Sunday, 6 July 2008

Revisiting Continuous-time Finance (Part 2 of 2)

I don’t know what finance textbooks say about arbitrage these days; I haven’t read one in years. But in the 1980s and well into the 1990s, they had only one example of arbitrage: buying IBM at New York Stock Exchange for, say, $120 and simultaneously selling it in the Pacific Stock Exchange for $120.5 and thus pocketing 50 cents profit. Just like that!

To say that the example flew in the face of the reality and insulted the reader would be an understatement. But I understand why the nonsense stayed around for so long. To really analyze arbitrage, to even define it, one has to know the Theory of Speculative Capital.

Arbitrage is a category in finance. It means buying low and selling high simultaneously. Obviously, that cannot be done with the same commodity or security; that would entail an infinite supply of rich fools. An arbitrageur, rather, must buy (or go long) one position and simultaneously sell (short) an equivalent position.

Equivalent means the equality of certain aspects of two qualitatively different things. In geometry, for example, a circle and a square are said to be equivalent if they have equal areas.

What makes two securities or positions equivalent in finance is the equality of their cash flows, Modern Finance declared. The equivalent positions, furthermore – securities or portfolios with equal cash flows – must trade at the same price. If they did not, an arbitrageur could buy the cheaper position, sell the more expensive position and secure a riskless profit – riskless because the equivalent positions hedged one another and profit because the two positions had to eventually trade at the same price.

That is the Contingent Asset Argument, the boldest and most important theory of modern finance.

Under strict conditions, the reasoning behind CAA is valid. But emboldened by the success of the Black Scholes model, the cheerleader of Modern Finance espoused it with an in-your-face aggressiveness that turned the “argument” into the inevitability of a natural law. “Greed is good,” the memorable line of “risk arbitrageur” Ivan Boesky perfectly captured this belief and attitude.

The focus on the cash flow is the view of a deal maker. It is finance as understood by Brooklyn business brokers. From the get-go, then, the arrogant pioneers of Modern Finance were in fact mouthpieces of half-educated traders and businessmen. The theoretical poverty helped set the stage for the rise of speculative capital and, from there, the systemic crisis in finance that we are witnessing. That is why Continuous-Time Finance merits a revisit.

I have shown in Vols. 2 and 3 of Speculative Capital and then briefly in Credit Woes series how, in blindly following traders, Black, Scholes and Merton entirely misunderstood options. But the reach of CAA goes beyond option valuation and touches all parts of markets.

The equivalency of positions and the deviation of their difference from the “norm” is established through either CAA or statistical analysis. Both methods are utterly unsuitable for the business in hand. In these methods, we have before us the fundamental contradiction between an arbitrageur’s business and his tools of trade. His business is quantifying qualitative differences. His tools of trade are purely mathematical, void of any qualitative content. It is that incompatibility which brings him to the gallows. There would never be an arbitrage-related loss, much less systemic risk, if the relation between the markets were purely mathematical and could be determined as such.

Defining equivalent positions in terms of cash flows is an egregious oversimplification. I will show in Vol. 4 of Speculative Capital how two positions with equal cash flows could have different prices with the difference remaining and even widening because of the impact of various factors.

The empirical evidence refuting the synchronous movement of equivalent positions was there even in the early days. Here is a Wall Street Journal story from 1996.

A Morgan Stanley trader took a $25 million loss on a position in Office Depot Inc. convertible bonds … [The trader] tried to hedge the … bond position by selling short...a mix of Office Depot common stock and call options...Office Depot reported worse-than-expected … earnings, sending its common stock tumbling 23% the next day. The trouble was that the convertible bonds fell more than expected, amid mounting concerns about the company.
The equivalent positions going the opposite way, the hedges behaving badly, is the main theme of the current crisis that has resulted in over $300 billion in losses with no end in sight. The latest victim was Lehman that lost $2.8 in June. The firm’s CFO, before she was let go, blamed the loss on the “divergence between the cash and derivatives market” and “ineffective hedges”.

The saga continues.

That is where Modern Finance now stands, with its intellectual palaces exemplified by Continuous-time Finance in ruins. Having faded, the insubstantial pageant leaves a wreck behind.