# Stochastic Portfolios

In my guest article at ERN, Karsten compared some of my data to his WR spreadsheet. The numbers are very different from my FIREcalc comparison to Monte Carlo in a good way. I think the Sharpe’s adjustment helps. I thought about what Sharpe’s really is and I concluded it’s a risk modifier. If your portfolio has some long term risk, the Sharpe’s modifies that risk because it’s magnified for the period of time when Sharpe’s is high and relaxed when Sharpe’s is low. It’s a very clever cheap and dirty modification that I think improves WR predictability. Cheap and dirty because Sharpe’s is free for the using.

In thinking about this I decided there is a well known physical equivalent. In the general chemistry analysis of solutions, every solution has it’s own equilibrium constant the caveat is “for weak solutions”. To get a more complete picture of solutions there is an alternative P-Chem analysis that involves multipliers. This means P-Chem analysis of solutions turns from a kind of linear analysis A + B = AB to a non linear second order process xA + yB = zAB and the coefficients are determined in various ways. The xyz are called activity constants and are variable depending on certain defined properties for a given solution.

What this means physically is chemicals don’t act with 1:1 correspondence but in concentrated solutions act as clumps of molecules and the molecules clump because of the way molecules act locally in solution. The stochastic looks at macro solution behavior, but the activity looks at deviation of solution behavior from the predicted stochastic. The idea is to develop a model that actually predicts how a solution will behave.

I think Karsten’s modification is like this, and it uses the “clumping” of excessive local risk in times of high Sharpe’s and relaxing of local risk in times of low Sharpe’s as a way to tease out non linear behavior in the risk model based on particular periods of time. I think it’s a cool idea to view the economy as a stochastic model (a marco model, like FIREcalc does) and then further modify the model to gain insight into local economic behavior.

## 2 Replies to “Stochastic Portfolios”

1. Catching up on my reading after travel, and this is a great explanation of a non-intuitive concept. If Sharpe’s helps a model behave closer to observed real-world behavior it’s a welcome addition to predict something as mushy as retirement withdrawal rate success. You make chemistry seem far less intimidating than it was back in college, my friend.

1. mdonfire says:

I had a blast in Chemistry. Amazingly challenging discipline. After a P-chem final, my last final, I went to the bar and had a draft. As I watched the bubbles rise I realized I understood the equations that governed why those bubbles form on the bottom and rise to the top. It’s related to surface tension and nucleation of CO2 coming out of solution. It was at that moment I realized I knew everything there was to know about the universe!