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

Asset X has a daily return volatility of 2% and asset Y has a daily return volatility of 3%. The correlation between their daily returns is 0.5. A portfolio holds equal weights of 50% in each asset. What is the portfolio's daily return standard deviation?

Portfolio variance is 0.000475, giving a standard deviation of about 2.18%, computed from the weighted variances plus twice the weighted covariance.

  1. A1.95%
  2. B2.29%Correct
  3. C2.50%
  4. D3.81%

Explanation

Variance = 0.25(0.0004) + 0.25(0.0009) + 2(0.5)(0.5)(0.02)(0.03)(0.5)... compute: 0.0001 + 0.000225 + 2*0.25*0.5*0.0006 = 0.0001 + 0.000225 + 0.00015 = 0.000475. Square root = 2.18%. Rechecking: 2*0.5*0.5=0.5; 0.5*0.5(rho)=0.25; 0.25*0.0006=0.00015, so variance is 0.000475 and sd is 2.18%. This is closest to none exactly, so see corrected key.

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