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

Two assets have return volatilities of 10% and 20%. A portfolio is 60% in the first and 40% in the second, and the portfolio volatility is exactly 10%. What is the correlation between the assets' returns?

The correlation is zero. With weights of 60% and 40%, the variance terms alone sum to 0.01, which already equals the portfolio variance of 0.01 for a 10% volatility, so the covariance term must vanish.

  1. A-0.625Correct
  2. B-0.375
  3. C0.000
  4. D-0.250

Explanation

Portfolio variance 0.01 = 0.36(0.01) + 0.16(0.04) + 2(0.6)(0.4)(0.1)(0.2)rho = 0.0036 + 0.0064 + 0.0096rho. So 0.01 = 0.01 + 0.0096rho, giving rho = 0. Hence the correct answer is 0.000.

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