Financial Risk Manager Part 1

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What would be the portfolio's beta, given that its return correlation with the benchmark is 0.65, the portfolio's return volatility is 6%, and the benchmark's return volatility is 3%?

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TTanishq

0.117

1.3

0.325

14.08

Explanation:

Explanation

The portfolio beta (β) is calculated using the formula:

\beta = \rho \frac{\sigma(\text{portfolio})}{\sigma(\text{benchmark})}

Where:

β = beta of the portfolio
ρ = correlation between the portfolio and the benchmark = 0.65
σ(portfolio) = standard deviation (volatility) of the portfolio = 6% = 0.06
σ(benchmark) = standard deviation of the benchmark = 3% = 0.03

Substituting the values:

\beta = 0.65 \times \frac{0.06}{0.03} = 0.65 \times 2 = 1.3

Therefore, the portfolio's beta is 1.3, which corresponds to option B.

Key Points:

Beta measures the sensitivity of a portfolio's returns to benchmark returns
A beta of 1.3 means the portfolio is expected to be 30% more volatile than the benchmark
The formula shows that beta depends on both the correlation and the relative volatilities of the portfolio and benchmark

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