Woodpecker, Inc., stock has an annual return mean and standard deviation of 12.4

Question

Woodpecker, Inc., stock has an annual return mean and standard deviation of 12.4 percent and 43 percent, respectively. What is the smallest expected loss in the coming month with a probability of 2.5 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Woodpecker, Inc., stock has an annual return mean and standard deviation of 12.4 percent and 43 percent, respectively. What is the smallest expected loss in the coming month with a probability of 2.5 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

First, we convert annual figures of mean and standard deviation to monthly statistics:

E(RP,T ) = 0.124 x 1/12 = 0.01033

S.D(P,T) = 0.43 x (1/12)1/2 = 0.1241

the 2.5% loss level is 1.96 standard deviations below the mean:

Pr[RP < 0.01033 – 1.96 x 0.1241] = 0.025

which simplifies to

Pr[R P < -0.2330] = 0.025

We can expect a loss of -23.30 percent or worse over the next month with a 2.5 percent probability.

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