Question

Consider the following historical rates of return:

                         Year   Stock X returns     

                        2014 -0.12   

                        2015                0.04            

                        2016               -0.01             

                        2017 0.05

                        2018               0.10

   2019 0.08

a.  Find standard deviation of these returns.

b. Find coefficient of variation (CV).

show all work manually!

Answer 1

Average of all returns (X1)=

= (-0.12 + 0.04-0.01+0.05+0.10 + 0.08) / 6

= 0.14 / 6

= 0.0233

Year	Return of Stock X	(X-X1)2
2014	-0.12	0.0205
2015	0.04	0.00028
2016	-0.01	0.0011
2017	0.05	0.00071
2018	0.1	0.00588
2019	0.08	0.00321

Sum of (X - X1)2 = 0.03168

Standard deviation(x)  = Sum of (X-X1)2 / n

= 0.03168 / 6

= 0.005281

Coefficient of variation = sd(x) / mean(x)

= 0.005281 / 0.0233

= 0.2266.

So, coefficient of variation is 22.66%.

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