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Theories Based on Expected Utility Theory

Extensions of EUT

While EUT has limitations, many influential theories built upon its foundation:

Modern Portfolio Theory (Markowitz, 1952)
Capital Asset Pricing Model (Sharpe, 1964)
Option Pricing Theory (Black-Scholes, 1973)
Arbitrage Pricing Theory (Ross, 1976)

All assume rational expected utility maximization.

Modern Portfolio Theory (MPT)

Core Idea: Optimize risk-return tradeoff using EUT framework.

Assumptions:

  • Returns normally distributed
  • Investors maximize expected utility of wealth
  • Only mean and variance matter (two-parameter utility)

Result: Efficient Frontier—portfolios offering max return for each risk level.

Contribution: Quantified diversification benefits mathematically.

Capital Asset Pricing Model (CAPM)

Extension: If all investors use MPT, what happens to market prices?

CAPM Formula: E(R_i) = R_f + β_i[E(R_m) - R_f]

Where:

  • R_f = risk-free rate
  • β_i = systematic risk
  • E(R_m) - R_f = market risk premium

Behavioral Critique: Assumes rational EUT investors, but real investors exhibit:

  • Home bias
  • Momentum trading
  • Disposition effect

Result: CAPM empirically fails—alphas exist, anomalies persist.

Arbitrage Pricing Theory (APT)

Alternative to CAPM: Multiple risk factors, not just market beta.

Form: E(R) = R_f + β₁F₁ + β₂F₂ + ... + βₙFₙ

Behavioral Issue: Still assumes rational arbitrageurs eliminate mispricings instantly. Reality: Limits to arbitrage allow behavioral biases to persist.

Option Pricing (Black-Scholes)

Foundation: Risk-neutral pricing using EUT.

Assumptions:

  • No arbitrage
  • Continuous trading
  • Log-normal stock prices
  • Constant volatility

Behavioral Deviations:

  • Volatility smile (violated assumptions)
  • Over/underpricing of out-of-money options
  • Disposition effect in option exercises

Behavioral Alternatives

When EUT-based theories fail empirically, behavioral models explain better:

Prospect Theory (Kahneman & Tversky, 1979): Replace EUT with reference-dependent value, loss aversion, probability weighting

Behavioral Asset Pricing (Barberis, Shleifer, Vishny, 1998): Model under/overreaction based on biases

Sentiment Models (Baker & Wurgler, 2006): Market mispricing driven by investor sentiment

Key Takeaways

  • EUT foundation: MPT, CAPM, APT, Black-Scholes all assume rational expected utility maximization
  • MPT: Efficient frontier from mean-variance optimization
  • CAPM: Links risk (beta) to expected return
  • APT: Multiple factor model
  • Limitations: All fail empirically where behavioral biases dominate
  • Behavioral alternatives: Prospect Theory, sentiment models better explain anomalies

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