At the ’96 Berkshire Hathaway annual meeting, a question was raised about diversification, to which Warren replies with the following:
We think diversification, as practiced, makes very little sense for anyone that knows what they’re doing. Diversification is a protection against ignorance. It is a perfectly sound approach for somebody who doesn’t feel they know how to analyze businesses… But it is a confession, in our view, that you don’t really understand the businesses that you own.
Then Charlie gets a quick jab in:
What he is saying is that much of what is taught in modern finance courses is toddle… You cannot believe this stuff.
I’ve always had trouble reconciling their views to that of Markowitz—that diversification is the only free lunch in finance. But what I’m starting to think is that it comes down to the investment return profiles.
Intuition
In a repeated game, large negative losses affect long-term profit disproportionately more than smaller losses. This is easy to show with numbers: a 10% drop only requires a subsequent 11% gain to break even, but a 50% drop requires a 100% gain. In a sense, a 50% decline is more than 5 times worse than a 10% decline is.
One of diversification’s benefits is that it dulls the impact of these major asset impairments. If you have a series of assets that have a max draw down of 50%, by finding a second uncorrelated asset, as you go from n=1 to n=2, the max draw down is cut in half, but it cuts down the risk by more than half.
So with an investment return profile that has a negative fat tail, you get a disproportionate benefit from diversifying, as you limit the potential downside. This an includes the return profiles of the equity market at large, which is mostly log normally distributed, as well as “short vol” type profiles, which have more pronounced tail effects. However, with a “long vol” return profile, the benefit of diversification isn’t as pronounced. If your max draw down of any given investment is only 10%, you don’t need as much downside dampening.
To prove this point (to myself) I ran a quick simulation.
Simulation
First I developed two inverse, but corresponding, return distributions.
Where the red line is the positively skewed return and the black is the negatively skewed. In building the distributions, I ensured that both had the same ergodic average – i.e., compound at the same rate over thousands of samples.
I then ran a series of simulations with portfolios of 1 – 10 assets. What I found is that while the long term average compounding rate for both improved with diversification, the improvement was more pronounced for the negatively skewed set.
Takeaways
So if you look at investors who very carefully take idiosyncratic risks with asymmetrical return profiles (Buffet, James Mai, Seth Klarman etc.) diversification doesn’t benefit them as much as it does for someone focusing on negatively skewed, or normally distributed, return profiles (Markowitz, most risk premia and risk parity investors).
While there will always be significant differences in worldviews, this could be a mathematical reconciliation between Buffet and Markowitz. And it could give some deep value investors some credence when they look at their portfolio of 5 – 10 bets.
