This is the last question from Konvexity Mock One PM
Relevant info, Fund A: IR=.5, active risk=10% Benchmark: Sharpe=.8, total risk=15%
In order to achieve optimal level of active risk, the investor invests 6.25% in the Benchmark and 93.75% in Fund A. What is the excess return over risk-free rate that is expected to be generated by the portfolio of the investor?
A) 12.69% B) 14.69% C) 16.69%
Is it C? 16.69?
The question asks for Rp - Rf , which is very similar to the sharp ratio.
This question has a few formulas, but basically you know the Sharpe ratio and the IR. Extrapolating from those:
SRb = .8 = (Rb - Rf) / STD_b , so Rb - Rf = .8 x .15 = .12
IRp = .5 = (Rp - Rb) / Active_Risk , so Rp-Rb = .5 x .10 = .05
Then you do (Rp-Rb) + (Rb-Rf) = Rp - Rf = .12 + .05 = .17
Since 93.75% is invested in the portfolio and 6.25% is invested in the benchmark, you would do: .17 x .9375 + .12 x .0625 = _ .1669 _