Friday, February 27, 2009

Why Bernoulli based models are rubbish - and why they might work

I've recently read from a brochure from a highly respected Canadian big bank about Behavioural Finance, particularly, the Gambler's Fallacy - The idea that future random events depend on past random events. It proposes the idea that if a stock rises five consecutive days in a row, that if you assumed it's less likely to rise on the sixth day, then you are a victim of a gambler's fallacy. Although I can see their rational, I strongly disagree.

If the analogy was taken into a casino, where future random events *are* independent of past events, then I would agree. However, I think that this model oversimplifies the stock market. And the principles on which this type of modeling is built, Bernoulli trials, should not hold under the Efficient Market Hypothesis.

The reason I'm so confident in making this statement is that I would like to believe that there are *some* rational value based traders out there who, when the stock price varies too far from its intrinsic value, will buy or sell accordingly. In this way, those traders who are doing their homework are essentially profiting off of those who are trading as if each day's outcome is random (or even if you model your risk management as if these outcomes are random). Prices *should* gravitate towards some number, and therefore each day's rise or fall *is* dependent on the day before it. A prime example is the price escalation we recently saw. Bernoulli trials would have simply labeled them as "unlikely" but I'd like to think that a value based trader would see a bubble forming.

Having said that, with all the emotional and fear based trading going on, this lack of faith causes high volatility in prices and using a Bernoulli type model might have some value as a risk management tool based on certain similarities. However, trying to get actionable value from it would be like attempting to profit from chaos which is risky and difficult (like creating a Garbage In Gold Out model).

However, those of you that can profit from this volatility will actually be providing a service to the economy in the form of marginal price stabilization. Anyone who is able to profiteer from the mood swings by reducing the spreads will bring us closer to something resembling that should happen under EMH.

But real stability won't happen until there is enough stable capital in the market that doesn't exhibit flight at the first hint of trouble. And that won't happen until there is broad based confidence in the fundamentals of the economy.


Anonymous said...

Wongster the basic question is whether or not financial movements occur in a Gaussian probabilistic sense. Obviously they're not (entirely) Gaussian. You can't appropriately apply the central limit theorem and there is no regression to the mean.

In a calm market, a security's price fluctuations around a theoretical risk-adjusted mean asset value DO seem to behave in a somewhat Gaussian, independent-probability sense. However, when there is a behavioural shift in the market, you can get inflated asset prices (bubbles) and senseless downswings (crashes), and these seem more like herd behaviour than mere exceedingly-unlikely-outcomes happening with independent probabilities...

There is no way that the whole movement of the market is expressly rational, and the fact that it has moved in a given way recently has an impact on how people think it is likely to move in the future, causing its expressly "logical" movement on the basis of asset values to be forgotten. Of course the market's movement itself impacts a trader's opinion of how it WILL move, independent of fundamentals.

This is also a tension seen between technical analysis and fundamental analysis. One ascribes the markets movements solely to the market's prior movements (technical), and the other ascribes the movement to the fundamentals of the underlying assets (fundamental). The obvious answer is that like the nature/nurture genotype/environment debate, both play a role and a phenotype emerges. But knowing that both fundamentals and the behaviour of the actors in the market have SOME influence in the resulting behaviour of the market itself is not good enough. It doesn't meanyou know how things will play out, and than is why I am not a billionaire.

Joshua Wong said...

In recently studying how fundamental and technical analysis works, I am absolutely fasincated by the mechanics (although I'm told that a proper understanding of technical analysis modeling requires a Ph.D level technical degree such as Math or Engineering).

I think that your assessment that a phenotype (interesting choice of words) emerges is very fair and accurate.

And simply put, it if was easy, everyone would be doing it (why we are not a billionaires... yet) ;)