English Portfolio Management

Mean-variance optimization: The most widely used investment model

The mean–variance model is the foundation for making asset allocation decisions for long-term horizon

Every investor follows an approach, with no formalization for some beginners to very complex models for the bigger alternative managers or sovereign funds. In any case, making the underlying assumptions and consequences of your investment decisions explicit is key for your success.

New investors should note the following:

  • The mean-variance approach to portfolio analysis is the primary model to invest between different assets by considering the trade-off between risk and return (e.g. equities have more risk/variance than bonds but a higher expected return);
  • By adding securities when making asset allocation decisions, the investor will gain diversifiation benefits without scarifying return;
  • If you are delegating decisions to robo-advisors, be aware that most use the mean–variance framework as the theoretical foundation of their asset allocation. Examples include Wealthfront and Betterment.

Interested readers or intermediate/advanced investors will find some further information below:

Since the theoretical basis exhibited by Markowitz in 1952, the mean–variance optimization approach has been refined over time. It is the default template for investors striving for diversification and having accepted the concepts of efficiency in the financial markets and mean reversion. In its simple form, you need to define your views on expected returns, on the corresponding risks and on your time horizon. This model provides the following advantages:

  • It helps in understanding the risk–return trade-off, in providing informative guideline for analyzing optimal allocations and in gaining insights into sensitivities to inputs or assumptions;
  • With the use of the proper investment vehicles (e.g. passive ETFs), implementation costs can be relatively low!

There are however several limitations to the model (in particular regarding the estimation of the input parameters and the portfolio sensitivity to changes in these inputs). Investors can use more or less advanced methods to address these limitations (add more constraints to portfolio weights, reduce the sensitivity of the estimates or control downside risk with measures such as conditional value at risk). Every investor should at least perform some basic simulations: This will support the assessment of the sensitivity of inputs to multiple regimes and help finding the portfolio that performs well under many scenarios.

In a nutshell, you can use the mean–variance model as the foundation of portfolio allocation for analyzing the trade-off between risk and return and for gaining diversification benefits. It should be your starting point for making asset allocation decisions for long-term horizon. You may then use other techniques, adopt other models and perform further manual adjustments before arriving at your final investment decision.

"Mean–Variance Optimization for Asset Allocation." J. H. Kim, Y. Lee, W. C. Kim, and F. J. Fabozzi. 2021 The Journal of Portfolio Management 47 (5).
“Portfolio Selection.” H. M. Markowitz. 1952 The Journal of Finance 7 (1).