Category Archives: Business Statistics

16/10/18: Data analytics. It really is messier than you thought


An interesting study (H/T to @stephenkinsella) highlights the problems with empirical determinism that is the basis for our (human) evolving trust in 'Big Data' and 'analytics': the lack of determinism in statistics when it comes to social / business / finance etc data.

Here is the problem: researchers put together 29 independent teams, with 61 analysts. They gave these teams the same data set on football referees decisions to give red cards to players. They asked the teams to evaluate the same hypothesis: are football "referees are more likely to give red cards to dark-skin-toned players than to light-skin-toned players"?

Due to a variation of analytic models used, the estimated models produced a range of answers, from the effect of skin color of the player on red card issuance being 0.89 at the lower end or the range to 2.93 at the higher end. Median effect was 1.31. Per authors, "twenty teams (69%) found a statistically significant positive effect [meaning that they found the skin color having an effect on referees decisions], and 9 teams (31%) did not observe a significant relationship" [meaning, no effect of the players' skin color was found].

To eliminate the possibility that analysts’ prior beliefs could have influenced their findings, the researchers controlled for such beliefs. In the end, prior beliefs did not explain these differences in findings. Worse, "peer ratings of the quality of the analyses also did not account for the variability." Put differently, the vast difference in the results cannot be explained by quality of analysis or priors.

The authors conclude that even absent biases and personal prejudices of the researchers, "significant variation in the results of analyses of complex data may be difficult to avoid... Crowdsourcing data analysis, a strategy in which numerous research teams are recruited to simultaneously investigate the same research question, makes transparent how defensible, yet subjective, analytic choices influence research results."

Good luck putting much trust into social data analytics.

Full paper is available here: http://journals.sagepub.com/doi/pdf/10.1177/2515245917747646.

16/10/18: Data analytics. It really is messier than you thought


An interesting study (H/T to @stephenkinsella) highlights the problems with empirical determinism that is the basis for our (human) evolving trust in 'Big Data' and 'analytics': the lack of determinism in statistics when it comes to social / business / finance etc data.

Here is the problem: researchers put together 29 independent teams, with 61 analysts. They gave these teams the same data set on football referees decisions to give red cards to players. They asked the teams to evaluate the same hypothesis: are football "referees are more likely to give red cards to dark-skin-toned players than to light-skin-toned players"?

Due to a variation of analytic models used, the estimated models produced a range of answers, from the effect of skin color of the player on red card issuance being 0.89 at the lower end or the range to 2.93 at the higher end. Median effect was 1.31. Per authors, "twenty teams (69%) found a statistically significant positive effect [meaning that they found the skin color having an effect on referees decisions], and 9 teams (31%) did not observe a significant relationship" [meaning, no effect of the players' skin color was found].

To eliminate the possibility that analysts’ prior beliefs could have influenced their findings, the researchers controlled for such beliefs. In the end, prior beliefs did not explain these differences in findings. Worse, "peer ratings of the quality of the analyses also did not account for the variability." Put differently, the vast difference in the results cannot be explained by quality of analysis or priors.

The authors conclude that even absent biases and personal prejudices of the researchers, "significant variation in the results of analyses of complex data may be difficult to avoid... Crowdsourcing data analysis, a strategy in which numerous research teams are recruited to simultaneously investigate the same research question, makes transparent how defensible, yet subjective, analytic choices influence research results."

Good luck putting much trust into social data analytics.

Full paper is available here: http://journals.sagepub.com/doi/pdf/10.1177/2515245917747646.

15/10/17: Concentration Risk & Beyond: Markets & Winners


An excellent summary of several key concepts in investment worth reading: "So Few Market Winners, So Much Dead Weight" by Barry Ritholtz of Bloomberg View.  Based on an earlier NY Times article that itself profiles new research by Hendrik Bessembinder from Arizona State University, Ritholtz notes that:

  • "Only 4 percent of all publicly traded stocks account for all of the net wealth earned by investors in the stock market since 1926, he has found. A mere 30 stocks account for 30 percent of the net wealth generated by stocks in that long period, and 50 stocks account for 40 percent of the net wealth. Let that sink in a moment: Only one in 25 companies are responsible for all stock market gains. The other 24 of 25 stocks -- that’s 96 percent -- are essentially worthless ballast."
Which brings us to the key concepts related to this observation:
  1. Concentration risk: This an obvious one. In today's markets, returns are exceptionally concentrated within just a handful of stocks. Which puts the argument in favour of diversification through a test. Traditionally, we think of diversification as a long-term protection against risks of markets decline. But it can also be seen as coming at a cost of foregone returns. Think of holding 96 stocks that have zero returns against four stocks that yield high returns, and at the same time weighing these holdings in return-neutral fashion, e.g. by their market capitalization.  
  2. Strategic approaches to capturing growth drivers in your portfolio: There are, as Ritholtz notes, two: exclusivity (active winners picking) and exclusivity (passive market indexing). Which also rounds off to diversification. 
  3. Behavioral drivers matter: Behavioral biases can wreck havoc with both selecting and holding 'winners-geared' portfolios (as noted by Rithholtz's discussion of exclusivity approach). But inclusivity  or indexing is also biases -prone, although Ritholtz does not dig deeper into that. In reality, the two approaches are almost symmetric in behavioral biases impacts. Worse, as proliferation of index-based ETFs marches on, the two approaches to investment are becoming practically indistinguishable. In pursuit of alpha, investors are increasingly being caught in chasing more specialist ETFs (index-based funds), just as they were before caught in a pursuit of more concentrated holdings of individual 'winners' shares.
  4. Statistically, markets are neither homoscedastic nor Gaussian: In most cases, there are deeper layers of statistical meaning to returns than simple "Book Profit" or "Stop-loss" heuristics can support. Which is not just a behavioral constraint, but a more fundamental point about visibility of investment returns. As Ritholtz correctly notes, long-term absolute winners do change. But that change is not gradual, even if time horizons for it can be glacial. 
All of these points is something we cover in our Investment Theory class and Applied Investment and Trading course, and some parts we also touch upon in the Risk and Resilience course. Point 4 relates to what we do, briefly, discuss in Business Statistics class. So it is quite nice to have all of these important issues touched upon in a single article.




3/10/17: Ambiguity Fun: Perceptions of Rationality?



Here is a very insightful and worth studying set of plots showing the perceived range of probabilities under subjective measure scenarios. Source: https://github.com/zonination/perceptions




The charts above speak volumes about both, our (human) behavioural biases in assessing probabilities of events and the nature of subjective distributions.

First on the former. As our students (in all of my courses, from Introductory Statistics, to Business Economics, to advanced courses of Behavioural Finance and Economics, Investment Analysis and Risk & Resilience) would have learned (to a varying degree of insight and complexity), the world of Rational expectations relies (amongst other assumptions) on the assumption that we, as decision-makers, are capable of perfectly assessing true probabilities of uncertain outcomes. And as we all have learned in these classes, we are not capable of doing this, in part due to informational asymmetries, in part due to behavioural biases and so on. 

The charts above clearly show this. There is a general trend in people assigning increasingly lower probabilities to less likely events, and increasingly larger probabilities to more likely ones. So far, good news for rationality. The range (spread) of assignments also becomes narrower as we move to the tails (lower and higher probabilities assigned), so the degree of confidence in assessment increases. Which is also good news for rationality. 

But at that, evidence of rationality falls. 

Firstly, note the S-shaped nature of distributions from higher assigned probabilities to lower. Clearly, our perceptions of probability are non-linear, with decline in the rate of likelihoods assignments being steeper in the middle of perceptions of probabilities than in the extremes. This is inconsistent with rationality, which implies linear trend. 

Secondly, there is a notable kick-back in the Assigned Probability distribution for Highly Unlikely and Chances Are Slight types of perceptions. This can be due to ambiguity in wording of these perceptions (order can be viewed differently, with Highly Unlikely being precedent to Almost No Chance ordering and Chances Are Slight being precedent to Highly Unlikely. Still, there is a lot of oscillations in other ordering pairs (e.g. Unlikely —> Probably Not —> Little Chance; and We Believe —> Probably. This also consistent with ambiguity - which is a violation of rationality.

Thirdly, not a single distribution of assigned probabilities by perception follows a bell-shaped ‘normal’ curve. Not for a single category of perceptions. All distributions are skewed, almost all have extreme value ‘bubbles’, majority have multiple local modes etc. This is yet another piece of evidence against rational expectations.

There are severe outliers in all perceptions categories. Some (e.g. in the case of ‘Probably Not’ category appear to be largely due to errors that can be induced by ambiguous ranking of the category or due to judgement errors. Others, e.g. in the case of “We Doubt” category appear to be systemic and influential. Dispersion of assignments seems to be following the ambiguity pattern, with higher ambiguity (tails) categories inducing greater dispersion. But, interestingly, there also appears to be stronger ambiguity in the lower range of perceptions (from “We Doubt” to “Highly Unlikely”) than in the upper range. This can be ‘natural’ or ‘rational’ if we think that less likely event signifier is more ambiguous. But the same holds for more likely events too (see range from “We Believe” to “Likely” and “Highly Likely”).

There are many more points worth discussing in the context of this exercise. But on the net, the data suggests that the rational expectations view of our ability to assess true probabilities of uncertain outcomes is faulty not only at the level of the tail events that are patently identifiable as ‘unlikely’, but also in the range of tail events that should be ‘nearly certain’. In other words, ambiguity is tangible in our decision making. 



Note: it is also worth noting that the above evidence suggests that we tend to treat inversely certainty (tails) and uncertainty (centre of perceptions and assignment choices) to what can be expected under rational expectations:
In rational setting, perceptions that carry indeterminate outruns should have greater dispersion of values for assigned probabilities: if something is is "almost evenly" distributed, it should be harder for us to form a consistent judgement as to how probable such an outrun can be. Especially compared to something that is either "highly unlikely" (aka, quite certain not to occur) and something that is "highly likely" (aka, quite certain to occur). The data above suggests the opposite.