Question

Given the following historical returns, what is the variance? Year 1 = 8%; year 2 = -12%; year 3 = 6%; year 4 = 1%; year 5 = -19%.

Select one:

a. 0.0089

b. 0.0394

c. 0.0139

d. 0.1178

e. 0.0063

Answer 1

Variance pf returns is the average of squared difference of individual returns and the expected (mean) return. Variance is square of standard deviation.This can be computed with the help of below formula-

and,

(as the returns are given for a sample, N-1 is used in the denominator)

Returns are shown in below table-

No. of years	Return (in %)	( Return - Mean return)	( Return - Mean return)2
1	8	11.2	125.44
2	-12	-8.8	77.44
3	6	9.2	84.64
4	1	4.2	17.64
5	-19	-15.8	249.64
Total return	-16
Mean -16/ 5=	-3.2

Mean = Total of all years return / No. of years

Variance = 554.8 / (5 - 1)

= 138.7 % sq

= 0.01387 or 0.0139

Correct answer is C. 0.0139

Hope it explains!