In which random portfolios are used as the vehicle for portfolio optimization.
The author is William Shaw. The paper goes by the succinct title of “Portfolio Optimization for VAR, CVaR, Omega and Utility with General Return Distributions: A Monte Carlo Approach for Long-Only and Bounded Short Portfolios with Optional Robustness and a Simplified Approach to Covariance Matching”.
The most interesting part of the paper to me is the discussion on generating random portfolios.
However, the main thrust of the paper is using random portfolios to find an optimal portfolio. The process is to generate a large number of random portfolios and use the one with the best objective as the optimal portfolio. The probability distribution of the random portfolios can have a big effect on the quality of the resulting optimal portfolio.
There is a substantial amount of commonality between what is described in the paper and the Portfolio Probe software.
They both use random algorithms to do portfolio optimization. This opens the door for both arbitrary utilities and arbitrary constraints. It tends to eliminate the urge to formulate the problem for mathematical niceties rather than practical reality.
The most important difference in my opinion is that the paper merely uses random portfolios as a means to an end. I see random portfolios as the main attraction — a tool that allows us to look deeply into markets.
The paper includes optimization with scenarios. For some applications this is a very good thing to do, but not a possibility in Portfolio Probe.
Portfolio Probe doesn’t allow control over the distribution of random portfolios as in the paper, but more general constraints are allowed.
The algorithm for optimization in Portfolio Probe is much more sophisticated than in the paper — it will get better answers than the paper’s algorithm for the same amount of computational effort.