Question

Your portfolio had real net returns of 5% in 2014, −4% in 2015, and 2% in 2016. The net inflation rate for each period was 2% in 2014, 4% in 2015, and −1% in 2016. What is the gross, nominal, compound return of your portfolio over those three years?

A) 1.09% B) 6.05% C) 9.04% D) −3.05% E) 2.82%

Answer 1

The nominal return each year = (1 + real return) * (1 + rate of inflation) - 1

The nominal return in 2014 = (1 + 0.05) * (1 + 0.02) - 1

The nominal return in 2014 = 0.071

The nominal return in 2015 = (1 - 0.04) * (1 + 0.04) - 1

The nominal return in 2015 = -0.0016

The nominal return in 2016 = (1 + 0.02) * (1 - 0.01) - 1

The nominal return in 2016 = 0.0098

The gross, nominal, compound return = [(1 + 0.071) * (1 - 0.0016) * (1 + 0.0098)]^(1/3) - 1

The gross, nominal, compound return = 1.07976540672^(1/3) - 1

The gross, nominal, compound return = 1.0259112758 - 1

The gross, nominal, compound return = 0.0259112758

The gross, nominal, compound return = 2.59112758%

Option E is correct: 2.82%