Post-modern portfolio theory
Post-modern portfolio theory (PMPT) is a portfolio optimization methodology that emphasizes the downside risk of investment returns rather than the total variance used in modern portfolio theory (MPT), measuring risk through the standard deviation of negative returns below a minimum acceptable return (MAR) threshold to better align portfolios with investors' goals of avoiding losses.[1][2] Developed by software designers Brian M. Rom and Kathleen W. Ferguson in 1991, PMPT emerged as a response to perceived flaws in MPT-based software and its assumption of symmetrical risk distributions, which treat upside and downside volatility equally despite investors' greater concern for losses.[1][2] The theory was formally introduced in their 1993 paper "Post-Modern Portfolio Theory Comes of Age," published in The Journal of Investing, where they argued that MPT's reliance on total standard deviation overlooks the asymmetrical nature of return distributions in real markets.[2] Central to PMPT are innovations like downside deviation, which calculates volatility only for returns falling below the MAR (often set at zero or an investor-specific target like inflation plus a buffer), and the Sortino ratio, a risk-adjusted performance measure that divides excess return by downside deviation to prioritize strategies minimizing harmful volatility.[1][3] Unlike MPT's single efficient frontier based on mean-variance optimization, PMPT generates multiple efficient frontiers tailored to varying MAR levels, enabling more personalized asset allocation that incorporates non-normal return distributions and investor-specific risk aversion.[4][2] PMPT has gained traction in performance measurement and software tools, influencing metrics like downside probability and the value-at-risk framework, though it requires more computational intensity due to its focus on historical downside data and scenario analysis.[1] By shifting emphasis from total risk to investor-relevant downside exposure, PMPT provides a more practical framework for portfolio construction in volatile markets, with applications in institutional investing and retirement planning.[4]Overview and Foundations
Definition
Post-modern portfolio theory (PMPT) represents an evolution of modern portfolio theory (MPT), shifting the emphasis from total volatility—measured by standard deviation—to downside risk, which captures only the negative deviations of returns below a specified target or minimum acceptable return (MAR).[5] This approach better aligns with investor objectives, such as fulfilling future financial obligations, by prioritizing the avoidance of losses relative to an individualized benchmark like inflation-adjusted spending needs or a fixed threshold (e.g., 5-7%).[6] Unlike MPT's symmetrical treatment of variance, PMPT views upside volatility as potentially beneficial and thus not penalizable in risk assessments.[5] The core purpose of PMPT is to construct and optimize portfolios that maximize returns for a given level of downside risk, reflecting real-world investor psychology where losses below expectations elicit stronger aversion than equivalent gains above them.[6] By focusing exclusively on harmful deviations, PMPT enables more precise risk management tailored to specific goals, reducing the overestimation of risk inherent in total volatility metrics.[5] Central to PMPT are concepts like target semi-deviation, which quantifies the dispersion of returns falling short of the MAR, serving as a refined proxy for investor-perceived risk.[6] Additionally, PMPT rejects the normal distribution assumption prevalent in MPT, acknowledging that actual return distributions are often asymmetrical and skewed, which allows for more realistic modeling of market behaviors and tail risks.[5]Comparison with Modern Portfolio Theory
Both Modern Portfolio Theory (MPT) and Post-modern Portfolio Theory (PMPT) seek to optimize investment portfolios by maximizing expected returns for a given level of risk through diversification, constructing efficient frontiers that represent sets of optimal portfolios.[7][8] These shared foundations emphasize the benefits of combining assets with low correlations to reduce overall portfolio volatility without sacrificing returns.[9] A primary difference lies in their definitions of risk: MPT, developed by Harry Markowitz in 1952, treats risk symmetrically as total variance or standard deviation of returns, assuming returns follow a normal distribution and employing mean-variance optimization.[7] In contrast, PMPT, emerging in the 1980s and formalized in the 1990s, defines risk asymmetrically as downside deviation below a specified target return, better accommodating real-world skewed return distributions where upside volatility is not penalized.[10][8] Philosophically, MPT focuses on absolute portfolio performance relative to the risk-free rate, rooted in rational investor assumptions under expected utility theory.[7] PMPT shifts toward relative performance against investor-specific benchmarks, integrating insights from behavioral finance, such as prospect theory, which highlights loss aversion and asymmetric preferences for gains and losses.[10] Historically, MPT established the baseline for quantitative portfolio management in the 1950s, influencing subsequent frameworks.[7] PMPT evolved as a refinement in the 1980s at institutions like the Pension Research Institute and gained prominence through key publications in the 1990s, addressing MPT's limitations amid observed market anomalies and behavioral critiques.[10][8]Historical Development
Origins
Post-modern portfolio theory (PMPT) originated in 1981 through empirical investigations at the Pension Research Institute (PRI) at San Francisco State University, where mathematicians and finance experts Hal Forsey and Frank Sortino began developing alternatives to traditional risk assessment methods for pension fund management.[10] Driven by the practical demands of institutional investors, their work sought to refine portfolio strategies by emphasizing risk measures that aligned more closely with real-world financial planning needs, particularly for retirement assets where preserving capital against losses was paramount. The core motivations stemmed from identified shortcomings in Modern Portfolio Theory (MPT), which relied on variance to quantify risk and assumed normally distributed returns—a model that overlooked the asymmetrical nature of actual investment outcomes and investors' greater aversion to downside deviations.[10] In the context of pension funds, this inadequacy was especially pronounced, as shortfall risk relative to required return targets directly impacted funding status and beneficiary security, prompting a shift toward metrics focused on below-target performance rather than total volatility. Intellectual foundations drew from earlier theoretical advancements, including Peter Fishburn's 1970s formulations of downside risk, which mathematically defined risk as the variability of returns below a specified threshold and provided proofs for its utility in decision-making under uncertainty. Complementing this were critiques of normality assumptions in return distributions, notably Aitchison and Brown's introduction of the three-parameter lognormal distribution, which better accommodated the positive skewness and bounded negativity observed in financial data. These elements converged in informal collaborations and experimental prototypes during the early 1980s, evolving into practical software tools at PRI that enabled downside-oriented analysis and optimization, laying the groundwork for PMPT's formal emergence.[11]Key Publications and Contributors
The seminal publications formalizing post-modern portfolio theory (PMPT) were the articles "Post-Modern Portfolio Theory Comes of Age" by Brian M. Rom and Kathleen W. Ferguson, published in The Journal of Investing in Winter 1993 (volume 2, issue 4, pages 27–33) and Fall 1994 (volume 3, issue 3, pages 11–17).[2][12] In these works, Rom and Ferguson, software developers at Sponsor Software Systems, Inc., introduced PMPT as a computational framework designed to overcome limitations in modern portfolio theory (MPT) software, such as the inappropriate use of symmetric variance as a risk proxy and assumptions of normal return distributions.[4] Their contributions emphasized practical implementation through software tools that generate investor-specific efficient frontiers based on downside risk relative to a minimum acceptable return.[1] The term "post-modern portfolio theory" was first used by the Pension Research Institute in an article published in Pensions & Investments magazine on May 2, 1988.[13] Key contributors to PMPT include Rom and Ferguson, who developed the first commercial applications of the theory starting in the late 1980s via their firm, later known as Investment Technologies.[14] Building on foundational research from the Pension Research Institute (PRI) in the 1980s, the theory incorporated behavioral insights from Daniel Kahneman and Amos Tversky's prospect theory, which informed PMPT's asymmetrical treatment of gains and losses, aligning with investor aversion to downside deviations.[15] The evolution of PMPT in the 1990s featured expansions through academic papers and industry conferences, such as those organized by the International Actuarial Association's AFIR colloquia, where downside risk concepts were refined.[16] Frank A. Sortino, director of PRI, played a pivotal role in these developments by advancing performance ratios like the Sortino ratio, which measures risk-adjusted returns using only negative deviations from a target threshold, thereby enhancing PMPT's applicability to non-normal returns.[17][14] By the mid-1990s, PMPT saw early adoption among pension funds and institutional investors, with over 60 organizations worldwide, including Banc One and Deutsche Bank, implementing its software tools for asset allocation and performance evaluation.[14] This uptake was driven by PRI's consulting efforts and Rom and Ferguson's commercial platforms, which demonstrated superior handling of real-world asymmetries in institutional portfolios compared to traditional MPT methods.[14]Core Concepts
Downside Risk
In post-modern portfolio theory (PMPT), downside risk is defined as the volatility associated with returns that fall below a specified target return, such as the minimum acceptable return (MAR), thereby focusing exclusively on deviations that are harmful to investors.[2] This measure captures only negative excursions from the target, distinguishing it from total variance, which treats upside and downside movements symmetrically. The mathematical formulation for target semi-deviation, a key quantification of downside risk, is expressed asd = \sqrt{\int_{-\infty}^{t} (t - r)^2 f(r) \, dr},
where t represents the target return, r denotes the portfolio return, and f(r) is the probability density function of returns. This integral computes the square root of the expected squared deviations solely for returns below the target (r < t), effectively measuring the dispersion of harmful outcomes while excluding beneficial upside volatility. The rationale for emphasizing downside risk in PMPT stems from its alignment with investor psychology, which views positive volatility as advantageous rather than risky, in contrast to modern portfolio theory's use of standard deviation that penalizes both upside and downside equally.[2] This approach is particularly enabled by the recognition of non-normal return distributions, where asset returns often exhibit significant skewness, allowing for the separation of downside deviations from overall variability.[2] Downside risk serves as the denominator in metrics like the Sortino ratio to evaluate performance relative to harmful volatility.