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Post-modern Portfolio Theory (PMPT)

Post-modern Portfolio Theory (PMPT) extends the traditional modern portfolio theory (MPT) introducing several refinements and additional considerations that address some of the limitations of MPT as shown in Table 11.6 “Post-modern portfolio theory (PMPT) vs. MPT”.

Table 11.6: Post-modern portfolio theory (PMPT) vs. MPT
Modern Portfolio Theory Post-modern Portfolio Theory
Return Objectives Focuses on maximizing the absolute return relative to the risk-free rate. The primary goal is to achieve the highest possible return for a given level of risk, measured by the standard deviation of portfolio returns. Emphasizes the return required to meet future, specified obligations. This approach is more aligned with the needs of investors who have specific financial goals, such as retirement, education funding, or other future liabilities. PMPT considers the investor’s required rate of return to meet these obligations, rather than just maximizing absolute returns.
Risk Measurement Uses standard deviation as the sole measure of risk, which assumes that returns are normally distributed and that investors are equally concerned with upside and downside volatility. Recognizes that investors are more concerned with downside risk than upside risk. PMPT employs measures such as semi-variance, value at risk (VaR), and conditional value at risk (CVaR) to better capture the risk of losses. These measures focus on the lower tail of the return distribution, providing a more accurate assessment of the risk that investors care about.
Utility Functions Assumes that investors have quadratic utility functions, which implies that they are risk-averse and their satisfaction increases at a decreasing rate with higher returns. Allows for more flexible utility functions that can better reflect the varying risk preferences of different investors. This flexibility enables PMPT to accommodate investors with different levels of risk aversion and different financial goals.
Diversification Advocates for diversification to reduce risk, based on the correlation between asset returns. The theory suggests that by combining assets with low or negative correlations, investors can achieve a more efficient portfolio. Builds on this principle but also considers the impact of downside risk and the investor’s specific return requirements. PMPT encourages diversification strategies that not only reduce overall portfolio risk but also ensure that the portfolio is aligned with the investor’s future financial obligations.

PMPT introduces the concept of downside risk and Sortino ratio to better conform to the real-world needs and preferences of investors:

Downside Risk

Focuses on the negative deviation from the target return, rather than overall volatility.

Sortino Ratio

Measures risk-adjusted return considering only downside risk. The Sortino Ratio is calculated as:

Sortino Ratio = E(Rp) − Rf ∑ i=1n min ⁡ (0,Ri − T)2∕n

where Rf is the risk-free rate and T is the target return, conventionally set to Rf unless you have a specific minimum-acceptable-return in mind. See section “Sortino ratio”.

Methodology of PMPT

The PMPT framework follows a structured process to optimize portfolios, which includes the following steps:

Observe Monthly Returns

Similar to MPT, PMPT begins by observing the monthly returns of a portfolio or fund.

Fit an Asymmetric Distribution

Unlike MPT, which assumes a normal distribution, PMPT fits a distribution that allows for asymmetry in the observed returns. This is essential because real-world returns often exhibit skewness and kurtosis that are not captured by the normal distribution.

Bootstrap Returns

The observed returns are then bootstrapped to generate a large number of pseudo-annualized returns. Bootstrapping is a resampling technique that helps in creating a more robust dataset for analysis.

Generate PMPT Statistics

Using the large number of bootstrapped returns, various PMPT statistics are empirically generated. These statistics provide a more comprehensive understanding of the portfolio’s risk and return characteristics.

Volatility Skewness

One of the primary innovations in PMPT is the introduction of volatility skewness, a portfolio-analysis statistic developed by Rom and Ferguson.70 Volatility skewness measures the ratio of a distribution’s percentage of total variance from returns above the mean to the percentage of the distribution’s total variance from returns below the mean.

Volatility Skewness = Variance from Returns Above the Mean Variance from Returns Below the Mean

Interpretation of volatility skewness:

Symmetrical Distribution

If the distribution is symmetrical, as assumed under MPT, the volatility skewness will be 1.00.

Positive Skewness

Values greater than 1.00 indicate positive skewness, meaning there is more variance from returns above the mean.

Negative Skewness

Values less than 1.00 indicate negative skewness, meaning there is more variance from returns below the mean.

While closely correlated with the traditional statistical measure of skewness (the third moment of a distribution), volatility skewness is argued to be more intuitively understandable to non-statisticians, who are the primary users of these tools.

By incorporating these additional considerations, PMPT provides a more comprehensive framework for portfolio optimization that better conforms to the real-world needs and preferences of investors.

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