Kelly vs. Markowitz Portfolio Optimization
In my book, I described a very simple and elegant formula for determining the optimal asset allocation among N assets:
F=C-1*M (1)
where F is a Nx1 vector indicating the fraction of the equity to be allocated to each asset, C is the covariance matrix, and M is the mean vector for the excess returns of these assets. Note that these “assets” can in fact be “trading strategies” or “portfolios” themselves. If these are in fact real assets that incur a carry (financing) cost, then excess returns are returns minus the risk-free rate.
Notice that these fractions, or weights as they are usually called, are not normalized – they don’t necessarily add up to 1. This means that F not only determines the allocation of the total equity among N assets, but it also determines the overall optimal leverage to be used. The sum of the absolute value of components of F divided by the total equity is in fact the overall leverage. Thus is the beauty of Kelly formula: optimal allocation and optimal leverage in one simple formula, which is supposed to maximize the compounded growth rate of one’s equity (or equivalently the equity at the end of many periods).
However, most students of finance are not taught Kelly portfolio optimization. They are taught Markowitz mean-variance portfolio optimization. In particular, they are taught that there is a portfolio called the tangency portfolio which lies on the efficient frontier (the set of portfolios with minimum variance consistent with a certain expected return) and which maximizes the Sharpe ratio. Left unsaid are
- What’s so good about this tangency portfolio?
- What’s the real benefit of maximizing the Sharpe ratio?
- Is this tangency portfolio the same as the one recommended by Kelly optimal allocation?
Based on popular demand, I have revised the dates for my online Mean Reversion Strategies workshop to be August 27-29.
Source: http://epchan.blogspot.com/2014/08/kelly-vs-markowitz-portfolio.html
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