You find a certain stock that had returns of 7 percent, –12 percent, 18 percent,

Question

You find a certain stock that had returns of 7 percent, –12 percent, 18 percent, and 19 percent for four of the last five years. If the average return of the stock over this period was 10.5 percent, the stock's return for the missing year was  percent. The standard deviation of the stock's return is percent. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))

You find a certain stock that had returns of 7 percent, –12 percent, 18 percent, and 19 percent for four of the last five years. If the average return of the stock over this period was 10.5 percent, the stock's return for the missing year was  percent. The standard deviation of the stock's return is percent. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))

Explanation / Answer

let Return for missing year = X

Average return = sum of return on stock /Number of years

10.5   =   ( 7 -12 +18 +19+ X) / 5

10.5 =    (32 +X)/5

32 +X = 10.5*5

X = 52.5 -32

X= 20.50 %

so return for missing year = 20.50%

2)

Standard deviation =Square root of (Variance/Number of years)

                          = square root of (747/5)

                        =square root of 149.40

                        = 12.22%

Year Return(X)(%) (X-Average return) , where average return = 10.5% (X-average return)^2 variance 1 7 (7-10.5) = -3.5 (-3.5)^2 = 12.25 12.25 2 -12 (-12-10.5) = -22.50 (-22.50)^2 = 506.25 506.25 3 18 (18-10.5) = 7.5 (7.5)^2 = 56.25 56.25 4 19 (19-10.5) =8.5 (8.5)^2 = 72.25 72.25 5 20.5 (20.5 - 10.5) = 10 (10)^2 = 100 100 Total 747

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