How Wealth Shapes Investor Risk Attitudes- Risk Theories

 

Traditional economic models assume investors always act rationally, maximizing returns while minimizing risk through steady preferences. However, real-world decisions often defy this, blending caution with gambles; this article explores three landmark theories that reveal why.

A- Friedman-Savage hypothesis (1948 by Milton Friedman and Leonard Savage)

The Friedman-Savage hypothesis is a theory in behavioral economics and utility theory designed to explain a specific contradiction in human behavior: why the same person might simultaneously buy insurance (to avoid risk) and lottery tickets (to seek risk).

Proposed by Milton Friedman and Leonard Savage in 1948, it suggests that an individual’s attitude toward risk is not constant but changes depending on their level of wealth.

The Paradox: Insurance vs. Gambling

Standard economic theory (the Bernoulli hypothesis) originally suggested that most people are "risk-averse" because they experience diminishing marginal utility—each extra dollar provides less satisfaction than the one before.

• Insurance: A risk-averse person pays a premium to avoid a large potential loss.
• Gambling: A risk-seeking person pays for a small chance at a large gain, even if the "expected value" is negative.

Friedman and Savage argued that because people often do both, a simple concave utility curve isn't enough to describe human behavior.

The "S-Shaped" Utility Function

To resolve this, they proposed a utility function with a unique, alternating shape:

Segment	Wealth Level	Marginal Utility	Behavior	Example
Lower	Low Income	Diminishing	Risk-Averse	Buying insurance to protect small assets.
Middle	Transition	Increasing	Risk-Seeking	Buying lottery tickets to "jump" to a higher social class.
Upper	High Income	Diminishing	Risk-Averse	Protecting newly acquired wealth through safe investments.

The Visual Curve

If you were to graph this, the curve looks like an elongated 'S':

1. It starts concave (curving down), representing risk aversion at low income.
2. It hits an inflection point and becomes convex (curving up), representing a "love of risk" as people try to escape their current socioeconomic status.
3. It hits a second inflection point and becomes concave again at very high wealth levels.

Socioeconomic Significance

The hypothesis is often used to explain social mobility.

• People in the lower-middle class might gamble because a small loss won't change their life, but a massive win (the lottery) could fundamentally move them into a higher socioeconomic bracket.
• The "pain" of losing a few dollars is outweighed by the "utility" of the potential life-changing jump in status.

B- Harry Markowitz’s Utility Theory (1952 by Harry Markowitz)

While Friedman and Savage focused on absolute levels of wealth; Harry Markowitz (the father of Modern Portfolio Theory, who won a Nobel Prize for Modern Portfolio Theory) argued that this was unrealistic. Markowitz pointed out that the Friedman-Savage model implied that people's risk preferences were tied to absolute wealth levels. He argued instead that people care about changes in wealth relative to their "current" position. In other words, Markowitz indicated that if utility depended on absolute wealth, a person’s behavior would change drastically every time their bank balance moved. Instead, he proposed that utility is determined by changes in wealth relative to a person's current position (a reference point).

The Markowitz Utility Function

Markowitz suggested a "doubly S-shaped" utility function. Unlike the single S-curve of Friedman-Savage, Markowitz’s curve centered around the individual's current wealth.

 

• Gains: People are risk-averse for small gains but risk-seeking for large gains (lottery behavior).
• Losses: People are risk-seeking for small losses but risk-averse for large losses (insurance behavior).

C- Prospect Theory (1979, by Daniel Kahneman and Amos Tversky)

 Kahneman and Tversky took Markowitz’s ideas and added psychological depth, creating Prospect Theory, which is now the foundation of modern behavioral finance. It describes how people actually make decisions under risk, rather than how "rational" people should make them.

 

 

Key Pillars of Prospect Theory

1. Reference Dependence: People do not evaluate outcomes in isolation. We evaluate them as gains or losses relative to a reference point (usually the status quo).
2. Loss Aversion: This is the most famous finding. Psychologically, the pain of losing is twice as powerful as the joy of gaining. Losing Rs 1,00,000 hurts much more than winning Rs 1,00,000 feels good.
3. Diminishing Sensitivity: The difference between Rs 0 and Rs 1000 feels huge, but the difference between Rs1,00,000 and Rs 1,01,000 feels marginal. This leads to the "S" shape: concave for gains (risk aversion) and convex for losses (risk seeking).
4. Probability Weighting: People tend to "overweight" small probabilities (which explains why we buy lottery tickets) and "underweight" large, certain probabilities.

The Value Function

The Prospect Theory curve is asymmetrical. It is steeper for losses than for gains, visually representing that losses makes larger impact than gains.

 

 Conclusion-

In finance, these theories explain why investors often "ride" losing stocks for too long (risk-seeking in the face of loss) while selling winning stocks too early (risk-aversion in the face of gain). This is known as the Disposition Effect (I have explained different kind of behavioral biases in my previous write-up titled “Behavioral Biases in Investing: How Psychology Shapes Financial Decisions”).

Comparison of the Three Theories
Feature	Friedman-Savage	Markowitz Theory	Prospect Theory
Driver of Utility	Absolute Wealth	Change in Wealth	Gains and Losses
Reference Point	None	Current Wealth	Subjective Reference Point
Key Behavioral Insight	Explains lottery/insurance paradox.	Utility depends on your "starting point."	Loss Aversion (Losses > Gains).
Shape of Curve	Concave-Convex-Concave	S-shaped on both sides of zero	Steeper for losses than gains

 

Sources

1-    https://www.journals.uchicago.edu/doi/abs/10.1086/256692 (The Utility Analysis of Choices Involving Risk- by Milton Friedman and L. J. Savage)

2-    https://www.journals.uchicago.edu/doi/abs/10.1086/257177  (The Utility of Wealth by Harry Markowitz)

3-    https://www.econometricsociety.org/publications/econometrica/1979/03/01/prospect-theory-analysis-decision-under-risk (An Analysis of Decision under Risk by Daniel Kahneman and Amos Tversky)