# 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.

- Written By Marguerita M. Cheng, CFP®, CRPC®, RICP®
Marguerita M. Cheng, CFP®, CRPC®, RICP®

Chief Executive Officer of Blue Ocean Global Wealth

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.

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Savannah Hanson
Savannah Hanson

Financial Editor

Savannah Hanson is an accomplished writer, editor and content marketer. She joined Annuity.org as a financial editor in 2021 and uses her passion for educating readers on complex topics to guide visitors toward the path of financial literacy.

Read More - Updated: August 15, 2022
- This page features 4 Cited Research Articles

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 to sell when the market price exceeds the intrinsic value.

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 would change in 1952 when economist Harry Markowitz published a journal article titled “Portfolio Selection” in the Journal of Finance. The ideas explored in that article form the foundation for the Modern Portfolio Theory and Markowitz won the 1990 Nobel Prize in Economic Sciences for his contribution.

In this article, we will explore what the modern portfolio theory is about and how investors have been using it to make investment decisions.

Ultimately, you will gain a better appreciation for a solid and popular investing strategy and consider how it fits into your personal finance 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.

But 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 in one does not affect the other. Meanwhile, some have a negative correlation — when one falls, the other rises and vice versa.

Consider a portfolio containing two assets — A and B — which are positively correlated. If asset A drops by 10%, B can also drop 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 respond to the fall in A, the entire portfolio will only fall by an average of 5%.

Though A fell by 10% in all three scenarios, the fall in the positively correlated portfolio is 15%, which is higher than the fall in asset A alone (10%); the fall in a zero-correlated portfolio is 5%, which is lesser than that of asset A; and a negatively correlated asset rose by 5% even when A fell by 10%.

From these scenarios, we see that investors can minimize risk by avoiding positively correlated assets and investing in a portfolio of zero-correlated or negatively-correlated assets.

The process where investors create such portfolios is called diversification. Diversification helps investors minimize systematic risk by investing in a number of zero-correlated or negatively correlated assets.

### The Efficient Frontier

The efficient frontier, or portfolio frontier, is a set of portfolios that can achieve the goal of risk-averse investors: maximize returns for a given level of risk.

According to Markowitz, they can achieve this goal by holding multiple portfolios (with different combinations of assets). All these efficient portfolios lie on the efficient frontier in a chart, plotting the risk and return of various portfolios.

The two dots that lie exactly on the efficient frontier represent two portfolios where the return is maximized for a certain level of risk or risk is minimized for a certain level of return.

### The Optimal Portfolio

While there are many efficient portfolios — as indicated 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 where the risk-adjusted return is the highest due to the addition of a risk-free asset.

### 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%*0.1 + 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%*0.1).

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 returns.

The standard deviation of a portfolio is a formula that takes into account the standard deviation of the individual assets, their weight in the portfolio and their correlation.

Let’s consider a modern portfolio theory example to see how it works. Suppose we have two portfolios with the following results:

**Portfolio A: **

Expected return: 10%

Standard deviation: 7%

**Portfolio B: **

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.

To summarize so far: MPT is a theory that investors can achieve their goal of minimizing risk for a given level of returns (or maximizing returns for a given level of risk) by investing in a diversified portfolio of zero-correlated or negatively correlated assets.

## 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

With MPT, investors can now create an efficient or optimal portfolio that matches their risk profile and invest consistently in such a portfolio without concern for current market volatility.

The world of robo-advisory and passive investing was founded on MPT. Robo-advisors now create efficient portfolios where investors can automatically invest with no concern for the technical details of the stock market.

**A typical broadly diversified MPT portfolio for a growth investor can include:**

- 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

**Alternatively, robo-advisors can create these portfolios with index funds and ETFs. Taking the latter, the portfolio can look like the following:**

- 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

The above might be the portfolio that will maximize the returns and minimize the risk of a certain growth investor using the MPT.

Due to movements in the market, this allocation formula will change from time to time. Robo-advisors will need to regularly rebalance the portfolio to maintain the original allocation formula, the efficient portfolio.

### Two-Fund Theory

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 50% in Vanguard S&P 500 Index ETF and 50% 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.

**Pros of Modern Portfolio Theory**

- 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 element in their investment portfolios — it was all about the returns. This meant that many investors carried too much extra risk without corresponding higher returns.

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 now seek efficient portfolios that provide higher returns for the same level of risk.
- Foundation of Passive Investing
- Since there are many efficient portfolios on the efficient frontier, every investor can have their own efficient portfolio given their risk capacity and tolerance.

It was this idea that was foundational to the development of passive investing. Once an investor has found their own efficient portfolio(s), they can keep investing in that portfolio without concern for the current (short-term) volatility in the market.

Instead of unsuccessfully timing the market at a higher cost, investors can stick to an efficient or optimal portfolio and automate their investing into such. - Useful for the Average Investor
- With MPT and passive investing, the average investor who does not understand much about the technical details of the market can also invest successfully. Today, there are robo-advisors that create efficient portfolios for average investors and help them automate their investments in such portfolios.

**Cons of Modern Portfolio Theory**

- It’s Only a Model
- Every economic model has its assumptions. MPT assumes a rational investor who wants more returns and less risk. It also assumes that more than one portfolio can be efficient. But these assumptions are not necessarily written in stone and without one of them, the MPT can break down.
- 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 real investment risk rather than the risk that an asset’s return will differ from its expected return.
- The Measure of Return
- Expected return calculations depend on the historical returns of an asset. Though historical returns are all we have to predict the future, there is no necessary coherence between past and future returns.

Similarly, MPT does not take transaction costs — broker fees, commissions, etc. — into account.

## What Are Some Alternatives to Modern Portfolio Theory?

As with any financial option, alternatives exist that may better suit your needs. Talk to a trusted financial advisor to determine the best option for you.

### Post-Modern Portfolio Theory

Investment analysts who believe that downside risk should be the measurement of risk instead of standard deviation have come up with a theory called Post-Modern Portfolio Theory (PMPT).

Brian M. Rom and Kathleen Ferguson designed this system in 1991. It holds to all the tenets of MPT except that they define risk as the probability of losing money rather than having returns that differ 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.

### MPT and Active Investing

We mentioned above that if an efficient portfolio moves away from its allocation formula, robo-advisors will rebalance the portfolio. They do this regularly to keep the portfolio efficient.

However, there are active investors who, though believing in efficient portfolios, prefer to tweak the allocation formula to take advantage of the current conditions of the market. Instead of a hands-off approach (passive investing), they prefer to profit from short-term volatility even if it means temporary inefficiency.

**Last Modified:**August 15, 2022

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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