1. What is the Arrow-Pratt Risk Aversion Coefficient?

The Arrow-Pratt risk aversion coefficient measures an individual's or investor's degree of risk aversion. It quantifies how much an individual dislikes uncertainty and is willing to pay to avoid risky situations.

2. How Does the Calculator Work?

The calculator uses the Arrow-Pratt absolute risk aversion formula:

Where:

• \( A \) — Absolute risk aversion coefficient
• \( U(W) \) — Utility function of wealth
• \( U'(W) \) — First derivative of utility function
• \( U''(W) \) — Second derivative of utility function
• \( W \) — Wealth level

Explanation: The coefficient measures the curvature of the utility function. Higher values indicate greater risk aversion.

3. Importance of Risk Aversion Calculation

Details: Understanding risk aversion is crucial for portfolio optimization, insurance decisions, and economic modeling. It helps determine optimal asset allocation and risk management strategies.

4. Using the Calculator

Tips: Select a common utility function (logarithmic, square root, etc.) and enter your wealth level. The calculator will compute the absolute risk aversion coefficient at that wealth level.

5. Frequently Asked Questions (FAQ)

Q1: What does a higher risk aversion coefficient mean?
A: A higher coefficient indicates greater risk aversion. Individuals with higher A values are more conservative and prefer certain outcomes over uncertain ones with higher expected returns.

Q2: What are typical utility functions used?
A: Common utility functions include logarithmic (U=ln(W)), power (U=W^γ), exponential (U=-e^(-αW)), and quadratic functions.

Q3: How does risk aversion change with wealth?
A: For constant absolute risk aversion (CARA), A remains constant. For decreasing absolute risk aversion (DARA), A decreases as wealth increases.

Q4: What is relative risk aversion?
A: Relative risk aversion is R(W) = W × A(W). It measures risk aversion relative to wealth level and is often more stable across wealth levels.

Q5: How is this used in finance?
A: Risk aversion coefficients are used in portfolio theory, option pricing, insurance premium calculations, and determining risk-adjusted returns.