DW Co. stock has an annual return mean and standard deviation of 15.5 percent an

Question

DW Co. stock has an annual return mean and standard deviation of 15.5 percent and 44 percent, respectively. What is the smallest expected loss in the coming year with a probability of 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.)

Smallest expected loss %

DW Co. stock has an annual return mean and standard deviation of 15.5 percent and 44 percent, respectively. What is the smallest expected loss in the coming year with a probability of 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.)

Smallest expected loss %

Explanation / Answer

Portfolio Average return = 15.5% or 0.155

Portfolio Standard Deviation = 44% or 0.44

Probability = 5% or confidence level = 100-5% = 95%

Assuming a normal distribution of returns, the minimum expected loss at a probability of 5% will be -1.65 standard deviations away from the mean which is 44%. The calculation of minimum expected loss for a period of one year would be

Minimum expected loss = -1.65 * Standard Deviation * Square root (Time period) + Mean return

                                             = -1.65 * 0.44 * square root (1) + 0.155

                                             = -0.726 +0.155

Minimum expected loss = -0.726 + 0.155 = -0.571

Smallest Expected Loss = 57.1 %

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