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Over the past five years, a stock produced returns of 11 percent, 14 percent, 4 percent,...

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?
- Greater than .5 but less than 1.0 percent.
- Greater than 1 percent but less than 2.5 percent.
- Greater than 2.5 percent but less than 16 percent.
- Greater than 84 percent but less than 97.5 percent.
- Greater than 95 percent.
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Answer #1

Average return =(0.11+0.14+0.04-0.09+0.05)/5 = 0.05 = 5%

Standard deviation of returns σ = √[1/(5 - 1)][(0.11 - 0.05)^2+ (0.14 -0 .05)^2+ (0.04 - 0.05)^2+ (-0.09 - 0.05)^2+ (0.05 - 0.05)^2] = 0.0886 = 8.86%

1) Stock will not lose more than 10 percent

z= (-0.1-0.05)/0.0886 = -1.6930

Hence,

Referring to the z-table, ( This is a one-tailed z-test)

z= -1.69 corresponds to Probability = 1-0.0455 = 0.9545

Hence, Greater than 84 percent but less than 97.5 percent ( while greater than 95 percent is also applicable, but 4th option is more suitable)

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