A pro folio has an expected return 5% and a volatility of 10% in the coming year

Question

A pro folio has an expected return 5% and a volatility of 10% in the coming year. 1. What is the probability of the portfolio losing 5% or worse in the coming year? 2. What is the probability of the portfolio losing 20% or worse in the next 4years? A pro folio has an expected return 5% and a volatility of 10% in the coming year. 1. What is the probability of the portfolio losing 5% or worse in the coming year? 2. What is the probability of the portfolio losing 20% or worse in the next 4years? 1. What is the probability of the portfolio losing 5% or worse in the coming year? 2. What is the probability of the portfolio losing 20% or worse in the next 4years?

Explanation / Answer

1) Mean=5%, Standard deviation =10%,
so -5% is -1 standard deviation away from the mean. Prob(R <= -5%) = (1-67%) / 2 = 0.17 or 17%

2) Mean=20%, Standard deviation =sqrt(4) * 10% =20%,
so -20% is -2 standard deviations away from the mean. Prob(R <= -20%) = (1-95%) / 2 = 0.025 or 2.5%

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