FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
Returns on assets A and B have variances 0.09 and 0.16 and correlation -1. What weight in A (with the remainder in B, weights summing to 1) produces a zero-variance portfolio?
The weight in A is 4/7. With perfect negative correlation, volatility is zero when 0.3w equals 0.4(1-w), so w is 0.4 divided by 0.7. The reversed weight of 3/7 would leave residual risk.
- A3/7
- B4/7Correct
- C0.5
- D3/4
Explanation
With correlation -1, sd = |wσA - (1-w)σB| = 0. With σA=0.3 and σB=0.4: 0.3w = 0.4(1-w), so 0.7w = 0.4 and w = 4/7. Option 3/7 reverses the weights.
Did you get it right without looking?
One question tells you little. A timed set on Measuring Return, Volatility, and Correlation shows your real accuracy, how long you take and where you lose marks.
More Measuring Return, Volatility, and Correlation questions
- An investment gains 30% in year 1 and loses 20% in year 2, both stated as simple returns. What is the average per-year log return over the t…
- Concordant and discordant pairs are used to compute Kendall's tau. For a sample of 6 paired observations (15 distinct pairs), 12 pairs are c…
- The VIX index is quoted at 20.00. Assuming the standard interpretation of the index as an annualized, 30-day expected volatility in percenta…
- An analyst finds that a stock's 30-day implied volatility is persistently above subsequently realized volatility, with the average gap of ab…
- Asset A has a daily return volatility of 2% and asset B has 3%. The covariance of their daily returns is 0.00045. A portfolio holds equal we…
- A risk manager finds that monthly returns on a portfolio have first-order autocorrelation of +0.30, while the monthly standard deviation is …