Question

The rate of return on Starks Inc., stock over the last 5 years was 16%, 11%, -2%, 5%, and 12%. Over the same period, the return on Wayne Inc.’s stock was 16%, 21%, -3%, 5%, and 13%. Calculate the arithmetic and geometric returns for both companies.

a) Arithmetic: Starks Inc. - 8.4%, Wayne Inc. - 10.4%; Geometric: Starks Inc. - 7.1%, Wayne Inc. - 8.4%
b) Arithmetic: Starks Inc. - 8.8%, Wayne Inc. - 10.4%; Geometric: Starks Inc. - 7.2%, Wayne Inc. - 8.5%
c) Arithmetic: Starks Inc. - 9.2%, Wayne Inc. - 10.6%; Geometric: Starks Inc. - 7.5%, Wayne Inc. - 8.7%
d) Arithmetic: Starks Inc. - 9.6%, Wayne Inc. - 10.8%; Geometric: Starks Inc. - 7.8%, Wayne Inc. - 9.0%

Answer 1

The arithmetic returns for Starks Inc. and Wayne Inc. are 8.4% and 10.4% respectively, while the geometric returns are 7.1% and 8.4% respectively.

Step-by-step explanation:

The question involves calculating the arithmetic and geometric returns for the stocks of two fictional companies, Starks Inc. and Wayne Inc., over a five-year period. To find the arithmetic return, you simply take the average of the yearly returns. So for Starks Inc., the arithmetic return is (16% + 11% - 2% + 5% + 12%) / 5 = 8.4%, and for Wayne Inc., it is (16% + 21% - 3% + 5% + 13%) / 5 = 10.4%. The geometric return, on the other hand, takes into account the compounding over the period and is calculated by taking the product of the returns (as a proportion of 1), taking the nth root where n is the number of years, and then subtracting 1 and converting back to a percentage. For Starks Inc., the geometric return is {[(1 + 0.16)(1 + 0.11)(1 - 0.02)(1 + 0.05)(1 + 0.12)]^(1/5) - 1} * 100 ≈ 7.1%, and for Wayne Inc., {[(1 + 0.16)(1 + 0.21)(1 - 0.03)(1 + 0.05)(1 + 0.13)]^(1/5) - 1} * 100 ≈ 8.4%.