FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
An analyst computes the variance of a portfolio of two assets using the formula w1²σ1² + w2²σ2². Relative to the correct variance, this will understate the variance when:
The formula understates variance when covariance is positive, because the omitted term 2w1w2Cov is then positive for long positions. With negative correlation the omission would overstate variance instead.
- Athe correlation between the assets is negative
- Bthe covariance between the assets is positiveCorrect
- Cthe weights are equal
- Dthe assets have equal volatilities
Explanation
The omitted term is 2w1w2Cov. With positive weights, a positive covariance makes the omitted term positive, so the formula understates variance. Negative correlation would cause overstatement.
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