Expected Utility in Investment Decisions

Applying EUT to Portfolios

Expected Utility Theory provides framework for portfolio construction under risk.

Process:

• Estimate return distributions for assets
• Define investor's utility function (risk tolerance)
• Calculate expected utility for portfolio combinations
• Choose portfolio maximizing expected utility

Mean-Variance Framework

Markowitz (1952) simplified EUT for portfolios:

Assumptions:

• Returns normally distributed
• Utility depends only on mean and variance
• Investors are risk-averse

Result: Efficient frontier—max return for given risk level.

Risk Tolerance & Utility

Risk-Averse Investor (typical):

• Concave utility: U(W) = √W or U(W) = ln(W)
• High risk aversion → More bonds, less stocks
• Willing to sacrifice return for lower volatility

Risk Tolerance Measurement:

• Questionnaires (crude but practical)
• Revealed preferences (actual portfolio holdings)
• Loss tolerance tests

Portfolio Choice Example

Options:

• Portfolio A: 100% bonds, E(R) = 6%, σ = 5%
• Portfolio B: 60/40 stocks/bonds, E(R) = 9%, σ = 12%
• Portfolio C: 100% stocks, E(R) = 12%, σ = 18%

Risk-Averse Investor (high risk aversion):

• Calculates EU for each
• Likely chooses A or B (lower volatility worth sacrificing return)

Risk-Tolerant Investor (low risk aversion):

• EU highest for C (extra return more than compensates for volatility)

Behavioral Modifications

EUT assumes:

• Symmetric treatment of gains/losses (false—loss aversion)
• Linear probability weighting (false—overweight extremes)
• Final wealth focus (false—reference dependence)

Prospect Theory Portfolios:

• Avoid "losers" more than seek "winners"
• Overweight familiar stocks (ambiguity aversion)
• Under-diversify (narrow framing)

Practical Portfolio Construction

EUT-Based (prescriptive):

• Efficient frontier optimization
• Mean-variance analysis
• Risk-adjusted return maximization

Behavioral-Aware (descriptive + prescriptive):

• Acknowledge loss aversion → Set floor on downside
• Combat home bias → Force international allocation
• Prevent overtrading → Auto-rebalancing only

Key Takeaways

• EUT: Choose portfolio maximizing expected utility given risk tolerance
• Mean-variance: Simplified EUT for normally distributed returns
• Risk aversion: Determines stock/bond allocation
• Behavioral reality: Loss aversion, probability weighting, reference dependence violate EUT
• Practice: Combine EUT optimization with behavioral guardrails

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