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Peter Westfall is a professor of statistics at Texas Tech University. He has more than 30 years of statistics experience including teaching, research, writing, and consulting. Peter teaches and performs statistical research with a focus on advanced statistical methods, regression analysis, multivariate analysis, mathematical statistics, and data mining. He specializes in using statistics in investing, technical analysis, and trading.
Investopedia / Matthew Collins
The modern portfolio theory (MPT) is a practical method for selecting investments in order to maximize their overall returns within an acceptable level of risk.
American economist 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.
A key component of the MPT theory is diversification. Most investments are either high risk and high return or low risk and low return. Markowitz argued that investors could achieve their best results by choosing an optimal mix of the two based on an assessment of their individual tolerance to risk.

The modern portfolio theory argues that any given investment's risk and return characteristics should not be viewed alone but should be evaluated by how it affects the overall portfolio's risk and return. That is, an investor can construct a portfolio of multiple assets that will result in greater returns without a higher level of risk.
As an alternative, starting with a desired level of expected return, the investor can construct a portfolio with the lowest possible risk that is capable of producing that return.
Based on statistical measures such as variance and correlation, a single investment’s performance is less important than how it impacts the entire portfolio.
The 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 returns of the individual assets. 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 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.
The MPT is a useful tool for investors who are trying to build diversified portfolios. In fact, the growth of exchange-traded funds (ETFs) made the MPT more relevant by giving investors easier access to a broader range of asset classes.
For example, stock investors can reduce risk by putting a 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, the 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 it would be if it consisted entirely of government bonds. Moreover, the expected returns are higher.
The modern portfolio theory allows investors to construct more efficient portfolios. Every possible combination of assets 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 combinations for a portfolio.
For example, suppose Portfolio A has an expected return of 8.5% and a standard deviation of 8%. 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.
Perhaps the most serious criticism of the MPT is that it evaluates portfolios based on variance rather than downside risk.
That is, 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. Another could have that variance because of rare but spectacular declines. Most investors would prefer frequent small losses, which would be easier to endure.
The post-modern portfolio theory (PMPT) attempts to improve on modern portfolio theory by minimizing downside risk instead of variance.
The modern portfolio theory (MPT) was a breakthrough in personal investing. It suggests that a conservative investor can do better by choosing a mix of low-risk and riskier investments than by going entirely with low-risk choices. More importantly, it suggests that the more rewarding option does not add additional overall risk. This is the key attribute of portfolio diversification.
The post-modern portfolio theory (PMPT) does not contradict these basic assumptions. However, it changes the formula for evaluating risk in an investment in order to correct what its developers perceived as flaws in the original.
Followers of both theories use software that relies on either MPT or PMPT to build portfolios that match the level of risk that they seek.

The modern portfolio theory can be used to diversify a portfolio in order to get a better return overall without a bigger risk.
Another benefit of the modern portfolio theory (and of diversification) is that it can reduce volatility. The best way to do that is to choose assets that have a negative correlation, such as U.S. treasuries and small-cap stocks.
Ultimately, the goal of the modern portfolio theory is to create the most efficient portfolio possible.
The efficient frontier is a cornerstone of the modern portfolio theory. It is the line that indicates the combination of investments that will provide the highest level of return for the lowest level of risk.
When a portfolio falls to the right of the efficient frontier, it possesses greater risk relative to its predicted return. When it falls beneath the slope of the efficient frontier, it offers a lower level of return relative to risk.
Harry Markowitz. "Portfolio Selection." The Journal of Finance, Volume 7, No. 1, 1952, Pages 77-91.
The Nobel Prize. "This Year's Laureates Are Pioneers In The Theory of Financial Economics and Corporate Finance." Accessed Sept. 10, 2021.
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