The study of decision-making under uncertainty is a cornerstone of economic theory, particularly in finance. Early attempts to model how individuals make choices when outcomes are not certain often struggled to reconcile observed behaviors with simplified assumptions. Two significant contributions in this realm are the Friedman-Savage hypothesis and the Markowitz hypothesis, both aiming to explain observed patterns of risk-taking and risk-aversion, albeit from different angles and with varying degrees of practical applicability.

At its core, utility theory posits that individuals make decisions to maximize their expected utility, where utility is a measure of satisfaction or happiness derived from various outcomes, typically wealth. However, the exact shape of this utility function has been a subject of extensive debate. The classical expected utility theory, particularly as formalized by von Neumann and Morgenstern, generally assumed a concave utility function, implying diminishing marginal utility of wealth and thus universal risk aversion. This assumption, while elegant, struggled to explain why the same individuals might simultaneously buy insurance (risk-averse behavior) and lottery tickets (risk-seeking behavior). It was this apparent paradox that prompted the development of more nuanced models of utility.

Friedman-Savage Hypothesis

The Friedman-Savage hypothesis, proposed by Milton Friedman and Leonard J. Savage in their 1948 paper “The Utility Analysis of Choices Involving Risk,” was a pioneering attempt to reconcile the observed dual behavior of individuals who are simultaneously willing to pay a premium for insurance (to avoid risk) and to buy lottery tickets (to embrace risk). Their central insight was to propose a non-linear, S-shaped utility function of wealth, which departs significantly from the universally concave utility function assumed by earlier models.

The utility function proposed by Friedman and Savage has three distinct segments:

  1. Concave Segment: At low levels of wealth, the utility function is concave. This implies diminishing marginal utility of wealth, meaning that each additional unit of wealth provides less satisfaction than the previous one. In this region, individuals are risk-averse and would be willing to pay a premium to avoid risk, such as buying insurance. For example, a person with very little wealth would find the loss of a small sum more impactful than a wealthy person, making them more risk-averse.
  2. Convex Segment: At intermediate levels of wealth, the utility function becomes convex. In this region, individuals exhibit increasing marginal utility of wealth, meaning that each additional unit of wealth provides more satisfaction than the previous one. Here, individuals are risk-seeking and would be willing to accept an unfair gamble or buy a lottery ticket, hoping for a large gain. This convex portion is crucial for explaining the demand for lotteries. The idea is that an individual at an intermediate wealth level might find the prospect of moving to a significantly higher wealth level extremely attractive, outweighing the small probability of losing a small amount.
  3. Concave Segment (again): At very high levels of wealth, the utility function again becomes concave, signifying a return to diminishing marginal utility of wealth and risk-averse behavior. This suggests that even very wealthy individuals would eventually become risk-averse again, perhaps because the utility derived from further wealth accumulation starts to plateau.

The inflection point, where the utility function switches from concave to convex, represents a critical wealth level where an individual’s attitude towards risk changes. Friedman and Savage posited that this inflection point typically falls within the range of wealth levels experienced by most people, thereby explaining the simultaneous engagement in insurance and gambling. Their hypothesis implies that a person’s attitude towards risk is not fixed but depends on their current absolute level of wealth relative to this inflection point.

While groundbreaking, the Friedman-Savage hypothesis faced several limitations. Firstly, it relied on the specific shape of the utility function being universal and fixed for all individuals, with the inflection point being a static benchmark. It struggled to explain why people might engage in small, repeated gambles (like minor office pools) even if their wealth level doesn’t align with the convex part of the curve. Secondly, it primarily focused on explaining the decision to take single, isolated gambles rather than complex investment portfolios. It did not offer a framework for understanding how investors might combine multiple risky assets to manage overall risk. Moreover, the hypothesis did not explicitly incorporate the concept of probability distributions of outcomes beyond simply the expected value and the shape of the utility curve. It offered a descriptive model of behavior rather than a prescriptive tool for optimal decision-making.

Markowitz Hypothesis (Modern Portfolio Theory)

The Markowitz hypothesis, developed by Harry Markowitz and published in his seminal 1952 paper “Portfolio Selection,” represents a monumental leap forward in understanding investment decision-making under uncertainty. Unlike Friedman and Savage, who focused on the general shape of an individual’s utility function of absolute wealth, Markowitz shifted the focus to the characteristics of an investment portfolio and the trade-off between risk and return. His work laid the foundation for what is now known as Modern Portfolio Theory (MPT), for which he later received a Nobel Memorial Prize in Economic Sciences.

Markowitz’s core insight was that investors do not (or should not) evaluate individual assets in isolation but rather how each asset contributes to the overall risk and return of a diversified portfolio. He formalized the idea that investors are primarily concerned with two characteristics of a portfolio:

  1. Expected Return (Mean): The anticipated average return of the portfolio over a given period. This is calculated as the weighted average of the expected returns of the individual assets within the portfolio.
  2. Risk (Variance/Standard Deviation): The variability or dispersion of the actual returns around the expected return. Markowitz quantified risk using the statistical measure of variance (or its square root, standard deviation). A higher variance implies greater uncertainty and thus higher risk.

Markowitz’s model makes several key assumptions:

  • Risk Aversion: Investors are generally risk-averse. This means that, given two portfolios with the same expected return, investors will choose the one with lower risk. Conversely, given two portfolios with the same risk, they will choose the one with higher expected return. This contrasts with Friedman-Savage’s mixed risk attitudes.
  • Rationality: Investors are rational and aim to maximize their expected utility.
  • Mean-Variance Framework: Investor utility can be expressed solely as a function of the portfolio’s expected return and its variance. This assumption holds strictly true if investor utility functions are quadratic or if asset returns are normally distributed.
  • Information Availability: Investors have access to information about expected returns, variances, and covariances of all available assets.

The groundbreaking contribution of Markowitz was the introduction of diversification as a systematic way to reduce portfolio risk without necessarily sacrificing expected return. He demonstrated that the risk of a portfolio is not simply the weighted average of the risks of individual assets. Instead, it depends crucially on the covariance (or correlation) between the returns of the assets within the portfolio.

  • Positive Correlation: If two assets’ returns tend to move in the same direction (positive covariance/correlation), combining them provides limited diversification benefits.
  • Negative Correlation: If two assets’ returns tend to move in opposite directions (negative covariance/correlation), combining them can significantly reduce portfolio risk, as the losses from one asset might be offset by gains from another.
  • Zero Correlation: If two assets’ returns are unrelated, combining them still offers diversification benefits, though less than negatively correlated assets.

By combining assets that are not perfectly positively correlated, an investor can construct a portfolio whose overall risk (variance) is lower than the weighted average of the individual asset risks. This is the essence of diversification, often summarized by the adage “don’t put all your eggs in one basket.”

Markowitz developed the concept of the Efficient Frontier. This is a set of optimal portfolios that offer the highest possible expected return for a given level of risk, or the lowest possible risk for a given expected return. Any portfolio that lies below the efficient frontier is suboptimal because it either provides less return for the same risk or higher risk for the same return. Rational investors will always choose a portfolio on the efficient frontier based on their individual risk tolerance.

Markowitz as an Improvement of Friedman-Savage

The Markowitz hypothesis represents a significant improvement over the Friedman-Savage hypothesis in several critical ways, fundamentally changing the landscape of financial economics and investment management:

  1. Shift from Absolute Wealth to Portfolio Characteristics: Friedman-Savage’s model explained utility as a function of an individual’s absolute wealth level, attempting to describe why people with different wealth might exhibit different risk behaviors (e.g., a poor person gambling small amounts to escape poverty, or a middle-class person buying lottery tickets for a chance at extreme wealth, while also buying insurance). Markowitz, however, shifts the focus from the utility of total wealth to the characteristics of returns on an investment portfolio. His model explicitly deals with the statistical properties (mean and variance) of the distribution of future returns, which is far more directly applicable to financial decisions.

  2. Explicit Quantification and Management of Risk: Perhaps the most profound improvement is Markowitz’s explicit mathematical quantification of risk as variance (or standard deviation) of portfolio returns. Friedman-Savage describes risk-seeking or risk-averse behavior through the curvature of the utility function. While insightful for explaining behavioral paradoxes, it doesn’t provide a quantitative measure of risk that can be directly managed. Markowitz, by contrast, provides a precise, measurable definition of risk that allows for optimization. This enables investors to calculate, compare, and minimize risk for a given return target, or maximize return for a given risk tolerance.

  3. Incorporation of Diversification: This is the most revolutionary aspect of Markowitz’s work and a concept entirely absent from the Friedman-Savage framework. Friedman-Savage’s model is focused on the decision concerning a single gamble or a single change in wealth. It cannot explain why or how combining different assets can reduce overall risk. Markowitz, through the inclusion of covariance among assets, rigorously demonstrated the benefits of diversification. He showed that systematic diversification can eliminate “unsystematic risk” (risk unique to an individual asset) without sacrificing expected return, a cornerstone principle of modern investment. This practical insight revolutionized portfolio construction and risk management.

  4. Actionable Investment Framework: Friedman-Savage’s hypothesis is largely a descriptive model, aiming to explain why individuals might engage in both insurance and gambling. It offers little in the way of a prescriptive framework for making optimal investment decisions. Markowitz, on the other hand, provides a powerful normative (prescriptive) framework. It offers a clear, step-by-step methodology for constructing an “optimal” portfolio based on an investor’s expected returns, risks, and correlations of assets, leading to the identification of the efficient frontier. This makes it a practical tool for fund managers, financial advisors, and individual investors.

  5. Generality and Foundation for Modern Finance: Markowitz’s mean-variance framework is remarkably general and has proven foundational for much of modern financial theory. It led directly to the development of the Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), and numerous other asset pricing models and risk management techniques. Its principles are applied universally in institutional and individual investing, portfolio management, and performance evaluation. Friedman-Savage, while historically important, remains primarily a behavioral economics curiosity rather than a practical investment guide.

  6. Addressing the “Paradoxes” Differently: While Friedman-Savage explicitly created their S-shaped utility function to address the insurance/lottery paradox, Markowitz’s model, by assuming general risk aversion (diminishing marginal utility of wealth in the context of portfolio returns), provides a more consistent framework. The “risk-seeking” behavior of buying lotteries is less directly addressed by pure MPT, but MPT focuses on rational investment behavior in portfolios of assets with meaningful probability distributions, rather than small, entertainment-oriented gambles. For serious investment, the assumption of risk aversion and the desire to manage risk through diversification is highly appropriate and empirically observed.

  7. Mathematical Rigor and Optimization: Markowitz’s approach is highly mathematical and amenable to quantitative analysis and optimization techniques. This allowed for the development of sophisticated computational tools for portfolio selection. Friedman-Savage’s model, while visually intuitive with its S-curve, is less amenable to direct mathematical optimization for portfolio construction.

In essence, while Friedman-Savage took an important conceptual step by challenging the purely concave utility function, their model remained largely descriptive and focused on individual gambles and the absolute level of wealth. Markowitz, conversely, introduced a revolutionary framework that shifted the paradigm from individual wealth utility to the statistical properties of portfolio returns. His explicit quantification of risk, the groundbreaking concept of diversification through covariance, and the derivation of the efficient frontier provided a practical, mathematically rigorous, and prescriptive methodology for rational investment decision-making under uncertainty. This fundamental difference in focus and methodology solidified Markowitz’s contribution as a monumental improvement, laying the bedrock for modern portfolio theory and finance management as we know it today.