“If 5 cats can catch 5 rats in 5 minutes, how many cats do you need to catch 100 rats in 100 minutes?”
That’s a recent conundrum posed by Actuarial Post, a UK-based actuarial website, whose updates¹ I subscribe to. The answer, they claim, is 5. That answer is based on the logic that 5 cats can, between them, catch rats at the rate of one per minute. But whoever came up with that answer doesn’t know much about cats (or rats.) Most cats I know would happily take a nice long nap after catching a rat; most rats would leave the scene pretty quickly after seeing their erstwhile friends and relations taken out by predators.
Which doesn’t matter much in the context of a conundrum on an actuarial website. But a great deal of economics and investment market analysis is based on similarly flawed oversimplifications, and that matters a lot.
For example, linear regression is convenient math and very widely used in investment analysis. But few of the relationships that really matter are linear. The Capital Asset Pricing Model is elegant and can be used to highlight some significant theoretical points about markets. However, it’s not a particularly good model. Despite that, it has somehow become part of the standard language of finance: in his book Models Behaving Badly,² Emanuel Durman tells of searching without success on Bloomberg, Yahoo and Google for the volatility of stocks and markets. Where he expected to find volatility, he could only find beta. He concludes: “it is a sign of the political power of models that commercial websites publish the value of a beta, a parameter in a model that doesn’t work that well, but not the more fundamental and model-neutral volatility statistics”.
Regular readers of this blog will recognize an old theme here: don’t marry a model. It’s a drum I’ve banged elsewhere. But, since it’s a message that shows no sign of being heard by the investment community at large, it’s a drum I make no apologies for keeping on banging.
¹These updates contains articles and news on matters of interest to actuaries, but the actuarial mind’s dopamine is supplied by solving puzzles, so each issue ends with a conundrum such as the example I started with.
²Durman, E. (2011) Models. Behaving. Badly. The Free Press, Simon & Schuster. New York.