Xmas reading, asset allocation, and how much gold?

Down in the bottom right hand corner of this blog, I keep a list of Interesting People.  Generally, what qualifies someone as sufficiently interesting to make the list is that they have published a collection of works that are worth reading.  Someone that I recently added to the list is Michael Mauboussin.  He has written some interesting articles in the investing game theory space, and a particularly relevant article on the importance of position sizing (asset allocation) in investing called Size Matters.

The point of that article is that, just because you have a strategy with a positive expectation value, doesn't mean that you should go all in on your first bet.  You might lose, and then you'd have nothing.  Clearly, this is not the best way to play a game that, in theory, gives you an edge and should allow you play profitably over the long term.


The article shows that there is a formula, called the Kelly formula, which can be used to determine the optimal size of a series of bets.  In simple cases, the formula can be expressed as:

Percentage of portfolio to bet = winning expectation value / actual winnings if you win

Let's say we have $100 and are playing a game whereby a dice is rolled.  If the dice lands on the 6, odds of 20:1 are paid.  All other roll outcomes result in no return.  Our expectation value is positive (20/6), so we definitely play, but what should be the size of our initial bet?  Using the formula, it should be: (20/6) / 20, or $16.66 .  To quote the paper(ish):

The optimal amount to bet is 16.66 percent of your bankroll in each round. Said differently, betting 16.66 percent will lead to a greater accumulation of wealth, on average, than any other betting strategy.

Applying this to investing is obviously more complicated that simple games with easy to calculate expectation values and outcomes.  I'm yet to try it in earnest with one of my portfolio's but will try to at some point in the future.

In the mean time, let's see if it can answer the question of: how much gold should I own?

Here's the way that I see the probabilities:

Outcome	Likelihood	Return
Gold re-monetized by Central Banks	30%	25x
Gold increases due to inflation	30%	2x
Gold bubble pops	40%	-1x

Now, collapsing the above so that we only have 2 outcomes, we get:

Outcome	Likelihood	Return
Gold goes up	60%	13.5x
Gold goes down	40%	-1.0x

which equates to an expectation value of 4.8 + -0.4 = 4.4x and a "winning" value of 13.5.

Therefore, given that the above probabilities (as well as my rusty maths) are sufficiently accurate, one should allocate 4.4/13.5, or 33% of your portfolio to gold.  Feel free to adjust the outcome likelihoods to suit your beliefs.