You\'ve observed the following returns on Doyscher Corporation\'s stock over the
ID: 2714713 • Letter: Y
Question
You've observed the following returns on Doyscher Corporation's stock over the past five years: -29.7 percent, 16.8 percent, 36.6 percent, 3.9 percent, and 22.9 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 10.06 % Requirement 2: 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 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
Year
Returns (A)
(A - 10.1)
(A - 10.1)2
1
-29.7(NOTE 1)
-39.8
1584.04
2
16.8
6.7
44.89
3
36.6
26.5
702.25
4
3.9
-6.2
38.44
5
22.9
12.8
163.84
Totals
50.5
2533.46
A denotes the Returns.
(NOTE 1):- First year return of 29.7 is in negative (loss).
Requirement 1 :-
Arithmetic average return = 50.5 / 5 = 10.1
Requirement 2 :-
a) Variance of returns = 2533.46 / 5 = 506.692
b) Standard deviation of returns = Under root of Variance = 22.51 (approx)
Conclusion:-
Note:- Always remember that variance is the square of Standard deviation.
OR
Standard deviation is the square root of variance.
Year
Returns (A)
(A - 10.1)
(A - 10.1)2
1
-29.7(NOTE 1)
-39.8
1584.04
2
16.8
6.7
44.89
3
36.6
26.5
702.25
4
3.9
-6.2
38.44
5
22.9
12.8
163.84
Totals
50.5
2533.46
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