Problem 12-7 Calculating Returns and Variability [LO1]

Problem 12-7 Calculating Returns and Variability [LO1]

	Returns
Year	X			Y
1		15	%		22	%
2		29			30
3		10			10
4	–	22		–	27
5		10			21

  

Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. (Do not round intermediate calculations. Enter your average return and standard deviation as a percent rounded to 2 decimal places, e.g., 32.16, and round the variance to 5 decimal places, e.g., 32.16161.)

  

	X	Y
Average return	%	%
Variance
Standard deviation	%	%

rev: 09_29_2015_QC_CS-27339

 

Explanation:

The average return is the sum of the returns, divided by the number of returns. The average return for each stock was:

Remembering back to “sadistics,” we calculate the variance of each stock as:

The standard deviation is the square root of the variance, so the standard deviation of each stock is:

σX = (.03493)1/2

σX = .1869, or 18.69%

σY = (.05067)1/2

σY = .2251, or 22.51%