On Probability, Observation, and Investing
Investors need to think about exactly what they mean when they use terms from probability. They need to appreciate the role of the observer (and his limited knowledge). For instance, if I flip a coin and cover it before you can see how it has landed, is it really correct to say there’s a 50% chance the coin has landed head-side up?
The problem is that we know that the class of (fair) coin flips will be populated by as many instances of heads as tails; therefore, if we know that a coin flip belongs to the class of fair coin flips (but know nothing else about the special case), we may say that there is a 50% chance the coin will land head-side up.
But, there is one somewhat unsettling matter to consider. Once I have flipped the coin and it has landed, we can all agree that it has either landed head-side up or tail-side up. The event has already occurred. But, it hasn’t yet been observed. Of course, I could lift my hand a bit and sneak a peak. Then, I’ve observed the outcome, but you haven’t.
Speaking probabilistically, you might still say there’s a 50% chance the coin has landed head-side up. But, you would now know that there is a difference between the knowledge possessed by different observers. The unsettling part comes when you realize that a probabilistic statement can not be made independent of the observer (and her knowledge).
It may seem a trivial problem when we consider the observer to be a single individual. But, all our knowledge is dependent upon observation, and all our probabilistic statements are dependent upon our knowledge – so, all of our probabilistic statements are dependent upon our knowledge.
That’s obvious, because we only make such statements where our knowledge is limited (we know something about the class but not the special case). The problem for investors is that two analysts with the same data may interpret that data differently such that they arrive at two very different conclusions. Essentially, they will make two different probabilistic statements (largely based on what data they believe pertains to the special case in question).
For instance, you can make a statement about stocks trading at a P/E of 12, or stocks trading below book value, or stocks that have achieved a ROE of greater than 15% in nine of the last ten years. But, that may not be the best class to consider.
I just mentioned Harley-Davidson (HDI) in a previous post. Does Harley-Davidson belong to the class “stocks with a P/E of 15”? Or, does Harley belong to the class “stocks of companies with entrenched consumer brands”? After all, some stocks with a P/E of 15 may be in commodity businesses.
The investor needs to reference several different past records at once. She needs to consider the past record of entrenched consumer brands (how many had their earnings power diminished? How many of the brands lost their luster? …
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