A portfolio’s active risk is the square root of the sums of the squares of the weighted average active risk.

To calculate the active risk, subtract the expected market risk from the risk of each portfolio component. The large-cap strategy’s risk is 27.5%. Subtract the market’s 18.6% risk, and you have active risk of 8.9%. The small-cap strategy’s active risk is 11.5%, and the index fund’s active risk is 0%, because the index tracks the market. Here’s how to calculate the complete strategy’s active risk:

Large-cap strategy: 8.9%² × 15%² = 0.0178%.
Small-cap strategy: 11.5%² × 25%² = 0.0827%.
Index fund: 0%² × 60%² = 0%.

The sum of the squares is 0.1005%. The square root of 0.001005 is 3.17% and that is the portfolio’s active risk