# Pitfalls of Modern Portfolio Theory

investing
October 4, 2020

Modern Portfolio Theory (MPT) is one of the most influential theories in investment, which explains how diversification can improve return and minimize risk. Modern portfolio theory highlights the role of correlations between assets and the benefits of splitting investments into assets that do not correlate with each other. There is merit in MPT, and it has been applied effectively in practice. However, there are some shortcomings with the theory due to the way risk is quantified, and the heavy reliance on historical performance of assets.

Here is a list of the two most serious criticisms of modern portfolio theory.

## Reliance on historical performance

Asset correlations and historical returns are used in modern portfolio theory to find the optimal portfolio. This places a large reliance on historical performance data. A common adage in investing is that "Past performance is no guarantee of future results." Assets can perform in the future differently than from the past, and both the returns and relationships (correlations) between assets can change.

On the other hand, although historical performance does not predict future results with certainty, historical performance is often the best indicator of future results. When betting on horse races, you would have better luck with horses that have a track record of winning compared to horses that normally finish last.

## Variance is not the right measure of risk

Modern Portfolio Theory (MPT) relies on the variance, and the correlation between assets, which are statistical measures computed from historical data. One of the major criticisms is that variance is not the right measure to use for defining risk, since it only measures the variation in the asset's return, and does not make a distinction between gains and losses.

The formula for variance is:

$\text{variance} = \dfrac{1}{n} \sum_{n=1}^{n} (y_i - \bar{y})^2$

To compute the variance, you need to take a sample of $n$ returns, find their average $\bar{y}$, then take the average of the deviations of your samples from the average. If you have data points [5%, -10%, 5%] for three months, the variance is the same as with [15%, 0%, 15%], although the second case should be viewed as less risky. In fact, in the second case, there was no loss in any month.

When two portfolios have the same level of variance and returns, they are considered equally desirable under modern portfolio theory. One portfolio may have that variance because of frequent small losses. In contrast, the other could have that variance because of rare spectacular declines. Most investors would prefer frequent small losses, which would be easier to endure.

Post-modern portfolio theory (PMPT) attempts to improve on modern portfolio theory by using the downside risk instead of the variance, which is a measure for the risk of loss.

## Conclusion

Although the core ideas behind of modern portfolio theory are very useful, MPT is limited by measures of risk and return that do not always reflect the realities of the markets. It is important to be aware of these limitations when considering a quantitatively derived portfolio allocation. Your investment strategy should carefully consider the investment risks that are relevant to you and include a good amount of diversification and proper asset allocation.

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