "Foreplay," is being posted simultaneously with this commentary.

Looking ahead, I am celebrating my personal independence by not writing an Independence Day commentary, though new chapters of Rigged will continue to roll out every Monday and Thursday at the sibling site. The following Monday, July 12, if I still have the nerve and if the markets do nothing worthy of my attention, I will begin a multi-part series describing real life (or, better yet, my view of it) on Wall Street during the summers of 1971 and 1972--a golden age of liberated women and regulated commissions. You can judge whether truth is stranger than fiction.

Copyright 2004 by Miller Risk Advisors. Permission granted to forward by electronic means and to excerpt or broadcast 250 words or less provided a citation is made to