Question

A stock has reported returns of -15%, -5%, -19%, -1%, and 6% in five of the last six years. The average return over this period was -12%. Calculate the variance of these returns during this six-year period.

Answer 1

2.05%

Working:

a.	Calculation of return of one misiing year:
	Total Return over 6 years			=	-12%*6	=	-72%
	Total return of 5 years			=	-15%	+	-5%	+	-19%	+	-1%	+	6%	=	-34%
	Return of missing year			=	-72%	-	-34%		=	-38%
b.	Calculation of Variance;
		Year	return	Average return
			a	b		(a-b)^2
		1	-15%	-12%		0.09%
		2	-5%	-12%		0.49%
		3	-19%	-12%		0.49%
		4	-1%	-12%		1.21%
		5	6%	-12%		3.24%
		6	-38%	-12%		6.76%
			Total			12.28%
		Variance	=	12.28%	/	6	=	2.05%