An institutional investor assumes that returns for a specific asset class are normally distributed. The asset class has an expected annual return of 12% and a standard deviation of 8%. Based on the empirical rule, what is the approximate probability that the asset class will return less than 4% in a given year?

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Accepted Answer

The mean is 12% and the standard deviation is 8%. A return of 4% is exactly one standard deviation below the mean (12 - 8 = 4). According to the empirical rule, 68% of returns fall within ±1 SD. This leaves 32% in the tails. Since the distribution is symmetrical, the bottom tail (below -1 SD) is half of 32%, which is 16%.

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