## What Is Modern Portfolio Theory (MPT)?

Modern portfolio theory (MPT) is a theory on how risk-averse investors can construct portfolios to maximize expected return based on a given level of market risk. Harry Markowitz pioneered this theory in his paper "Portfolio Selection," which was published in the Journal of Finance in 1952. He was later awarded a Nobel Prize for his work on modern portfolio theory.

### Key Takeaways

- Modern portfolio theory (MPT) is a theory on how risk-averse investors can construct portfolios to maximize expected return based on a given level of market risk.
- MPT can also be used to construct a portfolio that minimizes risk for a given level of expected return.
- Modern portfolio theory is very useful for investors trying to construct efficient portfolios using ETFs.
- Investors who are more concerned with downside risk than variance might prefer post-modern portfolio theory (PMPT) to MPT.

#### Modern Portfolio Theory (MPT)

## Understanding Modern Portfolio Theory (MPT)

Modern portfolio theory argues that an investment's risk and return characteristics should not be viewed alone, but should be evaluated by how the investment affects the overall portfolio's risk and return. MPT shows that an investor can construct a portfolio of multiple assets that will maximize returns for a given level of risk. Likewise, given a desired level of expected return, an investor can construct a portfolio with the lowest possible risk. Based on statistical measures such as variance and correlation, an individual investment's performance is less important than how it impacts the entire portfolio.

MPT assumes that investors are risk-averse, meaning they prefer a less risky portfolio to a riskier one for a given level of return. As a practical matter, risk aversion implies that most people should invest in multiple asset classes.

The expected return of the portfolio is calculated as a weighted sum of the individual assets' returns. If a portfolio contained four equally weighted assets with expected returns of 4, 6, 10, and 14%, the portfolio's expected return would be:

(4% x 25%) + (6% x 25%) + (10% x 25%) + (14% x 25%) = 8.5%

The portfolio's risk is a complicated function of the variances of each asset and the correlations of each pair of assets. To calculate the risk of a four-asset portfolio, an investor needs each of the four assets' variances and six correlation values, since there are six possible two-asset combinations with four assets. Because of the asset correlations, the total portfolio risk, or standard deviation, is lower than what would be calculated by a weighted sum.

## Benefits of Modern Portfolio Theory (MPT)

MPT is a useful tool for investors trying to build diversified portfolios. In fact, the growth of exchange traded funds (ETFs) made MPT more relevant by giving investors easier access to different asset classes. Stock investors can use MPT to reduce risk by putting a small portion of their portfolios in government bond ETFs. The variance of the portfolio will be significantly lower because government bonds have a negative correlation with stocks. Adding a small investment in Treasuries to a stock portfolio will not have a large impact on expected returns because of this loss reducing effect.

Similarly, MPT can be used to reduce the volatility of a U.S. Treasury portfolio by putting 10% in a small-cap value index fund or ETF. Although small-cap value stocks are far riskier than Treasuries on their own, they often do well during periods of high inflation when bonds do poorly. As a result, the portfolio's overall volatility is lower than one consisting entirely of government bonds. Furthermore, the expected returns are higher.

Modern portfolio theory allows investors to construct more efficient portfolios. Every possible combination of assets that exists can be plotted on a graph, with the portfolio's risk on the X-axis and the expected return on the Y-axis. This plot reveals the most desirable portfolios. For example, suppose Portfolio A has an expected return of 8.5% and a standard deviation of 8%. Further, assume that Portfolio B has an expected return of 8.5% and a standard deviation of 9.5%. Portfolio A would be deemed more efficient because it has the same expected return but lower risk.

It is possible to draw an upward sloping curve to connect all of the most efficient portfolios. This curve is called the efficient frontier. Investing in a portfolio underneath the curve is not desirable because it does not maximize returns for a given level of risk.

Most portfolios on the efficient frontier contain ETFs from more than one asset class.

## Criticism of Modern Portfolio Theory (MPT)

Perhaps the most serious criticism of MPT is that it evaluates portfolios based on variance rather than downside risk. Two portfolios that have the same level of variance and returns 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 minimizing downside risk instead of variance.