FRM Part II · FRM Exam Part II · Factor Theory
An investor builds a two-factor portfolio with 50% in a value factor and 50% in a momentum factor. Each factor has volatility of 10% and the correlation between them is -0.20. What is the portfolio volatility?
Portfolio variance equals 0.0025 plus 0.0025 plus a covariance term of minus 0.001, giving 0.004. The square root is about 6.3% volatility. The negative correlation lowers risk below the 7.1% obtained if correlation were zero.
- AApproximately 6.3%Correct
- BApproximately 8.9%
- CApproximately 10.0%
- DApproximately 7.1%
Explanation
Variance = 0.25(0.01)+0.25(0.01)+2(0.5)(0.5)(-0.2)(0.1)(0.1) = 0.0025+0.0025-0.001 = 0.004. The square root is 6.32%. Ignoring correlation (zero) gives 7.07%, and 10% would assume correlation of 1 only for 100% in one factor, so those are wrong.
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 portfolio manager regresses monthly excess returns of a fund on three factors (market, size, value). The regression R-squared is 0.85. Whi…
- Which statement about the stochastic discount factor (SDF) is correct?
- A portfolio manager wants to diversify across factors using the approach in which the investor allocates to factor premiums whose returns ar…
- Using a single-factor model, a portfolio manager estimates that Stock Z has a beta of 1.4 to the market factor. The risk-free rate is 3%, an…
- In a stochastic discount factor framework, the price of an asset is p = E[m x], where m is the SDF and x the payoff. A one-period risk-free …
- In a Brinson-style or factor-based performance attribution, a manager's portfolio return exceeds the benchmark. Which finding would most cle…