Explain Active Risk in this question
Cant beleive of all the L2 topics, the PM is getting me stumped .
Charles Griffith makes quarterly bets between stocks of industrial and utility sectors. Griffith’s strategy has an annualized active risk of 18%. Based on the information below, If Griffith wants to limit his active risk to 6%, what is the allocation to Utility sector when Griffith is bullish about Industrial stocks?
Answer is -13%..
If active risk is limited to 6%, the deviation from the benchmark weights of 80% and 20% is limited to 6%/18% or 33%. Hence when Griffith is bullish about industrials, the weight to that sector will be 80% + 33% or 113% and the weight to utility sector will be 20% - 33% or -13%.
Question: Not sure I’m following the logic. I thought that if the active portfolio is 18% active risk and we wanted to invest 6% active risk, then we would invest 6/18 = 33% into the active portfolio and than the remainder of 67% into the benchmark. To keep the bench market the same would be 80/20. So the overall portfolio would be Industrial 33% + .67*80% =86.6% and the Utility would be 13.4% . What did I do wrong?