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? How many increased their earnings power?).
Harley-Davidson might more properly be classified as a growth stock. Look at the annual rate of increases over the last ten years: Book value per share has increased at a 17.78% annual rate; EPS has increased at a 21.92% rate. Or, we could classify HDI as a stock that has consistently earned high returns on equity while employing very little debt. At this point, we haven’t even considered classifying it by industry. Is that an appropriate classification?
The investor is in the unenviable position of performing an overwhelming calculation. She has knowledge of the past records of countless other stocks and countless other businesses that are in some way related to the case at hand. But, how closely related are they? And in what way are they related? What is the proper weight to assign to each variable? And what is the proper estimate for that variable?
Some very smart investors (e.g., Warren Buffett, Peter Lynch, and Benjamin Graham) have pointed out the similarities between investing and gambling, but haven’t gone as far as suggesting there are similarities between the (intelligent) investor and the gambler. Why? Because investing really is a game of odds. But, no sane man would take the gambler’s position.
An intelligent investor bets only with the odds in his favor. He has no interest in luck. The investor looks for high-probability events and a margin of safety. He wants to tilt the odds in his favor; he doesn’t want to play a game of chance. But, his knowledge is always limited. Nothing is certain. So, the best he can hope for is playing a game of odds the way the house does. He begins with a clear advantage that will reduce the importance of the element of chance inherent to the game.
Some time ago, I wrote a short post on intrinsic value. I think it’s worth revisiting:
The intrinsic value of a business can not be determined through clairvoyance or calculus, prescience or projections – for even the best projections sit precariously atop a mountain of complex assumptions. Determining the intrinsic value of a business requires simple arithmetic, common sense, and a careful analysis of the past performance and current financial position of the firm. Most importantly, it requires the separation of those things which are both constant and consequential from those things which are either mutable or meaningless.
When your knowledge is limited (as the investor’s knowledge always is) you’ll do best to focus on those things which are both constant and consequential. Actually, I omitted one key word when I wrote that post on intrinsic value.
I’ve always believed an investor should focus on those things which are constant, consequential, and calculable.
You need to focus on those things that can be both known and weighed. The relative weights assigned to each variable are where most investors make their biggest mistakes. It tends to be the things they know, but can’t weigh, that kill them.
Just remember to be conservative in all your estimates – and, when in doubt, withhold your judgment. Investors have the luxury of inaction. That comes in handy whenever the question posed is complicated. You only need to know the easy answers – as long as you know when not to give an answer.