Financial Risk Manager Part 1

Explanation

The power law describes the probability of observing a random variable X greater than a given value x as:

$P(X > x) = kx^{-\alpha}$

Where k and α are constants.

Given:

• α = 4
• P(X > 20) = 0.01

Step 1: Find the constant k $`$0.01 = k \cdot 20^{-4}$$ $0.01` = k \cdot \frac{1}{20^4}$$ $0.01 = k \cdot \frac{1}{160,000}$$k = 0.01 \times 160,000 = 1,600$$

Step 2: Calculate P(X > 10) $P(X > 10) = 1,600 \cdot 10^{-4}$ $P(X > 10) = 1,600 \cdot \frac{1}{10,000}$ $P(X > 10) = \frac{1,600}{10,000} = 0.16$

Therefore, the probability that X > 10 is 0.16.