Stress Test Scenario

Time Limit: 2sMemory: 256MB

Problem

Given a portfolio of $n$ positions, each with a weight and a beta (sensitivity to the market), compute the portfolio's percentage loss under a market stress scenario.

Each position's loss is proportional to its weight, beta, and the market decline:

$\text{Portfolio Loss} = \sum_{i=1}^{n} w_i \cdot \beta_i \cdot \Delta_{\text{market}}$

Input Format

Line 1: integer n (number of positions)
Next n lines: two floats weight beta per position
Last line: float market_drop (percentage)

Output Format

The portfolio loss as a percentage, to 4 decimal places.

Examples

Example 1

Input(Line 1: integer n (number of positions))

3
0.4 1.2
0.3 0.8
0.3 1.5
10.0

Output

11.7000

Loss = 0.4*1.2*10 + 0.3*0.8*10 + 0.3*1.5*10 = 4.8 + 2.4 + 4.5 = 11.7%.

Example 2

Input(Line 1: integer n (number of positions))

2
0.5 1.0
0.5 1.0
5.0

Output

5.0000

Both positions have beta=1, so portfolio loss equals market drop.

Constraints

•1 ≤ n ≤ 100
•0 ≤ weight_i ≤ 1, weights sum to 1
•0 ≤ beta_i ≤ 5
•0 < market_drop ≤ 50 (in percent)
•Output portfolio loss percentage to 4 decimal places

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