Charles Griffith makes quarterly bets between stocks of industrial and utility sectors. The historical correlation between the returns of the two sectors is -0.20.Further information is as below:
Benchmark
Sector / E (R) / σ / Weight
Industrial / 12.00% / 13.0% / 80%
Utility / 5.2% / 2.5% / 20%
The annualized active risk of Griffith’s strategy is closest to:
A) 10.90%
B) 27.44%
C) 13.72%
The ans to this question is B. Their explanation to the ans is
Combined active risk = σ C = [σ I 2 -2σ I σ U r IU + σ U 2 ] 1/2
=[(0.13) ^2+( 0.025 )^2 – 2 (0.13)(0.025)(-0.20)]^ 1/2 = 0.1372 or 13.72%
Annualized active risk = 0.1372 x (4) 1/2 = 0.2744 or 27.44%