Question

Q6) A stock had the following annual returns: 5.13% , 12.05% , -10.06% , and 25.02%. Compute the following for the stock:

     a) Expected Return : (1.5 points)

     b) Variance : (1.5 points)

     c) Standard Deviation : (1.5 points)

I understand the expected return, but I'm having issues with the Variance and Standard Deviation.

Answer 1

Given about a stock's return for past 4 years.

Variance is calculated in the table below:

Expected return/Mean u = (r1+r2+r3+r4)/4 = (5.13+12.05-10.06+25.02)/4 = 8.035%

Mean - return = (u - x)

Variance = (sum of (x-u)^2)/n, here n = 4

So, variance = 0.064048/4 = 0.016

So, standard deviation = Variance^(1/2) = (0.016)^(1/2) = 0.1265 or 12.65%

year	Return(x)	(mean - return) = (x-u)	(x-u)^2
1	5.13%	2.91%	0.000844
2	12.05%	-4.02%	0.001612
3	-10.06%	18.10%	0.032743
4	25.02%	-16.99%	0.028849
mean(u)	8.04%	sum	0.064048