Question

if a portfolio regularly falls twice as much as a benchmark index rises, the portfolios beta coefficient is ________.

○ 0.5

○ 2.0

○ -2.0

○ -0.5

Explanation:

Step1: Recall Beta Definition

Beta measures a portfolio's volatility relative to a benchmark. If the benchmark rises (positive change), the portfolio falls (negative change), so beta should be negative.

Step2: Analyze Magnitude

The portfolio falls twice as much as the benchmark rises. So if benchmark change is \( \Delta I \), portfolio change is \( -2\Delta I \). Beta (\( \beta \)) is \( \frac{\text{Portfolio Return Change}}{\text{Benchmark Return Change}} = \frac{-2\Delta I}{\Delta I} = -2.0 \).

Answer:

-2.0 (Option: -2.0)