Problem 13-13 Value-at-Risk (VaR) Statistic (LO4, CFA6) a. A stock has an annual

Question

Problem 13-13 Value-at-Risk (VaR) Statistic (LO4, CFA6) a. A stock has an annual return of 11 percent and a standard deviation of 44 percent. What is the smallest expected loss over the next year with a probability of 1 percent? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round the z-score value to 3 decimal places when calculating your answer. Enter your answer as a percent rounded to 2 decimal places.) Smallest expected loss b. Does this number make sense? O No O Yes

Explanation / Answer

A)

1% probability is 2.33 standard deviations below mean.

return = 0.11

SD = 0.44

Therefore

P(R <=0.11 - 2.33(0.44)) = 1%

P(R<=0.11 - 1.0252) = 1%

P(R<=-0.9152) = 1%

Hence,

Smallest possible loss = -0.9152 = -91.52%

B)

This loss might seem extremely significant. ie -91.52% may be very high. But this is still possible, as it is for a probability of 1%. A stock easily fall by 91% on a probability basis of 1%.  

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