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CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns

Holding the expected return and standard deviation of a portfolio constant, an investor raises the minimum acceptable return from 2% to 4%. The portfolio's safety-first ratio will most likely:

The ratio will decrease and the shortfall probability will increase. Raising the threshold shrinks the excess of expected return over the threshold in the numerator, so the threshold sits fewer standard deviations below the mean and a below-threshold outcome becomes more likely.

  1. Adecrease, and the probability of a shortfall will increaseCorrect
  2. Bdecrease, and the probability of a shortfall will decrease
  3. Cincrease, and the probability of a shortfall will decrease

Explanation

The numerator is E(Rp) minus RL, so a higher RL reduces it while the standard deviation is unchanged. A lower ratio means the threshold is fewer standard deviations below the mean, so the probability of returning less than the threshold rises.

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