Question

Assume stock A’s recent 5-year return is 8%, 5%, -2%, 6% and 3%. What is the standard error of stock A using the information in the past 5 years?

Follow up question: now there is another stock, stock B, that has an expected return of 4.60% and a standard deviation of 3.20%.

Which one would you prefer?

Follow up question: now there is another stock, stock C, that has an expected return of 5.20% and a standard deviation of 4.75%.

Among stock A and stock C, which one would you prefer?

Answer 1

Requirement (a):

Year	Return on Stock A	Deviation from Mean	Square of Deviation
1	8%	4%	16%2
2	5%	1%	1%2
3	-2%	-6%	36%2
4	6%	2%	4%2
5	3%	-1%	1%2
			58%2

Mean of Return = Total of retun over period / Number of years

= 20% / 5 years i.e. 4%

Variance = Sum of all deviations / Number of years

= 58%2 / 5 years

= 11.6%2

Standard Deviation of Stock A = Variance i.e. 3.4059%

Standard Error of Stock A = Standard Deviation / Number of years

= 3.4059% / 5

= 1.5232%

Requirement (b):

	Mean	Standard Deviation
Stock A	4%	3.41%
Stock B	4.60%	3.20%

As we can clearly see that Stock B has higher average return (means return) with a lower standard deviation from the Stock A, Stock B will be preferred over Stock A

Requirement (c):

	Mean	Standard Deviation
Stock A	4%	3.41%
Stock C	5.20%	4.75%

Stock C is preferred over Stock A as it has higher earning potential in comparison with Stock A because it has higher earning potential despite of higher standard deviation of Stock C.