April 8, 2013: Shannon's Demon

If I offered you the chance to play a coin flip game with a 50/50 chance of doubling or halving your money, would you take it?

For a player who gambles his entire bankroll each round, it appears to be a wash. No matter the order of returns, if there are an equal number of heads and tails, the player ends up having exactly as much as he did at the start.

For example...

  • Starting bankroll: $100 
  • Round 1 (heads): $200 
  • Round 2 (tails): $100 
  • Round 3 (tails) $50 
  • Round 4 (heads): $100 

However, for a sophisticated investor this game would represent an incredible profit opportunity. Claude Shannon illustrated this by proposing that an intelligent player would wager only half of their bankroll each round. This seemingly small differences turns the game into a winner.

  • Starting bankroll: $100 
  • Round 1 (heads): $150 
  • Round 2 (tails): $112.5 
  • Round 3 (tails) $84.375 
  • Round 4 (heads): $126.5625 

Converting this game into investment-speak, Claude Shannon proposed a portfolio of 50% coin flip and 50% cash. This portfolio was rebalanced at the beginning of each round. The results of this game are quite profound. It shows that risk reduction has the ability to increase returns by bringing your realized portfolio geometric return closer to the weighted arithmetic returns of the portfolio's components.

Taking the bankroll management strategy in a slightly different direction, we can observe how a diversified portfolio of coin flip games that is rebalanced each round offers a return that is far greater than the weighted performance of the individual games.

(This chart will update automatically every 10 minutes or so, offering a new randomized experiment each time.)

Internalizing the benefits of diversification takes time, but I can’t imagine going back to a concentrated portfolio. Diversification combined with rebalancing offers the opportunity to increase returns while simultaneously decreasing risk. Although the real world is far more complicated than a simple coin flip operation, I think the game can help investors understand how looking at assets in isolation never makes sense. Sophisticated investors only care about what an asset will do to a diversified and periodically rebalanced portfolio. If you enjoyed the topic of this post, try Googling phrases such as “volatility pumping”, “volatility harvesting”, “Shannon’s Demon”, and “Kelly criterion.” Additionally a well done paper on the subject can be found here.

March 24, 2013: PP vs. Risk Parity Funds

Before jumping into the body of this post, please be sure to check out the new "long term performance" section. I have vastly improved it.

Risk parity is a buzzword in pension finance right now. Ray Dalio of Bridgewater popularized the concept and he has become one of the biggest names in the institutional investment community. His strategy is simple: 1) Don't try and predict the future. 2) Allocate your capital across different asset classes that respond differently to different economic environments so that you have a neutral portfolio.

This should sound familiar because it is exactly what the Permanent Portfolio does. The risk parity guys complicate things by weighting assets inversely to their volatility (which changes over time), but the principles are the same. After all gold, stocks, and LTT all have roughly equivalent volatility so the equal split with the PP's weightings is no coincidence. It is essentially a risk parity strategy.

AQR and Invesco have launched a couple of funds within the last few years, and I think it will be very interesting to watch their performance vs. the PP over time. Although they are guided by essentially the same framework as the PP, their execution of the philosophy is much more complicated (and expensive).
These charts will update automatically every month, so be sure to check back in the future if you are curious about the relative performances.

January 17, 2013: Focus on Causation, Not Correlation

Correlation coefficients are a common way of quantifying diversification benefits. If you hold an equity portfolio and can find another asset class that will exhibit low correlation to equities, you will likely be reducing the risk of your portfolio if you include the low correlation asset class.

The problem is that correlation coefficients between asset classes are notoriously unstable. Therefore, relying on ex-post observations of low correlation can give you a false sense of security when constructing a portfolio.

Below I have charted the trailing twelve month correlation coefficients of the 3 volatile asset classes that comprise the Permanent Portfolio.


If you were to attempt to arrive at weightings based off of correlation coefficients you would be totally lost. Instead of focusing on correlations between asset classes the PP framework focuses on the underlying macroeconomic causations that drive asset class returns. Causations can be deduced from basic understanding of macroeconomics in a fiat economy and the chain of causation is much more stable over time. If you understand how changes in inflation/deflation and growth/contraction affect the asset, you never need to rely on unstable coefficients. Even if you are using a different strategy than the PP, I think that a fundamental understanding of what drives asset classes will help you build a portfolio with more robust diversification.