Statistical Measures of Asset Returns: practice question
A quantitative analyst at Delmora Bank estimates the covariance between the annual returns of the Wrentham Equity Fund and the Osier Bond Fund at 0.0108. The funds' return standard deviations are 18.0% and 12.0%, respectively. The correlation between the two funds' returns is closest to:
- 0.33
- 0.50
- 2.00
Show answer and explanation
Correct answer: B
Working: Corr = Cov/(s1 x s2) = 0.0108/(0.18 x 0.12) = 0.0108/0.0216 = 0.50.
Explanation: Correlation is the covariance scaled by the product of the two standard deviations: 0.0108/(0.18 x 0.12) = 0.0108/0.0216 = 0.50, indicating a moderately strong positive linear association between the funds' returns. The 0.33 option pairs the equity fund's standard deviation with itself, 0.0108/(0.18 x 0.18), a slip that matters here precisely because the two funds' dispersions differ. The 2.00 option inverts the formula, dividing 0.0216 by 0.0108; a correlation outside the feasible range of -1 to +1 should by itself signal that the arithmetic went wrong.
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