Over the past four years, a stock produced returns of 13, 6, -5, and 18 percent,...

Over the past four years, a stock produced returns of 13, 6, -5, and 18 percent, respectively.
What is the standard deviation of these returns? What would be the standard deviation of these returns if they were exactly twice the return shown for each year? please show your work.

Expert Solution

Year	Yearly Return	Xi - Average Return	(Xi - Average Return)^2
i	A = Xi	B = A - 8%	C = B^2
1	13	5	25
2	6	-2	4
3	-5	-13	169
4	18	10	100
Average	8		298

Variance = Sum(Xi - Average Return)^2 / n

Variance = 298 / 4

Variance = 74.5%

Standard Deviation = Square Root of Variation

Standard Deviation = 74.5^(1/2)

Standard Deviation = 8.63%

If they were exactly twice the return shown for each year, The standard deviation also doubles as it is a relative measure.

Year	Yearly Return	Xi - Average Return	(Xi - Average Return)^2
i	A = Xi	B = A - 8%	C = B^2
1	13**2 = 26	10	100
2	6%*2 = 12	-4	16
3	-5% * 2 = -10	-26	676
4	18%*2 = 36	20	400
Average	16		1192

Variance = Sum(Xi - Average Return)^2 / n

Variance = 1192 / 4

Variance = 298%

Standard Deviation = Square Root of Variation

Standard Deviation = 298^(1/2)

Standard Deviation = 17.26%

jeff jeffy answered 2 years ago

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