Interesting post.

This is neither a criticism nor a direct response – just a random thought occasioned by your post. In fact, the following is, I think, perfectly consistent with your (IMO) sensible approach. So, to reiterate, what follows is a discussion and in no way an argument or disagreement. (I wish such disclaimers were not necessary, but this is, after all, the Internet . . . .)

Risk is a funny thing. Consider the following example:

Suppose there is a random number generator that randomly generates a number between 1 and 100. You are given the opportunity to pick any number between 1 and 100 and then bet all of your wealth on whether the next generated number is that number or is not that number. E.g., suppose you pick 47 – if the next number is 47, you lose your entire wealth; if it is any number other than 47, you double your entire wealth. (Assume that everything is guaranteed to be in the up and up here, which of course is absurd, but we are just doing a thought experiment.)

Now, based on expectation values, you should definitely do this bet, right? 99% of the time you double your money; 1% of the time you lose all of your money. The average result of doing this bet is a 98% return! Incredible!

And this will always be true, right? The expected return after N trials will equal (1-.99^N)*0 + (.99^N)*(2^N), which is a number that grows incredibly fast.

Yet, we also have to consider the mode – the result that is most likely to occur. And as N grows, the mode soon becomes zero (the average gets higher and higher because even though more and more of the outcomes are zero, the ones that are not zero are growing astronomically). Eventually, we are almost certain to have a zero result, after a whole lot of trials, even though our “expected value” is gigantic.

So the sort of qualitative take-away from this is that we have to give serious thought to the tail outcomes, because they can take us out of the game entirely. And this is particularly relevant when considering leverage – for example, maybe we should think about what 2008 would have done to our portfolios, and consider if we should protect against that scenario.

Rich

Once A Drumlin Daisy

Now Once Daisy and Chance Elder Dancer