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Modern Portfolio Theory: What Is It & How Is It Used?

Modern Portfolio Theory (MPT) is a mathematical justification for building a portfolio of assets maximizing returns while considering risk.

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Even half a century after modern portfolio theory was introduced by Nobel Prize winner and economist Harry Markowitz, the theoretical model continues to be a pinnacle of multiple investing strategies.

Meanwhile, the launch of automated passive investing platforms and robo-advisors has brought an increased interest in knowing the details of this theoretical model. In fact, many robo advisors like Betterment, Wealthfront, and Ellevest use Modern Portfolio Theory today to create an automated asset allocation, taking into consideration risk tolerance and financial needs.

With that in mind, the following article aims to provide more information about Markowitz’s assumptions and propositions so you can learn how to apply his model to improve your portfolio allocation techniques.

What Is Modern Portfolio Theory?

Modern portfolio theory (MPT) is a model that aims to illustrate and identify the optimal combination between two or more asset classes to maximize profits given a certain level of risk.

This model was first proposed by the American economist Harry Markowitz in 1952 and he received a Nobel Prize for it 38 years later as a result of his work, which has served as the foundation for many other studies about how capital can be allocated optimally to maximize portfolio returns.

In essence, MPT proposes that investors can increase the return produced by their portfolios by analyzing the historical performance and risk. In other words, MPT is a mathematical justification to allocate assets in a portfolio to maximize returns for a given level of risk.

Meanwhile, MPT assumes that the following statements are true for the financial markets:

  • Asset returns follow a normal distribution;
  • Investors are entirely rational and avoid unnecessary risks;
  • Taxes and trading expenses are zero;
  • There is a consensus on the expected returns to be realized from all asset classes and instruments; and
  • Investors will always seek to maximize the returns of their portfolios.
Pro Tip: Modern Portfolio Theory states that investors are able to reduce portfolio risk simply by diversifying holdings across a number of instruments that are not correlated.

How Does Modern Portfolio Theory Work?

The first step to build a model that follows modern portfolio theory is to calculate the average historical return and risk of each asset class or instrument that comprise the portfolio.

For increased accuracy, this analysis is performed for periods of 20 or more years to smooth potential one-time above-average results. Both returns and standard deviations are analyzed on an annual basis and they are expressed in percentage or decimal terms.

Once that data is collected, the investor will now build the MPT model by establishing different percentages for each of the assets included to establish the lowest risk level at which returns are maximized.

An Efficient Frontier
Source: Young Research & Publishing

The graph above is an example of what an MPT model looks like. In the graph, returns are displayed in the Y-axis while risk — measured as the standard deviation of results as a percentage of the average — is displayed in the X-axis.

The graph shows that the optimal allocation for a portfolio composed of stocks (S&P 500 index) and bonds (Merryl Lynch 7-10 year US Treasuries Index) is 75% bonds and 25% stocks since that particular mix generates the highest possible return at the lowest level of risk.

From that point forward, higher returns can only be achieved by exposing the portfolio to a higher level of risk. This is known as the efficient frontier.

​​To illustrate how to calculate the expected return in a portfolio let’s use an example of a two-asset portfolio (i.e. Asset A and Asset B). 

Asset A = $600,000 and it has an expected return of 8%

Asset B = $400,000 and it has an expected return of 6%

Portfolio Worth = $1,000,000

The expected return of the portfolio is calculated as a weighted sum of the individual assets’ returns. If our portfolio has two equally weighted assets with expected returns of 8 and 12% respectively, the portfolio’s expected return would be:

Expected Return A = ($600,000 / $1,000,000) * 8% = 4.8%

And you do the same for the second asset:

Expected Return B = ($400,000 / $1,000,000) * 6% = 2.4%

So now you add the expected returns of both assets, and the entire portfolio can expect a return of 7.2%.

The portfolio’s risk, on the other hand, is calculated using the variances of each asset and the correlation of each pair of assets.

What Is the Efficient Frontier?

The efficient frontier is another innovative and enlightening concept of MPT that highlights the optimal portfolio allocation that produces the highest returns for a given level of risk.

The efficient frontier starts at the optimal allocation — highest return at lowest possible risk — and ends at the point in which one of the asset classes that comprises the portfolio is maxed to 100% of it.

Any allocation mix below the efficient frontier is considered sub-optimal since the same return produced by such allocation can be achieved at a lower risk by following the percentages illustrated by the efficient frontier.

How to Use Modern Portfolio Theory in Your Portfolio

Modern portfolio theory can be applied to any portfolio as long as the investor is willing to do his or her research. An MPT model can be built by identifying the average historical return and risk produced by a given asset class such as equities, bonds, precious metals, commodities, or cryptocurrencies, or it can be analyzed on an individual scale for a particular security such as gold, oil, or 10-year US Treasury bonds.

Once the investor analyzes which instruments he or she would like to incorporate into the portfolio, a combination of different percentages assigned to each asset class or individual security must be made to identify the optimal allocation — the point at which returns are maximized at the lowest possible risk.

Some brokerage firms and screening tools offer advanced software and tools that rely on long-dated databases to easily build MPT models that support multiple asset classes and securities. One example of this is Optifolio.

Using these tools will reduce the time-consuming task of compiling the data yourself as that could take weeks of work.

Advantages of Modern Portfolio Theory

  • Time-tested portfolio allocation tool that relies on objective data to determine the optimal mix of asset classes.
  • Easy-to-understand theoretical foundation that relies on two simple variables: historical returns and risks.
  • Many studies have been made to further enrich the practical uses of MPT in investing.

Disadvantages of Modern Portfolio Theory

  • Historical data must go back at least 20 years to avoid distortions in average returns and standard deviation by one-time, off-the-charts readings.
  • Even though the theory that backs MPT is fairly simple, building an MPT model in practice can be very time-consuming unless the user relies on advanced software, which is often expensive.
  • MPT models cannot be built for relatively new asset classes such as cryptocurrencies as historical data is insufficient to generate reliable averages.
  • Securities and asset classes whose performance does not follow a normal distribution could be unsuitable for MPT modeling as average returns and standard deviations could turn out to be unreliable.
Pro Tip: Modern Portfolio Theory recognizes two types of investment risk, systematic risk— inherent to the markets such as changes to interest rates and recessions—and unsystematic risk—inherent to each security, such as poor sales, lower earnings, changes in management, etc.

What Are the Alternatives to Modern Portfolio Theory?

Behavioral finance has emerged as the strongest rival of modern portfolio theory. Different from MPT, behavioral finance assumes that markets are dominated by emotional participants rather than objective players and this subjective nature is what influences the price action rather than fundamentals.

Moreover, behavioral finance also assumes that investors are not as rational as MPT suggests and, therefore, markets are not necessarily as efficient as MPT proposes.

Instead of studying objective data, behavioral finance suggests that investors should analyze how sentiment toward different asset classes and securities changes over time to draft potential directional forecasts for the performance of these assets.

In response to the growing adoption of this approach to portfolio management, many brokerage firms have incorporated sentiment trackers to their platforms to help investors in analyzing how market participants “feel” about a certain instrument or asset class as a potential indication of how the price could behave in the near future.

Final Thoughts

Modern portfolio theory has been the pinnacle of the asset management industry for decades due to its objective approach to portfolio design and management. However, like any other theoretical model, MPT has its flaws, including a set of assumptions that can be quite unrealistic.

That said, investors should learn how MPT works as the model highlights the benefits of portfolio diversification while it also allows investors to estimate the best potential mix of asset classes and securities that could help them in boosting their portfolio returns over time.

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