How Is Correlation Used in Modern Portfolio Theory?

Modern portfolio theory (MPT) asserts that an investor can achieve diversification and reduce the risk of losses by reducing the correlation between the returns of the assets selected for the portfolio. The goal is to optimize the expected return against a certain level of risk.

The modern portfolio theorist recommends that an investor measure the correlation coefficients between the returns of various assets in order to strategically select those that are less likely to lose value at the same time. That means determining to what extent the prices of the assets tend to move in the same direction in response to macroeconomic trends.

Perfect Correlation

MPT is a mathematics-based system for selecting investments that, in combination, will provide the best returns for a given level of risk.

The theory looks for the best correlation between the expected return and the expected volatility of various potential investments. The optimal risk-reward relationship was titled the efficient frontier by economist Harry Markowitz, who introduced modern portfolio theory in 1952.

A portfolio is known as “Markowitz-efficient” if its selection of assets has the highest expected return at a given level of risk.

In MPT, the efficient frontier is where the investor will find the combination of assets that offers the highest possible return for a chosen level of risk. These assets demonstrate the optimal correlation between risk and return.

The Correlation Scale

Correlation is measured on a scale of -1.0 to +1.0:

• If two assets have an expected return correlation of 1.0, that means they are perfectly correlated. If one gains 5%, the other gains 5%. If one drops 10%, so does the other.
• A perfectly negative correlation (-1.0) implies that one asset’s gain is proportionally matched by the other asset’s loss.
• A zero correlation indicates the two assets have no predictive relationship.

MPT stresses that investors should look for a consistently uncorrelated (near zero) pool of assets to limit risk. In practical terms, that virtually guarantees a diversified portfolio.

Criticisms of Perfect Correlation Theory

One of the major criticisms of Markowitz’s theory lies in its assumption that the correlation between assets is fixed and predictable. In the real world, the systematic relationships between different assets do not remain constant.

That means that MPT becomes less useful during times of uncertainty, which is exactly when investors need the most protection from volatility.

Others assert that the variables used to measure correlation coefficients are themselves faulty and the actual risk level of an asset can be miscalculated. Expected values are mathematical expressions of the implied covariance of future returns, and not historical measurements of real returns.