CFA Level IPortfolio ManagementHard
A stock has a standard deviation of returns of 35% and a correlation of 0.60 with the market portfolio, which has a standard deviation of 20%. What is the stock's beta?
- A0.60
- B1.05
- C0.34
- D1.75
Show answer & explanationAnswer & explanation
Correct answer: B. 1.05
Beta = ρ(i,m) × (σi / σm) = 0.60 × (35% / 20%) = 0.60 × 1.75 = 1.05. This can also be derived from Cov(i,m)/Var(m), since Cov(i,m) = ρ×σi×σm.
Why the other options are wrong
- A. This is just the correlation coefficient, not the beta.
- C. Incorrectly inverts the ratio of standard deviations.
- D. This is the ratio of standard deviations alone (σi/σm), without multiplying by correlation.
Beta via Correlation and Standard Deviations
Beta measures an asset's systematic risk relative to the market and can be calculated as correlation with the market times the ratio of the asset's standard deviation to the market's standard deviation.
- Formula: β = ρ(i,m) × (σi/σm) = Cov(i,m)/σm²
- Beta of 1.0 means the asset moves in line with the market
- Beta > 1 indicates higher systematic risk than the market
Memory trick: Correlation times the risk ratio gives you beta