Limits to arbitrage?

Behavioural finance used mean reversion cycles to challenge classical economics, but preferred to explain it through sentiment and not ‘time’. We can’t expect Markowitz and Fama to open up this fissure and fight back. They have to accept that classical economics failed to answer more than a few questions and accept that the finance we are still taught could be far from complete, undo 100 years of research and only then can there be a new academic war.

The new fissure (weak argument) behavioural finance has is that though there is a limit to what can be arbitraged and inefficiencies can last longer, price reversal happens every 2-3 years. So, what the practitioners say is that on a large time frame arbitrage, is possible (buying the worst 3- year losers and selling the best 3-year performers) but not on small time frames. Even this time they explain how it’s the sentiment and investor profile that is to blame. Because the investors are loss averse and overreact, pushing losers lower. Investors also suffer from underreaction. This is the reason momentum continues and tops extend. The overreaction and underreaction take years to unwind.

Above this, we have short selling constraint, which imbalances the selling and buying equation. There are also geographical bias which restricts diversification out of regional assets. The coincidence here is that the 3-year reversal also assumes performance-based ranking when choosing worst and best performers. We decided to test a year ranking case and see if it was indeed true that short-term worst performers did not reduce risk and enhance returns compared to best gainers.

We took the worst losers of 2005 among CNX 100 and pegged them against the best winners. However, instead of taking a static ranking of worst against best, we ranked them on a percentile basis and took the stocks above 80 per cent rankings as best and below 20 per cent as worst. This was a change in ranking methodology. We assumed ranking was not static but dynamic. There were 34 top rankers and eight worst rankers. We created two equal weighted portfolios. And for the first half of the year till May, the worst performers not only outperformed the best performer’s portfolio but the worst rankers portfolio was also less volatile, with lower drawdowns.

One could not ask for more than 6 months improved performance from yearly rankings. So, is it just about ranking that keeps behavioural finance from witnessing performance reversals in short time frames? Is it that easy? Correlation cycles have been witnessed between MSCI EAFE and S&P500 moving from 0.8 to zero on a regular basis.

Now, what would behavioural finance practitioners do, if more research is published on seasonality in statistical data? How much seasonality can sentiment explain? Our recent paper on time duration in Shiller’s exuberance data (SSRN) was an attempt to show an order in time data. In a recent paper on ‘Gambler’s fallacy, hot hand belief and time patterns’ published in judgment and decision making, the authors, Yanlong Sun and Hongbin Wang, from University of Texas, have illustrated how statistics of waiting time could explain some behavioural errors. Putting simply, the authors have shown that time duration between simple coin tosses has statistical order. This is not far from our work on Time Fractals.

The author is CMT, and co-founder, Orpheus CAPITALS, a global alternative research firm