Dan Goldstein of the London Business School was kind enough to contact me and show me more intellectually accurate ways of interpreting and explaining the concepts of cognitive bias after reading my blog post, “To Price Target or Not to Price Target…that is the question.” Through our conversations he forwarded along a paper written in 1979 by Robyn Dawes called the “The Robust Beauty of Improper Linear Models in Decision Making” and said, “this paper will change your life.” Now only a couple of dorks would make a statement like that about a paper on linear models, but, as my wife can attest, my dork status has been well solidified for years.
In fact, the paper really does change my life. No, I’m not going to become a monk, but it does give me renewed confidence and substantial credence to the idea that I have professed for years now…you can’t manage a portfolio in your head (read my article on the subject featured in “Institutional Investor” here).
Basic tenet of RBILMDM: hundreds of studies have proven that Proper Linear Models (regressions, etc.) are better at predicting dependent variables from independent variables than intuitively predicting the dependent variable. This paper shows that even improper linear models (experts define variables as positive or negative and then a simple linear function is built without being regressed) beat experts studying the independent variables and forecasting the outcome (heuristics).
One of the more explanatory studies was a group of doctors that analyzed the biopsies of 193 Hodgkin’s disease patients. They asked the doctors to predict the survival time of each patient. Their correlation with actual survival times were effectively 0, meaning the doctors’ forecasts had no predictive power. However, if you construct a linear model using the variables the doctors labeled as important on the biopsy, then you can accurately predict survival time. The point is that experts can intuitively determine the relationship of variables to outcome but do a poor job of synthesizing multiple variables to forecast an outcome.
What does this mean for investors? If we consider ourselves proficient in portfolio management then we could well define the variables that have a positive or negative influence on position size. For instance, I could quickly tell you if there is a positive or negative correlation between risk-adjusted return, liquidity, downside risk, and conviction level to position size. However, what the myriad of studies suggest is that I would not do a good job of accurately sizing the position given access to all of this data. This puts intuitive portfolio management at a significant deficit when compared to a basic linear model. If we know that the average expert (doctors in our previous example) are not able to make predictions without a model, why would we as investors try and make portfolio decisions without a simple linear model? In fact, I’m guessing that constructing a basic linear model would take a user no more than a few hours and would dramatically improve position sizing. Additionally, it would allow the portfolio management process to be dynamic and refined over time so that the model’s predictive power evolves.
The author says it best, “…paramorphic representations (improper linear models) consistently do better than the judges from which were derived” – Robyn Dawes, “The Robust Beauty of Improper Linear Models in Decision Making” (1979). I may not be an expert but I’m pretty sure I know the correlation between using a model to manage the portfolio and fund success and this would be my improper linear model: Stock Selection + Position Sizing + Risk Controls = Fund Success.