Textbooks present three forms of this statement. To quote McCauley (who gives credit for these to “finance theorists”): “Weak form: it’s impossible to develop trading rules to beat market averages based on empirical price statistics. Semi-strong form: it’s impossible to obtain abnormal returns based on the use of any publicly available information. Strong form: it’s impossible to beat the market consistently by using any information, including insider information.”
The strong form makes a person with a natural science education background wonder whether this is a “law of nature” or a “law” enforced by “law enforcement”. The weak form seems to be formulated in a falsifiable way. It is this form that can be falsified in spectacular ways by using world’s most liquid market — the forex market.
A book whose relevance seems to only grow with time since its first publication in 1898. Le Bon’s “crowd” is in most examples a group of people at the same physical location, seeing and hearing each other immediately, and responding to the stimuli they immediately observe. These days there emerges a global crowd interconnected by modern means of communication unheard of in le Bon’s age. As both the crowd and its scope of attention are thus expanded, the basic dynamics likely remains the same, as does the human nature. The relevance of the book grows with the crowd phenomenon it describes — that is, in proportion to the growth of the mass media and means of communication.
Here at ForexAutomaton.com where our business is to turn mood swings of the financial market crowd into profit opportunities, we cannot but add this book to our bookshelf (if not keep it on our desktop, as did Lenin according to some sources). What le Bon does using the methodology of the social siences, we do using that of the precise sciences. He describes, we measure. If you think markets become more fficient as their liquidity grows, think again or read le Bon: a larger crowd is still a crowd. And a crowd is driven by its own dynamics, and is less rational — and possibly is easier to predict and control — than any of its individul members, no matter who they are. This applies to a crowd of nineteenth century’s leading scientists in one of le Bon’s anecdotes as it may apply to a crowd of Wall Street CEOs in what created the subprime crisis episode of 2007-200?.
For a price time series p(t), discrete with a time increment dt, a logarithmic return variable is
x(t|dt) = log(p(t)/p(t-dt))
where dt is the time increment separating adjacent points in the time series.
This variable has several advantages. It is additive: the return of the entire series is the sum of the returns comprising the series:
x(tn|tn-t1) = x(t2|dt) + … + x(tn|dt),
dt = (tn-t1)/(n-1)
Non-negativity of the price is “built in” — especially useful when simulating artificial time series.
When used in the correlation analysis, logarithmic returns (as do ordinary returns p(t)/p(t-dt)) eliminate one trivial source of non-stationarity of the correlation functions which is the possible long time-scale trend in the time dependence of the price. Long-term absolute level of the price is almost irrelevant to a forex trader, what matters is relative movements.
Finally, the moments of the logarithmic returns may converge better than they would for the ordinary returns — although, notably, Mandelbrot postulated that the variance of this variable would be infinite.
A thought-provoking reading. The author definitely enjoys and thrives on expressing a number of well articulated sharp opinions on a number of subjects.
Among other things, Taleb uses a trend-on-top-of-noise model to make the point that larger time scale improves what a natural scientist would call signal-to-noise ratio in the analysis of investment performance. The short time scale is mostly meaningless; the significance of performance record grows with time scale. To quote Taleb: “This explains why I prefer not to read the newspaper (outside the obituary), why I never chitchat about markets, and, when in a trading room, I frequent the matematicians and the secretaries, not the traders. It explains why it is better to read The Economist on Saturdays than the Wall Street Journal every morning (from the standpoint of frequency, aside from the massive gap in intellectual class between the two publications).”
Econophysics is, very roughly speaking, economics or econometrics done by physicists or done the way physicists — or natural scientists for that matter — would do it. In particular, the emphasis is on quantitative real-life evidence and natural-science-style methods of inference.
On the particular subject of correlations (the little specialty of this site), the author states (Section 3.7) that “liquid markets (stock, bond, foreign exchange) are very hard to beat, meaning that to a good zeroth approximation there are no long-time correlations that can be exploited for profit”. More specifically: “Financial data indicate that strong initial pair correlations die out relatively quickly on a time scale of 10min of trading”.
In our Currency Alpha section we compare this with our own observations.