# The Seduction

Many are the victims that fall to her allure, to her intoxicating invitation, her indisputable beauty. The temptress? Mathematical prediction models, of course. The attraction is clearly understandable: the promise of precise answers to otherwise very difficult analytical problems.

Investors today are heavily indebted to great minds such as Pascal, Newton, Bayes and many others who made enormous contributions to mathematical advancement enabling areas such as statistical prediction. The investment hindrance, however, happens when there is too much calculation and too little thinking. There simply isn't a substitute for sound judgment in the analysis of investment problems.

Taking a look at two areas of great importance but equally great ability to mislead we can uncover instances of misplaced trust in mathematical massaging.

**Limits of correlation analysis**

Identifying relationships between data is a fundamental aspect of making investment decisions and correlation analysis is a useful help in achieving this. Though, among its limits perhaps the most common is misunderstanding the math as proof of a cause and effect association. Correlation does not necessarily imply causation, and that is very difficult to accept sometimes.

One form of spurious correlation has to do with correlation between two variables arising not from a direct relation between them but from their relation to a third variable. For instance, every time that I receive a bill in the mail the mailman is involved, without exception! There is a perfect, positive correlation which could lead me to have a strong dislike for my mailman. A less ridiculous example is that height could be positively correlated with the extent of a person's vocabulary, however the underlying relationships are between age and height and age and vocabulary. Most relationships are much harder to see through than these. That could well be the reason why statistical analysis would be used but also why correlations should be a compliment to, and not a sole deciding factor in, investment decision making.

**Limits of regression analysis**

In a demonstration exercise using an extensive search of variables in an international financial database, Leinweber (1997) found that butter production in Bangladesh explained 75 percent of the variation in U.S. stock returns as represented by the S&P 500. Such a pattern, with no plausible economic rationale, is almost certainly a random pattern particular to a specific time period.

Outside of the above extreme example which illustrates how data can be made to show predictive value where there obviously is none, a reasonable predicted affect on a dependent variable can be established realizing, however, you must come up with values for the independent variables being used to predict the dependent one. The independent variables, themselves, have drivers that could need to be regressed and layers upon layers of regression could be added until there is unusable complexity.

For example, a regression can establish a predicted value of a company's ratio of Enterprise Value to Invested Capital (EV/IC) based on the spread of the company's returns on capital over it cost of capital. The model can spit out a number to the 6th decimal place saying that for any given spread (ROIC minus WACC) I can expect the EV/IC to be Y. How then to determine the ROIC -WACC spread? More quant only methods can be used, but the drivers of return on capital at some point resist neat and precise quantitative prediction. Returns on capital result from volumes sold and margins. These are results of qualitative differentiators and competitive advantages that allow a business to improve or maintain pricing power.

The difference between poison and medicine can be only its dosage. Correlation and regression analysis can be overdosed on. Despite their beauty and (deceptive) precision, sound judgment must augment statistical conclusions.

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