Question

2. Suppose you are required to calculate a portfolio return using data for 2012 and 2013. Ob- servations are presented as follows. Period Return 2012 0.50 2013 - 0.50 Table 1: Statistics from the history of portfolio returns, 2012-2013

(a) Calculate the expected returns using the Arithmetic Average and the Geometric Average respectively.

(b) Which approach is a better way to measure the performance of portfolio? Why?

Answer 1

2.

A.

Expected return using arithmetic average = (.5 + (-.5))/2

Expected return using arithmetic average = 0%

Expected return using geometric average = ((1+.5)*(1-.5))^(1/2) - 1

Expected return using geometric average = -.134 or -13.4%

-----------

B.

Geometric average is a better way to measure the performance, because geometric average considers compounding during the calculation period. But, it is not considered when arithmetic average is considered. So, calculation becomes erratic when arithmetic average is chosen.