Relative Risk Aversion Formula

Relative Risk Aversion Formula:

\[ RRA = -\frac{u''(w) \cdot w}{u'(w)} \]

Relative Risk Aversion (RRA):

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1. What is Relative Risk Aversion?

Relative Risk Aversion (RRA) is an economic measure that quantifies an individual's willingness to take risks relative to their wealth level. It measures how risk aversion changes as wealth increases or decreases.

2. How Does the Formula Work?

The calculator uses the Arrow-Pratt measure of relative risk aversion:

\[ RRA = -\frac{u''(w) \cdot w}{u'(w)} \]

Where:

\( RRA \) — Relative Risk Aversion (unitless)
\( u''(w) \) — Second derivative of utility function with respect to wealth
\( u'(w) \) — First derivative of utility function with respect to wealth
\( w \) — Wealth level

Explanation: The formula measures the percentage change in marginal utility for a percentage change in wealth, indicating how risk preferences scale with wealth.

3. Importance of RRA Calculation

Details: RRA is crucial in portfolio theory, insurance decisions, and economic modeling. It helps determine optimal investment strategies and risk management approaches based on an individual's wealth-dependent risk preferences.

4. Using the Calculator

Tips: Enter the second derivative (u''(w)), first derivative (u'(w)), and wealth (w) values. Ensure first derivative is non-zero to avoid division by zero errors.

5. Frequently Asked Questions (FAQ)

Q1: What does a high RRA value indicate?
A: High RRA indicates strong risk aversion that increases with wealth - individuals become more cautious as they get wealthier.

Q2: What is the difference between absolute and relative risk aversion?
A: Absolute risk aversion measures risk aversion in absolute monetary terms, while relative risk aversion measures it relative to wealth percentage changes.

Q3: What are typical RRA values in economics?
A: RRA typically ranges from 1 to 4 in economic models, with 1 representing constant relative risk aversion (CRRA) utility functions.

Q4: How is RRA used in portfolio selection?
A: RRA determines the proportion of wealth invested in risky assets vs. risk-free assets in modern portfolio theory.

Q5: Can RRA be negative?
A: While theoretically possible, negative RRA is rare and indicates risk-seeking behavior that increases with wealth.