Portfolio optimization is a mathematical process of assigning the proportions of various asset classes or investment styles to be held in a portfolio, in a way as to construct the most efficient portfolio, given the expected rate of returns, expected return dispersion, and some other measures of risk. Portfolio optimization takes place in two stages, i.e., optimizing weights of the assets classes to be held in the portfolio, and optimizing weights of assets within each asset class.
Approaches to Portfolio Optimization
Since we live in a world that never lacks mathematics experts and professors who are experienced with optimization programs, there are a variety of portfolio optimization approaches and mathematical tools used in optimization, such as mean-variance portfolio optimization (quadratic programming), conditional Value-at-Risk (CVaR) optimization (linear programming), general nonlinear optimization (differential evolution algorithm), and many other approaches utilizing nonlinear programming, mixed integer programming, and meta-heuristic methods.
MPT is the most classical portfolio optimization approach. It involves defining an investment universe based on the return and standard deviation of assets, and then choosing the mix of assets that will achieve the best portfolio efficiency.
The Utilization of Portfolio Optimizers
In portfolio management practice, portfolio managers and investment advisers utilize and rely on portfolio optimizers, which they believe can determine the viability of a potential asset class mix, test for validity of input assumptions, analyze capital needs, and manage investor expectations. Portfolio optimizers use historical correlations and standard deviations as departure points for developing estimates of future correlations and standard deviations. Once the inputs for expected return, standard deviation, and correlations have been established for each asset class, it is a straightforward mathematical calculation to derive the asset allocations for portfolios on the efficient frontier.
A few popular optimization programs, including the MATLAB Financial Toolbox, provides a suite of mathematical modeling and statistical analysis for performing asset allocation and risk assessment. The Financial Toolbox was designed to have basic features, such as mean-variance and CVaR-based object-oriented portfolio optimization, cash flow analysis, time-series modeling, basic SIA-compliant fixed-income security analysis, Black-Scholes, binomial option pricing, regression and estimation with missing data, GARCH estimation, and simulation. FactSet Research Systems uses Barra Portfolio Optimizer to generate a list of necessary trades to construct an optimal portfolio. Some more advanced features of this optimizer include: 1) it sets limits on weights or turnover to ensure that the optimal portfolio complies with fund mandates; 2) it integrates security ranks or forecasted returns from alpha models.
Dr. Richard Michaud and Robert Michaud at New Frontier Advisors, LLC have developed a different solution to the problem regarding the uncertainty inherent in the inputs used in portfolio optimization. Their approach, “resampled efficiency,” uses a Monte Carlo simulation to create a variety of sets of alternative optimization inputs that are able to address some of the uncertainty inherent in the input estimates. To address this “re-sampling,” Markov Process International (MPI) developed its flagship product, MPI Allocator, which is another quick tool for asset allocation and optimization at both asset-class-level and fund-level construction. MPI Allocator was built with Calibrated Frontiers for re-sampling. Another unique feature is that it allows multiple models to choose from mean-variance optimization, Black-Litterman, downside optimization,and mean-benchmark tracking optimization.
Would Your Portfolio Optimizer Work For You?
Some portfolio managers and investment consultants, including myself at the beginning stage of my career, place far too much faith in the mathematics of portfolio optimization techniques, and those recommendations that result from applying optimization techniques to the portfolios. In fact, investors would benefit greatly from realizing that there is a substantial gap between portfolio theory and practice. Since the basis for most portfolio optimization programs is MPT, which again, suffers from a series of flaws, portfolio optimizers have inherent limitations:
- Asset classes are not well defined, nor are they stable. Portfolio optimizers are sensitive to changes in expected returns, standard deviation, and correlations between asset classes.
- Although it is commonly thought that there are universally accepted benchmarks for each investment style, no general consensus exists.
- Investors certainly care about a portfolio’s expected return and the risk/return trade-off, but in reality, they also care about some other factors which were not taken into account by the optimization tools.
- It is highly doubtful that anyone can consistently accurately forecast the previous factors.
- It is unlikely that all rational investors would want to own a portfolio that lies on the efficient frontier.
- Optimization models are incapable of providing forward-looking information with sufficient accuracy.
- Financial market is part of a dynamic economic system that has many complicate feedback processes; multiple extreme events occur more often than the theory suggests that there should be.
- In terms of private assets, many investors have a very strong preference for liquid investments, and they demand compensation in the form of substantially higher expected returns when making an illiquid investment.
References:
- Portfolio Optimization Theory Versus Practice by Roy Ballentine
- Portfolio Optimization by Robert F. Stambaugh, Miller Anderson & Sherrerd Professor of Finance
- Resampled Efficiency Equity Portfolio Optimizer by Richard Michaud and Robert Michaud
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