Blame it on Bachelier
Posted on October 22, 2009 by Richard Beddard
Filed Under Editor's choice, Investing, Markets |
A random walk into recession
You’ve got to watch these two interviews with Benoit Mandelbrot:
Mandelbrot saw the financial crisis of 2007 coming, He couldn’t have told you exactly when or how it would happen. His achievement was simply in recognising that big, and sometimes destructive events do happen in financial markets.
Maybe that’s obvious, but its surprising how many people, and investment banks, forgot it applied to their investments in 2007.
In his book, ‘The (Mis)Behaviour of Markets’ published in 2004, and over forty years earlier as he studied sequences of prices, he found the the models of modern finance wanting.
These models dominate financial theory, but Mandelbrot says they underestimate risk. If people who buy and sell financial assets and derivatives use the wrong financial models, they too will underestimate risk, which is, of course, wilfully or otherwise, exactly what many of them did in the years leading up to 2007, 2000, 1987 etc..
The mis-modelling started longer ago than you might think. Mandelbrot blames the PHD dissertation of an obscure but brilliant French mathematician, Louis Bachelier. He published his ‘Theory of Speculation’ in 1900, but it was largely ignored until the 1960’s when academics had the computing power to study prices.
Bachelier’s mathematics is beyond me, (it’s in this book, and this paper [PDF]) but Mandelbrot’s 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:
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.
It’s difficult for a practitioner, head buried most of the time in annual reports not equations, to referee this dispute, although I bet you can guess where my sympathies lie.
As Mandelbrot’s co-author Richard Hudson explained when I interviewed the two of them in 2004, well before the recent financial crisis:
Risk is the dominant theme in markets. We see that in the collapse of the internet bubble, we see that in every news event, we see that in 11 September - not the event itself but the way the markets reacted to it, we see that in the ‘87 crash.
As markets recover from the latest blow-out and investors emerge from crisis mode, we must remember that the odds of another crash with the potential to inflict losses so large we cannot fully recover are much higher than we might think.
People forget.
-
Some anomalies, for you
Here’s my weekly list of financially sound companies at cheap prices. The data is from Sharelockholmes.com. Please remember I have not verified it unless the company has already been included in the Thrifty 30 model portfolio. Explanations of the column headings are at the end of last week’s post.
-
The Horlicks Markets Hypothesis
Paul Woolley, founder of the Centre for the Study of Capital Market Dysfunctionality at the LSE, says professional investors make financial markets less efficient, “a complete Horlicks” in fact, not more efficient.
A transcript of a fascinating conversation with Benjamin Graham.
Yikes! Maybe I shouldn’t be too complacent about recovering manufacturers.
It’s official, technical analysis is a load of old cobblers. Tests on 5,000 trading rules over 49 countries confirm it.
In the board game Monopoly the bank never goes bust, and the game continues until every player bar-one goes bankrupt…
Comments
10 Responses to “Blame it on Bachelier”
Leave a Reply
The problem is that Mandelbrot does not provide us with an alternative. He, in effect, says, “you are valuing securities all wrong, but I have no idea how you should do it.”.
Hi Graeme. I agree, but demonstrating the current theory is based on a faulty premise (i.e. the random walk) is a start.
Also, the point I think I had in my mind when I started writing the article, but may have forgotten by the time I got to the end is that in the absence of credible pricing theories investors should pay less for investments than they think they are worth, since there is a big margin of error!
That of course is the value investing philosophy.
If the random walk is wrong, then technical analysis ought to work…..
There is a great Buffet quote to the effect that DCF is right, but he never actually calculates one because if an investment is good enough to buy then it will be obvious that DCF value will be much higher than the price.
Oops, types without thinking and being too smart-alecky, should have said, what Mandlebrot is saying, is not that it is not a random walk, but rather a different random process. Critically, it is not a continuous process: i.e. the underlying equations cannot be differentiated.
That said, it does not look likely the patterns in price movements that he suggests are predictable in a way that will let you profit from them.
Hi Richard,
I agree with the ’positive feedback’ idea also. It makes intuitive sense. Certainly, anything based on continuous functions (e.g. random walks and fluid dynamics) does not accurately describe what is happening. Chinese Whispers might be the closest analogy! In fact, if you filled a room with people and whispered slightly different messages to a few people in different parts of the room, and then told them to ‘pass it on’, then this might be about as accurate as you can get. Anyone who heard two conflicting messages would have to decide how to communicate it to the next person
It would be interesting to find the earliest reference, where the EMH is discredited in a widely available book. Certainly I have a book published in 1994 where the author says about EMH that it is ‘absurd and demonstrably untrue’. However, anyone trying to sell a book which says you can ‘beat the market’ would have to say that, wouldn’t they
[...] Beddard’s post on a recent FT two part interview of Benoit Mandelbrot focuses on his comments on Bachelier and the [...]
Well, here is a Chinese Whisper. The FTSE is about to have a big correction.
If UK GDP goes up then the stock markets will be encouraged and push up the prices.
If UK GDP goes down then the stock markets will be encouraged because of more quantatitve easing and push up prices.
It is a win-win situation, and therefore is unlikely to happen!
Well done Robin, you were wrong/right!
Give it time, the chinese whisper still needs to spread out
Hi,
For information:
Finance & Mandelbrot
http://www.facebook.com/group.php?gid=53108760302