IIQE Paper 5 Investments question: standard deviation of return

Answer: C. 10.61%

Answer: 10.61%. The expected return is 6.25% + 5% - 1.25% = 10%. Weighted squared deviations are 0.25 x (15%)^2 x 2 = 1.125%. The square root of 0.01125 is 0.1061, or 10.61%.Working:• Expected return = 0.25 x 25% + 0.5 x 10% + 0.25 x (-5%) = 10%• Deviations: +15%, 0%, -15%• 0.25 x 0.15^2 + 0.5 x 0 + 0.25 x 0.15^2 = 0.005625 + 0 + 0.005625 = 0.01125• Volatility = square root of 0.01125 = 0.1061 = 10.61%Why not the others:• 1.13%: This is the weighted sum of squared deviations (0.01125) shown as a percentage, without the square root.• 7.50%: This weights the plain 15% deviations by probability instead of squaring them first.• 12.25%: This averages the three squared deviations equally, ignoring the probabilities.Watch out: Skipping the square root, or weighting the deviations without squaring them.Rule: Find the expected return first, then volatility = square root of the probability-weighted squared deviations.Source: IA Investment-linked Long Term Insurance Examination Study Notes, 2024 Edition (7th ed., Nov 2024; for exams from 17 Feb 2025), 2.1.5(b), p. 2/6-2/7