Question

These are the yearly returns for a mutual fund. . Year Return 2013 15.00% 2014 -8.00% 2015 7.50% 2016 9.11% 2017 10.00% 2018 -7.62% 2019 4.00% Calculate the geometric return. For the Fidelity mutual fund exercises, this is also known as the "average annual return". Select one: a. More than 5.0% b. Less than 2.0% c. 2.0% to 3.0% d. 4.0% to 5.0% e. 3.0% to 4.0%

Answer 1

Geometric return = [(1+r1) x (1+r2) x…… x (1+rn)]1/n – 1

r1, r2, …. rn = Return for the periods 1,2…n

n = Number of periods

Year	Return	1+ Return
2013	0.15	1.15
2014	-0.08	0.92
2015	0.075	1.075
2016	0.0911	1.0911
2017	0.1	1.1
2018	-0.0762	0.9238
2019	0.04	1.04

Geometric return = (1.15 x 0.92 x 1.075 x 1.0911 x 1.1 x 0.9238 x 1.04)1/7– 1

                              = (1.31148301401031)1/7– 1

                              = (1.31148301401031) 0.142857142857143 – 1

                              = 1.03949699591692 – 1

                              = 0.03949699591692 or 3.95 %

Geometric return is 3.95 % i.e. between 3 % and 4 %

Hence option “e. 3.0 % to 4.0 %” is correct answer