Question

Assume total annual returns for retail properties nationally over a five-year period were 7.6%, 6.4%, 12.9%, 16.2%, and -6.3%, respectively. Determine the arithmetic and geometric mean annual returns for the series, respectively.

9.88% and 8.12%

7.36% and 6.82%.

9.88% and 7.22%

7.36% and 7.07%

Answer 1

ANS: Arithmetic Mean = 7.36% and Geometric mean = 7.07%

Working :

Given: Total annual returns for retail properties nationally over a five-year period are as follows

Year	Return
1	0.076
2	0.064
3	0.129
4	0.162
5	-0.063

A)  Calculation of the arithmetic of annual returns for the series

where n = number of years

Mean = (0.076+0.064+0.129+0.162+(-0.063)) /5
Mean = 0.368 / 5
Mean = 0.0736 or 7.36%

B) Calculation of geometric mean of annual returns for the series

where n = number of years

GM = 1.070727 -1
GM = 0.070727 or 7.07%