A stock had returns of 15 percent, 8 percent, 12 percent, -15 percent, and -4 percent for the past five years

A stock had returns of 15 percent, 8 percent, 12 percent, -15 percent, and -4 percent for the past five years. Based on these returns, what is the approximate probability that this stock will return at least 20 percent in any one given year?    A.  less than 0.5 percent B.  greater than 0.5 percent but less than 1.0 percent C.  greater than 1.0 percent but less than 2.5 percent D.  greater than 2.5 percent but less than 16 percent E.  greater than 16.0 percent Average return = (0.15 + 0.08 + 0.12 - 0.15 - 0.04)/5 = 0.032 σ = √[1/(5 - 1)] [(0.15 - 0.02)2 + (0.08 - 0.02)2 + (0.12 - 0.02)2 + (-0.15 - 0.02)2 + (-0.04 - 0.02)2] = 0.1248 Upper end of 68 percent range = 0.032 + 0.1248 = 15.68 percent Probability of earning at least 20 percent in any one year is less than 16 percent but greater than 2.5 percent.

75.

A stock had returns of 14 percent, 13 percent, -10 percent, and 7 percent for the past four years. Which one of the following best describes the probability that this stock will lose no more than 10 percent in any one year?    A.  greater than 0.5 but less than 1.0 percent B.  greater than 1.0 percent but less than 2.5 percent C.  greater than 2.5 percent but less than 16 percent D.  greater than 84 percent but less than 97.5 percent E.  greater than 95 percent Average return = (0.14 + 0.13 - 0.10 + 0.07)/4 = 0.06 σ = √[1/(4 - 1)][(0.14 - 0.06)2 + (0.13 - 0.06)2 + (-0.10 - 0.06)2 + (0.07 - 0.06)2] = 0.11106 Lower bound of 68 percent range = 0.06 - (1 × 0.11106) = -5.11 percent Lower bound of 95 percent range = 0.06 - (2 × 0.11106) = -16.21 percent Probability of losing more than 10 percent in any given year is between 2.5 and 16 percent. Thus, the probability of NOT losing more than 10 percent is between 84 and 97.5 percent.

76.

Over the past five years, a stock produced returns of 11 percent, 14 percent, 4 percent, -9 percent, and 5 percent. What is the probability that an investor in this stock will not lose more than 10 percent in any one given year?    A.  greater than 0.5 but less than 1.0 percent B.  greater than 1.0 percent but less than 2.5 percent C.  greater than 2.5 percent but less than 16 percent D.  greater than 84 percent but less than 97.5 percent E.  greater than 95 percent Average return = (0.11 + 0.14 + 0.02 - 0.09 + 0.05)/5 = 0.05 σ = √[1/(5 - 1)][(0.11 - 0.046)2 + (0.14 - 0.046)2 + (0.04 - 0.046)2 + (-0.09 - 0.046)2 + (0.05 - 0.046)2] = 0.0886 Lower bound of 68% probability range = 0.05 - (1 × 0.0886) = -3.86 percent Lower bound of 95% probability range = 0.05 - (2 × 0.0886) = -12.72 percent The probability of losing 10 percent or more is greater than 2.5 percent but less than 16 percent. Thus, the probability of NOT losing more than 10 percent is greater than 84 percent but less than 97.5 percent.