(Not So) Modern Portfolio Theory — "How To" Balance Expected Returns Against Risk

October 3rd, 2023

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This is a guest article by Mike from, a tool that makes it easy to do everything you read about in this article (and reduces the time needed for stock fundamental analysis to seconds).

Have you ever wondered how investment professionals make informed decisions about entire portfolio construction? Are you curious about the underlying principles and strategies that guide their choices? Take a look Modern Portfolio Theory (MPT), a groundbreaking investment approach that has revolutionized the world of finance.

MPT was developed by Harry Markowitz in 1952, who was later awarded the Nobel Prize in Economic Sciences in 1990 for this significant contribution. We’ll delve into the key concepts, types of investment risks, asset classes, and alternative approaches. Learn how to build portfolios that simply works!

Investment Portfolios: Asset Allocation Strategies

Traditional Asset Allocation Strategy

An ability to balance risk and return is crucial to successful portfolio management. Let's discover the world of asset allocation strategies, from traditional methods like equal weighting or subjective preferences, to more advanced approaches, such as Hierarchical Risk Parity (HRP).

Understanding the strengths and weaknesses of each investment strategy can help you make informed decisions about asset allocation, leading to a more robust and high-performing portfolio.

Traditional Asset Allocation

Traditional asset allocation methods, such as equal weighting or subjective preferences, have their limitations. Equal weighting, for instance, means that each asset in a portfolio is assigned the same value regardless of its potential risk or return. While this approach is simple to implement, it may not optimize portfolios due to varying asset volatilities and cognitive biases, which can lead to suboptimal investment decisions.

Traditional asset allocation strategies might not be the best choice for investors seeking to maximize expected returns while minimizing market risks.

Mathematical and Data-Driven Approaches to Asset Allocation

An asset allocation model can help address these issues by providing a more systematic and objective approach to asset allocations.

Several mathematical and data-driven approaches have been developed in an attempt to lower risk, optimize returns, including the Modern Portfolio Theory (MPT), Hierarchical Risk Parity (HRP), and the Black-Litterman model. MPT is a groundbreaking approach that seeks to optimize overall portfolio risk and return through diversification. It's based on historical data and mathematical models.

In contrast, the Hierarchical Risk Parity (HRP) methodology developed by Marcos Lopez de Prado in 2016 is a more advanced approach to asset allocation. It uses a hierarchical clustering and risk parity algorithm to allocate individual assets, providing a more balanced portfolio.

Another option to be chosen is betting on The Black-Litterman model, related to the market equilibrium. You can read about it in detail in this text a little lower, in the paragraph on alternative portfolio management metrics.

Understanding Modern Portfolio Theory: the matter of asset classes

Asset Allocation of a Diversified Portfolio

Modern Portfolio Theory MPT’s potential lies in diversification. Spreading investments across exemplary two asset classes and markets creates a well-diversified portfolio, reducing risk while enhancing returns. Mutual funds and exchange traded funds (ETFs) play a vital role in achieving this diversification, allowing investors to own a small fraction of numerous investments within each asset class. The goal is to strike a balance between risk and return by selecting the right combination of assets, thereby maximizing the potential for growth while minimizing the chance of loss.

The Birth of MPT

MPT has become an essential component of investment management. MPT’s demonstration of how portfolio diversification can minimize investment risk has revolutionized portfolio construction techniques among wealth managers.

MPT has evolved and expanded, but its core principles remain deeply ingrained in the world of finance.

Key Concepts

In MPT are 3 fundamental principles:

1. Risk and return trade-offs: Investors must accept a certain level of risk in order to achieve a higher return.

2. Diversification: The process of allocating investments across different asset classes and markets to reduce risk and enhance returns.

3. The efficient frontier: A concept that represents the optimal portfolio mix that offers the highest expected return for a given level of risk, consisting of plotting all possible combinations of high risk assets in a risk-expected return space results.

The Efficient Frontier and Optimal Portfolios

The efficient frontier represents the optimal portfolios that offer the highest expected return for a given level of risk. This concept is central to MPT and provides a clear roadmap for investors looking to strike the perfect balance between risk and return. Understanding it empowers you to make informed decisions about asset allocation and portfolio development, thereby optimizing your portfolio’s performance.

Constructing the Efficient Frontier

In a nutshell, this theory is about putting all possible combinations of asset weights on a scale and deciding whether it is more important for an investor to (1) minimize volatility or (2) to maximize risk-adjusted return. The process involves:

- Plotting all possible combinations of selected assets on a scale of return (y-axis) against risk (x-axis).

- Examining the potential combinations of these investments

- Identifying the optimal portfolio.

The goal is to generate a set of portfolios that offer the greatest returns for a specified level of risk, providing a visual representation of the optimal balance between risk and return. However, these simulations would have worked perfectly only in the past, because efficient frontier is entirely dependent on archival data.

Beyond the Efficient Frontier

The efficient frontier is a powerful tool for ideal portfolio optimization: it can be further enhanced by combining it with a risk-free asset. The addition of a risk-free asset, like a government bond, to a stock portfolio on the frontier potentially amplifies returns.

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Criticisms and Limitations of Modern Portfolio Theory

One of the major criticisms of MPT is its reliance on archival data and assumptions about investor behavior, which may not always hold true in real-world scenarios.

MPT’s heavy reliance on historical data to analyze past returns, volatilities, and correlations for constructing portfolios can be a double-edged sword. While such data can provide valuable insights into the performance of different assets, it may not guarantee future portfolio performance due to potential changes in market conditions and other factors. One such tool used in this analysis is the correlation matrix, which helps in understanding the relationships between various assets.

It all make MPT’s predictions less reliable and more susceptible to deviations from actual market behavior.

Investor Behavior Assumptions

MPT assumes that most investors are rational and risk-averse, seeking to optimize returns while minimizing risk. However, investor behavior may not always align with these assumptions, as cognitive biases and emotions can often influence investment decisions.

Acknowledging the limitations of MPT’s assumptions about investor behavior paves the way for exploring alternative portfolio management approaches that cater more effectively to the complexities and nuances of real-world investing.

Alternative Portfolio Management Approaches

MPT has its limitations, prompting the development of alternative approaches such as Post-Modern Portfolio Theory (PMPT) and the Black-Litterman Model. These approaches seek to address some of the shortcomings of MPT by incorporating downside risk, investor preferences, and market equilibrium into their models.

Understanding the pros and cons of each approach equips investors to make informed decisions about the method that aligns best with their investment goals and risk tolerance.


Post-Modern Portfolio Theory (PMPT) is an extension of MPT that focuses on downside risk and incorporates investor preferences. By emphasizing the importance of managing downside risk, PMPT offers a more tailored approach to portfolio development that takes into account individual investor preferences and objectives, as well as portfolio variance considerations.

While PMPT still relies on archival data, it addresses some of the limitations of MPT by providing a more nuanced understanding of risk and return.

Black-Litterman Model

The Black-Litterman Model offers a more flexible approach to optimie the portfolio by combining investor views with market equilibrium. This Bayesian approach enables investors to:

- Incorporate their own views into the one portfolio improving process

- Consider the market’s equilibrium

- Result in a more robust and adaptable solution for an optimized portfolio.

Although the Black-Litterman Model is not without its drawbacks, such as its reliance on historical data, it provides a valuable alternative to MPT for investors seeking a more flexible approach to portfolio management.

The Black-Litterman model, alternatively, blends market equilibrium and investor views to offer a more adaptable method for optimizing the portfolio. Think of market equilibrium as a state where the supply of an asset (how much of it is available for sale) matches the demand for that asset (how much buyers want to buy). This balance forms the market price. This model takes this balance into account, along with the investor's own perspectives and predictions, to give a more personalized approach to managing your investments. Incorporating these approaches into portfolio selection strategy can result in an optimized, resilient portfolio, adept at navigating the complex and ever-changing financial landscape.

Summary or Reimagining Total Portfolio Risk

Each fan of Modern Portfolio Theory argues that over 80 years ago it revolutionized the world of finance, providing a framework for optimizing overall risk and return through diversification and the efficient frontier.

Investment Portfolio Optimization is a rapidly developing field - so it's important not to fall behind the competition in it, and to keep on the lookout for more newer and niche alternatives yourself.

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