Post-Modern Portfolio Theory (PMPT)

Contributor Image
Written By
Contributor Image
Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.

Post-Modern Portfolio Theory (PMPT) emerged as a response to the limitations and criticisms of Modern Portfolio Theory (MPT), which has been the cornerstone of portfolio management since its introduction by Harry Markowitz in the 1950s.

MPT focuses on optimizing risk and return through diversification and asset allocation based on historical data.

However, PMPT brings new perspectives to portfolio management, considering investor preferences, behaviors, and alternative investments.

Below we look at the origins, key differences, and applications of PMPT, as well as its impact on portfolio construction, institutional investment management, and the future of portfolio management.


Key Takeaways – Post-Modern Portfolio Theory (PMPT)

  • Post-Modern Portfolio Theory (PMPT) emerged as a response to the limitations of Modern Portfolio Theory (MPT) and incorporates investor preferences, behaviors, different assessments of risk, and alternative investments into portfolio management.
  • PMPT focuses on downside risk and recognizes the influence of behavioral biases on investment decisions, leading to more personalized and effective investment strategies.
  • Alternative investments play a crucial role in PMPT, providing diversification benefits and helping manage downside risk, especially during periods of market volatility and uncertainty.

Why Was Post-Modern Portfolio Theory Introduced? (Criticisms of Modern Portfolio Theory)

Modern Portfolio Theory, despite its significant contributions to portfolio management, has faced several criticisms over time, leading the development of new models like PMPT.

The primary concern is MPT’s reliance on historical data and assumptions about asset returns and risk, which may not accurately predict future market behavior.

Unlike “closed systems” where you know the future is going to be like the past (e.g., chess, musical notes) and can apply the same theory to future applications, financial markets are “open systems” where the past isn’t necessarily representative of the future (as the common financial disclosure always alludes to).

Additionally, MPT assumes that investors are rational, utility-maximizing agents, overlooking the reality of behavioral biases and individual preferences that influence trading/investment decision-making.

Another criticism is MPT’s focus on variance or standard deviation as the sole measure of risk, which fails to differentiate between upside and downside risks (leading to the development of metrics like the Sortino ratio).

In response to these concerns, Post-Modern Portfolio Theory was introduced to address the limitations of MPT and provide a more comprehensive framework for portfolio management.


Key Differences between Modern Portfolio Theory and Post-Modern Portfolio Theory

The primary distinction between MPT and PMPT lies in their approach to risk measurement.

While MPT uses variance or standard deviation, PMPT adopts downside risk, which is more relevant to investors as it accounts for the potential loss in value.

MPT treats all volatility as risk. In reality, volatility is a good thing if it causes the asset to move in a way that’s beneficial to you (or, e.g., causes an option you hold long to increase in value).

This difference leads to more meaningful risk-return trade-offs and efficient frontiers that better align with investors’ risk tolerance and preferences.

Another key difference is PMPT’s consideration of investor preferences and behaviors.

PMPT acknowledges the influence of cognitive biases, emotions, and individual preferences on investment decisions, incorporating them into the portfolio construction process.


Understanding the Importance of Investor Preferences and Behaviors in Post-Modern Portfolio Theory

In PMPT, investor preferences and behaviors play a critical role in shaping investment decisions and portfolio construction.

Unlike MPT, which assumes investors are rational and utility-maximizing, PMPT recognizes that investors are prone to behavioral biases, such as loss aversion, overconfidence, and anchoring, which can significantly impact their investment choices.

By acknowledging and accounting for these preferences and biases, PMPT enables portfolio managers to build portfolios that better align with investors’ unique risk tolerance, time horizon, and financial goals.

This leads to more personalized and effective investment strategies.


The Role of Alternative Investments in Post-Modern Portfolio Theory

PMPT’s emphasis on downside risk and investor preferences has increased the importance of alternative investments in portfolio construction.

Alternative investments, such as private equity, hedge funds, cash-flowing real estate, and commodities, can provide additional diversification benefits, as well as the potential for higher returns and reduced downside risk.

In the PMPT framework, alternative investments play a crucial role in enhancing portfolio performance and managing downside risk, particularly during periods of market volatility and uncertainty.


Applying Post-Modern Portfolio Theory in Investment Decision-Making

Investment decision-making in the context of PMPT involves a comprehensive understanding of investor preferences, behaviors, and risk tolerance.

Portfolio managers must assess downside risk, explore alternative investments, and tailor investment strategies to the unique needs and goals of each investor.

This process may involve behavioral assessments, scenario analysis, and stress testing to better evaluate potential trading/investment outcomes and ensure that portfolios are resilient to market fluctuations.


The Impact of Post-Modern Portfolio Theory on Portfolio Construction and Diversification

PMPT has significantly influenced portfolio construction and diversification by emphasizing downside risk management and the incorporation of trader/investor preferences and behaviors.

In PMPT-based portfolios, diversification is not solely based on historical correlations between asset classes; instead, it takes into account the potential for market disruptions and extreme events that may challenge traditional asset allocation strategies.

By considering downside risk, PMPT encourages the inclusion of alternative investments and assets that can help mitigate losses during periods of market stress.

This results in more resilient and dynamic portfolios that can adapt to changing market conditions and investor preferences.


Implementing Post-Modern Portfolio Theory in Institutional Investment Management

Institutional investors, such as pension funds, endowments, and insurance companies, have increasingly embraced PMPT as a framework for managing their portfolios.

By adopting PMPT principles, institutional investors can better address the unique challenges they face, including long-term liabilities, regulatory constraints, and the need for stable returns.

The implementation of PMPT in institutional investment management typically involves a more holistic approach to risk management, incorporating downside risk, scenario analysis, and stress testing.

This enables institutional investors to develop more robust asset allocation strategies, better manage tail risks, and align their investment portfolios with their long-term objectives and obligations.


Exploring the Future of Post-Modern Portfolio Theory and its Implications for Portfolio Management

As financial markets continue to evolve and become more complex over time, the importance of alternatives to traditional MPT in portfolio management can be expected to grow.

The theory’s emphasis on downside risk, investor preferences, and alternative investments will likely become increasingly relevant as non-traditional risks become more important over time (e.g., pandemics, acts of nature, war, geopolitical risks, currency risks, etc.).

Advances in technology, such as artificial intelligence and machine learning, can also play a role in the application of PMPT.

These technologies can help portfolio managers better understand investor behaviors, preferences, and risk tolerance, leading to more personalized and better investment strategies.


Approaches to Post-Modern Portfolio Theory

A number of different approaches have been developed under the umbrella of PMPT, reflecting diverse theoretical perspectives and practical applications.

Behavioral Portfolio Theory

Behavioral portfolio theory acknowledges that investor behavior may not align with the rational, utility-maximizing assumptions of traditional economic theory. Instead, investors may construct portfolios based on psychological factors, leading to less optimal, yet behaviorally consistent, investment decisions.

Stochastic Portfolio Theory

Stochastic portfolio theory uses probability theory to model uncertainties in the investment environment. One specific approach within this theory is chance-constrained portfolio selection, which aims to optimize portfolios by taking into account the probability of different market scenarios.

Maslowian Portfolio Theory

Drawing inspiration from psychologist Abraham Maslow’s hierarchy of needs, Maslowian portfolio theory prioritizes investments that meet basic financial needs before considering higher-risk investments.

Dedicated Portfolio Theory

This approach is specific to fixed income investments. Dedicated portfolio theory involves matching the cash flows from a portfolio to known future liabilities, reducing interest rate risk.

Risk Parity

Risk parity focuses on the allocation of risk, rather than capital, across different asset classes in a portfolio. The goal is to achieve a balance where each investment contributes equally to the portfolio’s overall risk.

Tail Risk Parity

Tail risk parity is an extension of the risk parity approach. It aims to manage the risk of extreme losses (or “tail events”) by distributing risk equally across different investments, considering both normal market conditions and tail events.


Optimization Considerations in PMPT

Optimizing a portfolio under PMPT involves a number of considerations.

Pareto Efficiency

In portfolio management, Pareto efficiency refers to an allocation of assets in which no investor can be made better off without making another investor worse off.

Bayesian Efficiency

Bayesian efficiency is an approach that incorporates prior beliefs and observed data to make probability-based decisions.

Multiple-Criteria Decision Analysis

Multiple-criteria decision analysis (MCDA) involves assessing and ranking different investment options based on multiple criteria, not just a single measure of return or risk.

Multi-Objective Optimization

Multi-objective optimization aims to balance multiple goals simultaneously, such as maximizing return while minimizing risk.

Stochastic Dominance

Stochastic dominance is a rule used to rank portfolios based on their return distributions.

Second-order stochastic dominance considers both the mean and variance of returns, while marginal conditional stochastic dominance also accounts for changing market conditions.

Downside Risk

Downside risk refers to the potential for a portfolio’s value to decrease.

It is of particular interest in PMPT because investors often care more about potential losses than gains.

Volatility Skewness

Volatility skewness measures asymmetry in the distribution of returns.

It can provide valuable information about potential downside risk.


Semivariance is a measure of downside risk that focuses on the variability of returns below a certain benchmark.

Expected Shortfall

Expected shortfall (ES), also known as conditional value at risk (CVaR), average value at risk (AVaR), or expected tail loss (ETL), measures the expected loss in the event of a significant market downturn.

Tail Value at Risk

Tail value at risk is another measure of downside risk, focusing on the worst losses that could occur in the tail of the return distribution.

While the probabilities of these large losses are small they can be significant when the time comes.

Statistical Dispersion

Statistical dispersion is a measure of the variability or spread in a set of data.

Discounted Maximum Loss

Discounted maximum loss is a measure of the worst-case scenario for a portfolio, considering the time value of money.

Indifference Price

Indifference price is the price at which an investor would be indifferent between holding a risky asset or not.


Measures in PMPT

Various measures are used to evaluate the performance of portfolios under PMPT.


The dual-beta concept distinguishes between downside beta and upside beta.

Downside beta measures an investment’s sensitivity to negative market movements, while upside beta measures its sensitivity to positive market movements.

Upside Potential Ratio

The upside potential ratio compares the potential for gains against the risk of losses in a portfolio.

Upside Risk

Upside risk refers to the potential for higher-than-expected returns, which may also indicate higher risk.

Downside Risk

As mentioned previously, downside risk refers to the potential for losses in a portfolio’s value.

Sortino Ratio

The Sortino ratio measures the risk-adjusted return of an investment or portfolio, but unlike the Sharpe ratio, it only considers downside volatility.

Omega Ratio

The Omega ratio measures the likelihood of achieving a minimum target return, considering both upside and downside returns.

Bias Ratio

The bias ratio measures the tendency of a risk estimate to over- or underestimate the actual risk.

Information Ratio

The information ratio compares the active return of a portfolio to its active risk.

Active return is the difference between the portfolio return and a benchmark return, while active risk is the standard deviation of the active return.

Deviation Risk Measure

The deviation risk measure captures the risk of deviation from an expected return, considering both upward and downward deviations.

Distortion Risk Measure

The distortion risk measure assigns different weights to gains and losses, reflecting investor preferences.

Spectral Risk Measure

Spectral risk measures consider the entire distribution of returns and can be adjusted to reflect the risk aversion of the investor.

Related: Risk Measures in Trading & Finance


Optimization Models in PMPT

There are several models that can be used to optimize portfolios in the context of PMPT.

Black-Litterman Model

The Black-Litterman model combines trader/investor views with market equilibrium to generate portfolio allocations.

Universal Portfolio Algorithm

The universal portfolio algorithm uses machine learning techniques to optimize portfolio allocations based (generally) on historical data.


Post-modern portfolio theory explained: Sortino ratio and volatility skewness (Excel)



What Is the Definition and Overview of Post-Modern Portfolio Theory?

Post-Modern Portfolio Theory (PMPT) is an advanced approach to portfolio management that addresses the limitations of Modern Portfolio Theory (MPT) by focusing on downside risk, trader/investor preferences and behaviors, and the benefits of alternative investments.

PMPT is grounded in the belief that traditional measures of risk, such as standard deviation, fail to capture the true nature of risk and do not differentiate between upside and downside risk.

What Does PMPT Say About Downside Risk?

PMPT emphasizes the importance of downside risk, which refers to the potential loss in value that an investment may experience.

By focusing on downside risk rather than overall risk, PMPT acknowledges that traders/investors are more concerned about potential losses than potential gains associated with that volatility, and it provides a more accurate representation of the risks they face.

This approach leads to more meaningful risk-return trade-offs and efficient frontiers that better align with investors’ risk tolerance and overall preferences.

Why Did PMPT Introduce the Sortino Ratio?

The Sortino Ratio, introduced in the context of PMPT, is a measure of risk-adjusted return that takes into account downside risk.

It is similar to the Sharpe Ratio but uses downside deviation instead of standard deviation as the measure of risk.

This allows for a more accurate comparison of investment performance, as it reflects the investor’s primary concern: avoiding losses while generating returns.

What Does PMPT Say About Volatility Skewness?

Volatility skewness refers to the asymmetry of returns distribution, which can impact an investor’s perception of risk.

PMPT acknowledges the importance of skewness by considering it in the portfolio construction process.

By accounting for skewness, PMPT can help investors identify and mitigate tail risks and achieve a more diversified and resilient portfolio.

As we found in our look at various portfolio approaches, the easiest way to reduce negative skew in portfolio returns is to diversify among different asset classes.


What Takeaways Can Traders/Investors Get from PMPT on Portfolio Construction and Optimization?

PMPT offers insights for traders and investors in constructing and optimizing their portfolios.

Some takeaways:

  • Focusing on downside risk to better align portfolios with investor risk tolerance.
  • Considering investor preferences and behaviors to create tailored investment strategies.
  • Incorporating alternative investments for enhanced diversification and downside risk management.
  • Evaluating portfolio performance using measures like the Sortino Ratio, which takes into account downside risk.

What Takeaways Can Traders/Investors Derive from PMPT on Financial Management?

PMPT provides valuable guidance for traders and investors in managing their finances.

Key takeaways include:

  • Recognizing the importance of behavioral biases and their impact on investment decision-making.
  • Employing a more comprehensive approach to risk management, considering factors such as downside risk, volatility skewness, and extreme market events.
  • Adopting a more dynamic and adaptive approach to asset allocation, taking into account changing market conditions and investor preferences.
  • Continuously monitoring and adjusting portfolios to ensure alignment with financial goals and risk tolerance.



Post-Modern Portfolio Theory (PMPT) is an investment theory that extends the Modern Portfolio Theory (MPT) developed by Harry Markowitz.

While MPT focuses primarily on the mean and variance of portfolio returns, PMPT recognizes that investors are more concerned with downside risk.

Post-Modern Portfolio Theory offers a more comprehensive and nuanced approach to portfolio management, addressing MPT’s limitations and providing a framework that better reflects the realities of today’s financial markets and investor needs.