Ed Thorp and Fortune's Formula - Part I

Ed Thorp and etc. wrote an article, "How does the Fortune's Formula-Kelly capital growth model perform?", which is published on The Journal of Portfolio Management, summer 2011.

Kelly capital growth model is a constant rebalanced portfolio strategy.  An article, "Dynamic Strategies for Asset Allocation", by Perold and Sharpe gives you a comparison of pros and cons of different investment strategies.  Investors can get a simple idea about in which environment people can get some advantages from rebalancing their portfolio periodically.

From Ed Thorp's point view, the Kelly strategy is good for long term investing.  Just investors have to choose a suitable factor to control the risks.  A full Kelly strategy is very risky for the short term.  Their article shows the results of different scenarios using full, 3/4, 1/2, 1/4, and 1/8 Kelly strategies.  Actually we don't have to run such simulations to get the sense of how Kelly strategies perform, we can just use a spreadsheet with simple calculations that would give you a better idea how Kelly strategies work and how Log utility works.

Investors should know that when we talk about the performance of an investment, it's a multidimensional thing.  We have to consider the risks, rewards, liquidity, taxes, transaction fees, and etc.  No matter how, we need to consider at least two components, risks and rewards.

An interesting point is how to compare (risks, rewards) together.  Some economists use Utility to describe human's behavior such as risk neutral or risk averse.  The utility curve of (risks, rewards) is different to different investors due to their preferences.  By the way, people should notice that Utility is not the only approach and it's not perfect.

The other thing to consider is when we say a strategy A is better than the strategy B.  What do we really mean?  Do we mean the expected return of A is better than the expected return of B?  Do we mean the chance of A's final asset larger than B's final asset is greater than 1/2?  Do we mean the expected growth rate of A's portfolio is better than the expected growth rate of B's portfolio?