Of science, homoscedascity and high returns | Outlook Business
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Soumik Kar

My Best Pick 2014

Of science, homoscedascity and high returns
Founder of Augment financial services feels the market is more of science and less of maths

For someone with a science background, like me, a question that frequently came to mind is which science best describes the characteristics of the stock market. To the casual observer, it may appear to be physics or mathematics. After all, markets contain so much complexity and calculations and are amenable to algorithms — it must be mathematics or physics. The reality seems different. Put simply, both physics and maths are subject to laws; for instance, the law of motion or the law of thermodynamics.

Most of maths is precise. The market does not seem to be amenable to any law. Actually, it is absence of law that is the most striking aspect of markets. Investing in markets is about empiricism and not theory. For example, generally speaking, it pays to buy inexpensive stocks and sell stocks with rich valuations. However, most market experts know, and quite painfully at times, that this doesn’t operate as a rule. Cheap stocks are sometimes cheap because they deserve to be so and expensive stocks can perform well over long periods.

This sounds so much like medical science. Medicine is an empirical science. It seems like smoking cigarettes can be a leading cause for lung cancer but not all cigarette smokers suffer from cancer and not all lung cancer patients are smokers. No two human bodies are the same. To the medical professional, the exceptions are as important as the rule. The reason why markets appear to be closer to the science of medicine rather than maths or physics is the overarching role of greed, fear and hope in determining economic and market cycles. Greed, fear and hope are basic human nature. This is why market economics gets it wrong at times. Just the way it is difficult to predict how bodies will behave to external stimuli (such as food, pollution, stress, exercise or even smoking), it is hard to say how a human being will react — however irrational it may appear to the logical mind. Indeed, that is where the inconsistency lies, which is that logic is mathematics and the market is really about biology.

One could have purchased the least expensive stocks a decade ago and made a superior return compared with the most expensive stocks, but this statistic hides the large number of outliers in both groups that did the opposite. Basically, several cheap stocks lost even though on an average it was a winning strategy. The exception to the rule is of paramount interest to the market participant as it is in the field of medical science. “Averages” is a good tool to drive home the efficacy of a rule but less useful when constructing portfolios. Each investment is an idiosyncratic case that requires independent examination, just like every medical case needs discrete scrutiny.

In fact, taking this point further, not only are stock markets like biology, they are less like maths or physics than they appear to be.  One of the most intriguing charts I have seen is the correlation between the prices of orange juice and DLF. Between September 2007 and September 2009, the correlation between these two prices had an R-squared of 85%. Put simply, it means there was an 85% association between the price movement of DLF in INR and the change in the New York futures of orange juice in USD, or for that matter the prices themselves. When I saw this chart, it struck me as an extreme example of the soaring correlations across risk assets in the world that had been in vogue since 2003. However, the degree of association between orange prices and DLF was just so unbelievable. The correlation since then has deteriorated to almost nothing; in fact, it has turned slightly negative. The collapse in correlations is as inexplicable as the high correlations. 

This chart exposes the danger for market practitioners when they use even simple statistical tools such as mean, median standard deviation and correlations for supporting an investment case. There is a fatal flaw in using these things. The shortcoming is that the use of these tools is valid under a set of assumptions and the variables that are being subjected to these tools need to comply with these assumptions. For example, calculations for correlations rely on a linear relationship between the variables, normality and homoscedascity (arguably, all three are violated in the above example). One of the key assumptions is that the variables are distributed under a well-defined curve, mostly the Gaussian or “normal” or bell curve.

Indeed, history tells us that stock returns, the variable most commonly tested, may not be distributed under a normal or bell curve. If one plots the distribution of weekly returns of the BSE Sensex going back 30 years, it resembles a bell curve but the predicted values of returns (using the properties of a bell curve) are very different from the actual outcome. The error in the observed value versus the theoretical value underpins the approximation in the assumption of the distribution pattern. If the distribution itself is unknown, the use of statistical tools to analyse the variable is inaccurate. Most of us make conclusions regarding stocks on much smaller samples than 30-year data, lending such inferences to higher error rates.  

How does this knowledge help those trying to predict what may happen in 2014? It appears that there are three known unknowns in 2014 — the Fed taper, the election result and the policy action that follows the election outcome. Based on where each one of these go, India equities could easily gyrate about 20% (or more) around their current level. While one could argue that the market will end 2014 largely unchanged from current levels, such an outcome carries a slightly better probability than a toss of a coin. The dilemma for the investor trying to make money on a relative short time horizon like 12 months has always been such for almost ever.  The better approach, in my view, is to focus on long-term investing in a well-diversified portfolio that fits the entire taxonomy of stocks — growth, value, cyclicals, defensives and quality. 

Again, the comparison with medical science is irresistible. We can fix diseases with medicine but proper sleep, a balanced diet, exercise and low stress is what should result in good health. Similarly, very little can be taken for granted in the poignant world of stocks — the role of luck, skill and emotions appear equally balanced.

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