FRM Part II · FRM Exam Part II · Illiquid Assets
A fund reports quarterly returns with smoothing parameter a = 0.60, meaning reported return R_t = 0.40 x true return r_t + 0.60 x R_(t-1). The latest reported return is 3.0% and the prior quarter's reported return was 2.0%. What is the unsmoothed (true) return for the latest quarter?
The unsmoothed return is 4.50%. Using r = (R_t − a·R_(t−1))/(1−a), the calculation is (3.0 − 0.6×2.0)/0.4 = 1.8/0.4 = 4.5%. This reverses the smoothing, and it reconciles because 0.4×4.5 + 0.6×2.0 equals the reported 3.0%.
- A4.50%Correct
- B3.00%
- C1.80%
- D6.00%
Explanation
True r = (R_t - a R_(t-1))/(1-a) = (3.0 - 0.6 x 2.0)/0.40 = (3.0 - 1.2)/0.40 = 1.8/0.4 = 4.5%. Check: 0.4 x 4.5 + 0.6 x 2.0 = 1.8 + 1.2 = 3.0. The 1.80% option omits dividing by (1-a).
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