Question

An investment in the “techstar” has been highly volatile over the past four years. An initial investment of $10,000 increased to $25,000 at the end of the 1^styear, increased to $35,000 by the end of the 2nd year, fell to $5,000 at the end of the 3^rdyear, and recovered to $10,000 by the end of the 4^thyear.

Calculate the arithmetic and geometric returns over the last four years.

Which measure of performance is more appropriate to use when analyzing past performance? Why?

Answer 1

1st year return = ( 25,000 - 10,000) / 10,000 = 1.5 or 150%

2nd year return = (35,000 - 25,000) / 25,000 = 0.4 or 40%

3rd year return = ( 5,000 - 35,000) / 35,000 = -0.85714 or -85.714%

4th year return = ( 10,000 - 5,000) / 5,000 = 1 or 100%

Arithmetic return = ( 1.5 + 0.4 - 0.85714 + 1) / 4

Arithmetic return = 0.510715 or 51.0715%

Geometric return = [(1 + 1.5 ) * ( 1 + 0.4 ) * ( 1 - 0.85714 ) * ( 1 + 1)]^1/4 - 1

Geometric return = [ 2.5 * 1.4 * 0.14286 * 2]^1/4 - 1

Geometric return = [1]^1/4 - 1

Geometric return = 0

Geometric performance is more appropriate

When considering investment returns it is the geometric average, not arithmetic average, that matters. Investment average returns must be figured as a geometric average in order to be accurate. This is because through compounding each successive term is dependent on the previous outcome.

In the above exapmle, eventhough investor is back to where he started, i.e, $10,000, arithmetic average shows a return of 51%. But geoemtric shows a return of zero which depicts a more accurate picture.