FRM Part II · FRM Exam Part II · Factor Theory
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 bond pays 1 for sure and is priced at 0.96. An asset has expected payoff E[x] = 1.10 and Cov(m, x) = -0.0384. What is the price of the asset?
The price is 1.0176. The risk-free bond sets the expected SDF at 0.96, so the discounted expected payoff is 0.96 times 1.10, or 1.056. The negative covariance between the SDF and the payoff then reduces the price by 0.0384, giving 1.0176.
- A1.0176Correct
- B1.0944
- C1.0560
- D1.0752
Explanation
E[m] = 0.96 because the risk-free bond pays 1. p = E[m]E[x] + Cov(m,x) = 0.96 x 1.10 - 0.0384 = 1.056 - 0.0384 = 1.0176. Ignoring the covariance gives 1.056, and adding it gives 1.0944, both wrong.
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