The concept of balancing portfolio risk and return through asset allocation traces its roots to Modern Portfolio Theory (MPT) developed by Harry Markowitz in the 1950s.64 MPT is a framework for constructing a portfolio that maximizes expected return for a given level of risk. The Markowitz formulation brilliantly quantifies the two basic objectives of investing: maximizing expected return and minimizing risk.
The core concepts include:
Reducing risk by investing in a variety of assets.
The set of optimal portfolios offering the highest expected return for a defined level of risk.
Balancing potential returns against the risk of those returns.
The mathematical foundation of MPT is based on the mean-variance optimization, where the portfolio’s expected return is the weighted sum of the individual assets’ expected returns, and the portfolio’s risk is the variance of the portfolio’s return.
MPT quantifies the benefits of diversification and provides a framework for selecting an optimal portfolio based on an investor’s return objectives and risk tolerance.
The Markowitz model significantly advanced our understanding of portfolio diversification by examining the number of securities in a portfolio and their covariance relationships. This model illustrates how diversification impacts portfolio risk and reward. Despite its theoretical appeal, mean-variance (MV) optimization, a core component of the Markowitz model, is challenging to implement practically. The asset weights in MV optimization are highly sensitive to input values, which are difficult to estimate accurately. Furthermore, this model does not allow investors to incorporate their views on relative asset performance or their confidence in their expected returns.
Mathematical risk measurements are useful only to the extent that they reflect investors’ true concerns. Minimizing a variable that is not relevant in practice is pointless. Variance, a symmetric measure, counts abnormally high returns as just as risky as abnormally low returns. However, the psychological phenomenon of loss aversion suggests that investors are more concerned about losses than gains, indicating that our intuitive concept of risk is fundamentally asymmetric. Other risk measures, such as coherent risk measures, might better reflect investors’ true preferences.
MPT has also been criticized for assuming that returns follow a Gaussian distribution and for not accounting for asymmetry in asset correlation.
More recently, Nassim N. Taleb has also criticized modern portfolio theory on this ground, writing:65
After the stock market crash (in 1987), they rewarded two theoreticians, Harry Markowitz and William Sharpe, who built beautifully Platonic models on a Gaussian base, contributing to what is called Modern Portfolio Theory. Simply, if you remove their Gaussian assumptions and treat prices as scalable, you are left with hot air. The Nobel Committee could have tested the Sharpe and Markowitz models—they work like quack remedies sold on the Internet—but nobody in Stockholm seems to have thought about it.
A few studies66 have argued that “naive diversification”, splitting capital equally among available investment options, might have advantages over MPT in some situations.