Saturday, November 13, 2010

More on Bachelier, from a wise heretic...

Benoit Mandelbrot, who passed away recently, liked to call himself an indepedent man and most likely he was. Creating a new branch of mathematics called fractal geometry and applying it to a variety of fields was Mandelbrot's tour de force. He is said to move orthagonally -- at right angles to every fashion. To him, a stock exchange was a black box, a system at once complex, variegated, and elusive -- to be studied with conceptual and mathematical tools that build upon physics. Starting 1960s, this approach ushered in a scientific way to approach markets.

Yet, he has made some important observations regarding the recent financial crisis. His main criticism is the assumption that share price movements are continuous and random where the probability of the next move being up or down is 50:50, the same as if you were tossing a coin.

In this ‘random walk’ extreme moves, equivalent of, say, a hundred sequential coin-tosses with the same result are so rare, they should never happen.

Mandelbrot, the mathematician who invented fractal geometry and applied it to finance, was self-taught and, perhaps, less inclined to follow convention. He recognised prices jump around all over the place. Sometimes wildly varying prices cluster around huge spikes.

Although he developed more convincing models than the random walk, Mandelbrot’s work, like Bachelier’s, was ignored. Perhaps it is ahead of its time. The architects of modern finance building on the random walk had developed mathematical tools to help construct portfolios and manage risk. Mandelbrot’s models:

… promised a great amount of work, and trouble, and effort.

He says,

And the other offered capital on which one could live for a while.

For the random walk to be an accurate representation of the stockmarket its proponents needed to explain why an investor can’t profit from new information, a company’s results say. If analysing financial information can lead to superior insights about future prices, then prices aren’t random, they’re predictable, at least to a degree.

Enter the Efficient Markets Hypothesis, proposed by Eugene Fama, a kind of umbrella of assumptions underlying modern finance theory. The EMH (which also stands for Emergency Medical Hologram in Star Trek, judge for yourself which is more plausible) proposes that prices adjust so quickly to new information that investors simply don’t have time to profit from it.

The hypothesis assumes that investors all have the same motivation, to buy assets for less than they are worth, and that they make judgements almost instantaneously. As soon as new information reveals a share is cheap, investors buy it and the price rises to a realistic level.

In fact, a long history of financial manias and panics demonstrates investors often loose sight of value, and there’s plenty of evidence that prices don’t adjust instantly to news. ‘Value shares’, where the price is low in relation to an accounting measure like book value, earnings, or cash flow, do better than the stockmarket average, which shows investors who take the time to evaluate companies can profit from that information.

These days, the EMH seems to be going out of fashion and investors’ attitudes are more likely to be defined by the degree to which they think the market is inefficient, and how much effort they are prepared to put into finding investments that are cheaper, or more expensive, than they think the investments are truly worth.

The financial pages and journals buzz with insight as to why such ‘anomalies’ exist. I think some of the best fall under the heading of ‘feedback’. The simplest example of feedback comes from behavioural finance and shows investors are seduced by rising prices into buying more shares (or properties, or collateralised debt obligations), which pushes prices up further, which induces investors to buy more, and so on.

It’s easy to see how, when feedback is operating in the market, current prices are dependent (to a degree) on past prices (as Mandelbrot says, they have memory), and they can move to extremes, the odds of successive price rises, or falls, increases.

The question now is whether successive attempts to advance financial theory will fix it. Or whether we need a new theory. Mandelbrot replies:

Some brilliant persons still hope that by fiddling with the existing theory they will make it better and account for the data. I don’t think so, because there is a qualitative difference between a continuing varying process [a random walk] and [when] the most important events are the occasional jumps… So it’s better to start again.

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