You’ve observed the following returns on Doyscher Corporation’s stock over the p

Question

You’ve observed the following returns on Doyscher Corporation’s stock over the past five years: –25.8 percent, 14.2 percent, 31.4 percent, 2.6 percent, and 21.6 percent. Requirement 1: What was the arithmetic average return on the stock over this five-year period? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Arithmetic average return 8.80 % Requirement 2: (a) What was the variance of the returns over this period? (Do not round intermediate calculations. Round your answer to 6 decimal places (e.g., 32.161616).) Variance (b) What was the standard deviation of the returns over this period? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Standard deviation %

Explanation / Answer

Answer-

1-To find the average return, we sum all the returns and divide by the number of returns, so:

Arithmetic average return = (–0.258 +0.142 + 0.314 + 0.026 + 0.216)/5= 0.0880 or 8.80%

2-(a) Using the equation to calculate variance, we find:

               Variance = 1/4[(–.258 – .088)2 + (.142 – .088)2 + (.314 – .088)2 + (.026 – .088)2 +

                                               (.216 – .088 )2]

               Variance = 0.048475

(b) The standard deviation is:

               Standard deviation = (0.048475)1/2

               Standard deviation = 0.2201 or 22.01%

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