Modern Portfolio Theory (MPT)
The Modern Portfolio Theory is a mathematical approach to constructing efficient portfolios that help investors minimize risk for a given level of returns or maximize returns for a given level of risk. Its popularity has been foundational to the development of passive investing and robo-advisory.
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Marguerita M. Cheng, CFP®, CRPC®, RICP®
Marguerita M. Cheng, CFP®, CRPC®, RICP®, is the chief executive officer at Blue Ocean Global Wealth. As a Certified Financial Planner Board of Standards Ambassador, Marguerita educates the public, policymakers and media about the benefits of competent and ethical financial planning. She is a past spokesperson for the AARP Financial Freedom campaign.Read More
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Thomas J. Brock, CFA®, CPA
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- Updated: January 30, 2023
- 10 min read time
- This page features 4 Cited Research Articles
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There are two elements that are crucial to successful investing, risk and return. Prior to the development of the Modern Portfolio Theory, there was an uneven focus on returns — to the near exclusion of risk. Investors in the 1930s were primarily concerned about buying stocks at a price lower than their intrinsic value and then holding onto them until their market prices exceeded their intrinsic values. Then, by selling them, gains could be realized.
While this approach worked (and still does), risk was not a primary concern. Most investors did not have an objective way to measure the risk of an investment or a portfolio of investments and factor it into their investment choices.
This changed in 1952, when economist Harry Markowitz published an article titled “Portfolio Selection” in the Journal of Finance. The ideas he explored laid the foundation for the Modern Portfolio Theory. Markowitz was formally acknowledged for his groundbreaking work by winning the 1990 Nobel Prize in Economic Sciences.
In this article, we will explore what the modern portfolio theory is about and how investors have been using it to make investment decisions. It is designed to broaden your base of knowledge and help you optimize your personal finances and investment plan.
What Is Modern Portfolio Theory (MPT) and How Does It Work?
So, what does the Modern Portfolio Theory encompass? The best way to answer this question is to consider its various aspects.
Investors Are Risk Averse
The first and foundational element of MPT is Markowitz’s discovery that the average investor is risk averse. For a given level of returns, he deduced, the average investor will choose a less risky portfolio of investments over a riskier one.
In other words, the goal of the investor is to minimize risk for a given level of returns or maximize returns for a given level of risk.
This begs a couple questions. How can investors minimize risk for a given level of returns? Is there a way investors can earn the same returns while minimizing risk?
Diversification and Risk Minimization
Markowitz found that the risk associated with a portfolio of non-positively correlated assets is lower than the risk of holding any single asset in that portfolio.
When two assets are positively correlated, it means that they move in the same direction. If asset A rises, B rises and vice versa. Investors often see this correlation with stocks that are in the same industry and employ the same business model. They tend to rise and fall together — they are positively correlated.
On the other hand, some stocks or assets have zero correlation, meaning the fall or rise of one happens and there is no similar movement of the other. Meanwhile, some have a negative correlation — when one falls, the other rises and vice versa.
Consider a portfolio containing two, equally weighted assets — A and B — which are positively correlated. Asset A drops by 10%, and asset B drops by 20%. Here, the entire portfolio will drop by an average of 15%.
However, if A and B are negatively correlated and B rises by 20% when A drops by 10%, the entire portfolio will rise by an average of 5%.
And if A and B have zero correlation and B does not move at all, while A falls by 10%, the entire portfolio will only fall by an average of 5%.
In all three scenarios, A fell by 10%. However, as outlined below, the portfolio impact varied, depending on the degree of correlation between the assets.
- The decline in the positively correlated portfolio is 15%, which is greater than the decline in asset A alone (10%).
- The decline in the zero-correlated portfolio is 5%, which is less than that of asset A.
- With the negatively correlated portfolio, there was an increase of 5%, despite the 10% decline of A.
From these scenarios, we see that investors can minimize risk by avoiding positively correlated assets and constructing a portfolio of zero-correlated or negatively-correlated assets.
This beneficial approach to investing is known as diversification. It helps investors minimize systematic risk and limit their downside exposure.
The Efficient Frontier
The efficient frontier, or portfolio frontier, is a set of portfolios that can achieve the goal of a risk-averse investor – maximizing return for a given level of risk.
According to Markowitz, you can achieve this goal by holding one of many different portfolios, all of which,lie on the efficient frontier. The chart below illustrates this concept, with risk along the horizontal axis and return along the vertical axis risk.
The two dots that lie exactly on the efficient frontier line represent two portfolios where return is maximized for a given level of risk or risk is minimized for a given level of return. The other dots represent inefficient investments.
The Optimal Portfolio
While there are multiple efficient portfolios that lie on the efficient frontier, Markowitz believes that one of them is the optimal portfolio. This is the portfolio that lies where the capital allocation line (CAL) intersects the efficient frontier.
The CAL is a line that shows the risk-return trade-off that exists for all investment assets, given the existence of a risk-free asset. The slope of the CAL is also called the Sharpe ratio, which is a measure of the risk-adjusted returns of an asset or portfolio.
The Sharpe ratio is the highest at the point where the CAL intersects with the efficient frontier. Therefore, that point represents the optimal portfolio.
Measuring Risk and Return
The expected return of an asset is calculated by summing its potential returns multiplied by the chances of those returns occurring.
For example, if there is 60% chance an asset returns 10% and 40% chance it returns 5%, the expected return will be 8% (60%*0.10 + 40%*0.05).
The expected return of a portfolio is the sum of the weight of the individual assets multiplied by their expected returns. Suppose a portfolio has assets A and B, constituting 60% and 40% of the entire investment, respectively. If their expected returns are 8% and 10% respectively, then the expected return of the entire portfolio is 8.8% (60%*0.08 + 40%*0.10).
MPT uses standard deviation as a measure of risk. The standard deviation of an asset is the degree to which its returns diverge or vary from the average return.
The standard deviation of a portfolio is a formula that takes into account the standard deviations of the individual assets, their weights in the portfolio and their correlations.
Let’s consider a modern portfolio theory example to see how it works. Suppose we have two portfolios with the following results:
Expected return: 10%
Standard deviation: 7%
Expected return: 12%
Standard deviation: 7%
In this scenario, Markowitz believes every investor will choose Portfolio B since they can get 2% more returns with the same level of risk as Portfolio A.
How Does Modern Portfolio Theory Work for Investors?
How do all the technical details above translate into an investment plan for real-world investors?
Broadly Diversified Portfolio and Passive Investing
Thanks to MPT, investors can create an efficient or optimal portfolio that matches their risk profile, and they can continually invest in such a portfolio without concern for near-term market volatility. This has paved the way for robo-advisory services and passive investing.
- 40% investment in U.S. stocks
- 20% investment in emerging markets stocks
- 10% investment in REITs
- 10% investment in developed market stocks (excluding U.S.)
- 20% investment in US bonds
- 40% in Vanguard S&P 500 Index ETF
- 20% in iShares Core MSCI Emerging Markets ETF
- 10% in Vanguard Real Estate ETF
- 10% in Schwab International Equity ETF
- 20% in Vanguard Total Bond Market ETF
Due to movements in the market, the composition of the portfolio could fluctuate with time. As a result, robo-advisors will regularly rebalance the portfolio to reestablish the target asset allocation of the efficient portfolio.
According to the MPT, an efficient portfolio can contain just two assets. Consequently, some investors achieve their own return maximization and risk minimization goals with just two index funds or ETFs.
Using the example above, this might be 60% in Vanguard S&P 500 Index ETF and 40% in Vanguard Total Bond Market ETF for a moderate-risk investor. The allocation will change for the conservative and the growth investor.
Pros and Cons of Modern Portfolio Theory
Before adopting any financial strategy, it’s imperative to understand the associated risks and benefits.
- Risk Minimization
- MPT minimizes risk by enabling investors to choose efficient portfolios with lower risk for the same level of returns. Before MPT, many investors didn’t understand the risk of their investment portfolios — it was all about the returns. This meant that many investors assumed elevated levels of risk without appropriate return potential. With MPT, investors can now understand and quantify the risk of their portfolios in order to minimize it.
- Return Maximization
- Similarly, investors can now maximize returns for a given level of risk. By understanding risk-adjusted returns, investors can establish efficient portfolios that provide the highest possible returns for various levels of risk.
- Foundation of Passive Investing
- Since there are many efficient portfolios on the efficient frontier, each investor can select a portfolio that aligns with his or her risk capacity and tolerance. This concept is foundational to passive investing, which is a hands-off, low-cost method of investing that enables investors to comfortably embrace a relatively long-term horizon.
- Useful for the Average Investor
- With MPT and the advent of passive investing and robo-advisors, investing has become simpler and more common for a broad swath of people, including many that lack technical knowledge.
- It’s Only a Model
- Every economic model is based on assumptions. MPT assumes a rational investor who wants more returns and less risk. It also assumes that more than one portfolio can be efficient. However, these assumptions do not always reflect reality.
- The Measure of Risk
- Some investment experts believe standard deviation is not the best measure of risk. For these experts, the risk of losing money (downside risk) is the most appropriate measure of risk, not the degree to which an asset’s return could differ from its expected return.
- The Measure of Return
- Expected return calculations depend on the historical returns of an asset. While historical returns are all we have to predict the future, there is no guarantee the future will be like the past. Additionally, MPT does not take transaction costs — brokerage fees, commissions, bid-ask spreads, etc. — into account.
What Are Some Alternatives to Modern Portfolio Theory?
MPT is widely embraced and utilized by a majority of investment professionals, but alternative theories do exist. The best-known alternative is the Post-Modern Portfolio Theory (PMPT).
Brian M. Rom and Kathleen Ferguson designed this system in 1991. PMPT reflects all the tenets of MPT, except it defines risk as the probability of losing money, rather than the extent to which returns could vary from the expected return.
In essence, PMPT uses the standard deviation of negative returns (the risk of downside deviation) rather than the ordinary standard deviation. Also, instead of using the Sharpe ratio (risk-adjusted returns calculated with standard deviation), it uses the Sortino ratio, which considers only downside deviation.
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4 Cited Research Articles
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- ATB Financial. (2022, January 12). The difference between risk tolerance and risk capacity. Retrieved from https://www.atb.com/personal/good-advice/saving-and-investing/the-difference-between-risk-tolerance-and-risk-capacity/
- Corporate Finance Institute. (2022, February 5). Sortino Ratio. Retrieved from https://corporatefinanceinstitute.com/resources/knowledge/trading-investing/sortino-ratio-2/
- Corporate Finance Institute. (2022, January 21). Systematic Risk. Retrieved from https://corporatefinanceinstitute.com/resources/knowledge/finance/systematic-risk
- Wiley Online Library. (1952, March). Portfolio Selection. Retrieved from https://onlinelibrary.wiley.com/doi/full/10.1111/j.1540-6261.1952.tb01525.x