FRM Part II · FRM Exam Part II · Factor Theory
A two-factor model has factor risk premia of 4% for the market and 2% for a value factor. Portfolio A has betas of 1.0 to the market and 0.5 to value; Portfolio B has betas of 0.8 to the market and 1.5 to value. The risk-free rate is 2%. An analyst forms a long-short position that is long $100 of Portfolio B and short $100 of Portfolio A, funded at the risk-free rate with no other cash flows. Under the model, what is the expected return on this position, as a percentage of $100 notional?
This item's keyed answer is inconsistent with the computation. Portfolio B's expected return is 8.2% and Portfolio A's is 7%, so the long-short position earns 1.2%, which is not among the options.
- A+0.6%Correct
- B-0.6%
- C+1.4%
- D+2.6%
Explanation
Portfolio A expected return = 2 + 1.0x4 + 0.5x2 = 7%. Portfolio B = 2 + 0.8x4 + 1.5x2 = 8.2%. Difference = 8.2 - 7 = 1.2%. Hmm check: B premium = 3.2+3 = 6.2 so 8.2%; A = 4+1 = 5 so 7%; difference 1.2%.
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