FRM Part II · FRM Exam Part II · Factor Theory
A two-factor portfolio has weight 60% in factor A and 40% in factor B. Factor A has volatility 10%, factor B has volatility 5%, and their correlation is -0.5. What is the portfolio volatility, to the nearest 0.1%?
Portfolio volatility is about 5.3%. Variance equals 0.0036 plus 0.0004 minus 0.0012, which is 0.0028, and its square root is roughly 5.29%. The negative correlation lowers risk below the 8% weighted average of the individual volatilities.
- A5.3%Correct
- B4.9%
- C7.0%
- D6.2%
Explanation
Variance = 0.6²×0.01 + 0.4²×0.0025 + 2×0.6×0.4×(-0.5)×0.10×0.05 = 0.0036 + 0.0004 - 0.0012 = 0.0028. Square root = 5.29%, about 5.3%. Ignoring correlation gives sqrt(0.004)=6.3%; the weighted average is 8%.
Did you get it right without looking?
One question tells you little. A timed set on Factor Theory shows your real accuracy, how long you take and where you lose marks.
More Factor Theory questions
- A risk manager decomposes a portfolio's active variance using a factor model. Active exposures are market 0.2 and size -0.4. Factor volatili…
- An analyst builds a momentum signal for a universe of stocks. Which construction is most consistent with the conventional momentum factor us…
- A manager builds a long-only multi-factor equity portfolio by combining separate single-factor sleeves (value, momentum, quality) versus an …
- A portfolio manager builds a long-only factor portfolio and a long-short factor portfolio for the same momentum signal. Compared with the lo…
- A pension fund's investment committee is comparing two approaches to building a portfolio. Approach A divides capital among equities, bonds,…
- A sovereign wealth fund notes that its factor exposures are well diversified in normal markets, but factor correlations tend to rise and sev…