IAI Actuarial Core Principles · Economic Modelling · Stochastic models for security prices
A discrete-time model has log-returns per month that are independent N(0.01, 0.04²). An investor holds Rs 1,00,000 for 4 months. Which pair gives the mean and the standard deviation of the 4-month log-return?
The mean is 0.04 and the standard deviation is 0.08. The means of independent monthly log-returns add, giving 4 × 0.01. The variances add, giving 4 × 0.0016 = 0.0064, whose square root is 0.08.
- AMean 0.04; standard deviation 0.16
- BMean 0.04; standard deviation 0.08Correct
- CMean 0.01; standard deviation 0.08
- DMean 0.02; standard deviation 0.04
- Mean 0.04; standard deviation 0.0016
Explanation
Means add over independent periods: 4 × 0.01 = 0.04. Variances add: 4 × 0.0016 = 0.0064, so the standard deviation is 0.08. Option 0 scales the standard deviation by 4 instead of by the square root of 4. Option 4 gives the variance of 0.0016 for one month.
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