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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

Returns on assets A and B have standard deviations of 4% and 6% and a covariance of 0.0012. What is the correlation, and what would it become if all of A's returns were multiplied by 3 (a change of scale)?

The correlation is 0.50 both before and after rescaling. It equals covariance 0.0012 divided by the product of volatilities, 0.04 times 0.06, which is 0.0024. Multiplying A by 3 scales covariance and A's volatility equally, so correlation is unchanged, unlike covariance, which triples.

  1. A0.50 and 0.50Correct
  2. B0.50 and 1.50
  3. C0.30 and 0.30
  4. D0.50 and 0.17

Explanation

Correlation = 0.0012/(0.04*0.06) = 0.0012/0.0024 = 0.50. Multiplying A by a positive constant multiplies covariance and A's standard deviation by 3, so the ratio is unchanged at 0.50. Covariance would triple, but correlation is scale invariant and bounded by 1, so 1.50 is impossible.

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