Expected Utility Calculator
Calculate expected utility for investment decisions under uncertainty. Compare different investment options based on your risk preferences and probability-weighted outcomes.
Expected Utility Results
Risk Analysis
Decision Analysis
Recommendation: Enter scenarios to see analysis
Utility Efficiency: 0%
Optimal Choice: N/A
Note: Higher expected utility indicates better risk-adjusted returns
Understanding Expected Utility Theory
Expected utility theory is a framework for understanding how people make decisions under uncertainty. It combines probabilities of different outcomes with the utility (satisfaction) derived from those outcomes to make rational investment decisions.
Expected Utility Formula
Expected utility is calculated as:
EU = S (p_i × u(x_i))
Where: EU = expected utility, p_i = probability of outcome i, u(x_i) = utility of outcome x_i
Utility Functions
- CARA (Constant Absolute Risk Aversion): u(x) = -e^(-ax) - risk aversion decreases with wealth
- CRRA (Constant Relative Risk Aversion): u(x) = x^(1-a)/(1-a) - risk aversion constant relative to wealth
- Linear (Risk Neutral): u(x) = x - no risk aversion, utility proportional to wealth
Risk Aversion
Risk aversion measures how much you dislike uncertainty. Higher values indicate greater preference for certainty over potentially higher but uncertain returns.
- Risk Averse (a > 0): Prefer certain outcomes over gambles with same expected value
- Risk Neutral (a = 0): Indifferent between certain and uncertain outcomes
- Risk Seeking (a < 0): Prefer gambles over certain outcomes
Certainty Equivalent
The certainty equivalent is the guaranteed amount that would provide the same utility as an uncertain prospect. It represents what you're willing to accept instead of taking the risk.
Risk Premium
The risk premium is the difference between the expected value and the certainty equivalent. It represents how much you're willing to pay to avoid uncertainty.
Applications in Finance
- Portfolio Selection: Choosing optimal asset allocations
- Insurance Decisions: When to buy insurance coverage
- Investment Analysis: Evaluating risky investment opportunities
- Capital Budgeting: Assessing project risk and returns
- Behavioral Finance: Understanding investor psychology
Limitations
- Allais Paradox: People don't always follow expected utility theory
- Loss Aversion: People fear losses more than they value gains
- Probability Weighting: People overweight small probabilities
- Ambiguity Aversion: People dislike unknown probabilities
Tip: Expected utility theory provides a rational framework for decision-making under uncertainty. Use this calculator to compare investment options and understand how your risk preferences affect your choices. Remember that real-world behavior often deviates from perfect rationality.