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Returns Year X Y 1 20 % 15 % 2 23 35 3 9 14 4 − 16 − 21 5 10 25 Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. X Y Average returns % % Variances Standard deviations % %

EBK CFIN

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Chapter12: Capital Structure

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Problem 10-7 Calculating Returns and Variability

	Returns
Year	X	Y
1		20	%		15	%
2		23			35
3		9			14
4	−	16		−	21
5		10			25

Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.

X Y

Average returns % %

Variances

Standard deviations % %

Expert Solution

Step 1

Standard Deviation:

It represents the dispersion in a set of data that is relative to the average or means.
Standard deviation is computed by taking the variance's square root.
In finance terms, standard deviation represents the asset's relative riskiness.

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