CFA Level I · CFA Level I Exam · The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models
A stock's returns have a standard deviation of 30%, the market's standard deviation is 20%, and the correlation between them is 0.60. The stock's beta is closest to:
Beta equals the correlation times the ratio of the stock's standard deviation to the market's. That is 0.60 multiplied by 0.30 over 0.20, or 1.5, giving 0.90. Ignoring correlation gives 1.50, and inverting the ratio gives 0.40.
- A0.40
- B0.90Correct
- C1.50
Explanation
Beta = correlation × (σ_stock/σ_market) = 0.60 × (0.30/0.20) = 0.60 × 1.5 = 0.90. Option C is the volatility ratio alone, ignoring the correlation. Option A inverts the ratio: 0.60 × 0.667 = 0.40.
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