Question

Calculate the variance of the following returns.

Year Return

1 0.06

2 -0.05

3   -0.16

4   0.28

5 0.08

Enter the answer with 4 decimals, e.g. 0.1234.

Answer 1

Variance can be calculated with the help of below formula -

(Note: here, n- 1 is used in the denominator as the returns are given for few years and these are assumed to be of a sample)

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

Returns are shown in below table-

No. of years	Return	( Return - Mean return)	( Return - Mean return)2
1	0.06	0.018	0.000324
2	-0.05	-0.092	0.008464
3	-0.16	-0.202	0.040804
4	0.28	0.238	0.056644
5	0.08	0.038	0.001444
Total return	0.21	Total	0.10768
Mean 0.21/ 5=	0.042

Variance = 0.10768 / (5 - 1)

= 0.10768 / 4

= 0.02692

Variance of the portfolio = 0.0269

Hope it helps!