Question

You are evaluating the performance of two investors. Fernando DeSoto runs the Conquistador investment fund, and Sean Valdez runs the Alpaca fund. Their annual returns are shown in the following table.

Year	Conquistador	Alpaca
2012	6.00%	3.00%
2013	6.00%	12.00%
2014	7.00%	19.00%
2015	6.00%	-7.00%
2016	5.00%	4.00%

Alpaca’s latest report to investors states that Alpaca’s average return was 6.20% over this period. Conquistador’s average return over this period was 6.00%.

Did Alpaca shareholders outperform Conquistador shareholders?

Hint: Compute the arithmetic and the geometric average returns!

Answer 1

NOTE: Total Time Period of Investment Performance Measurement = (2016 - 2012) + 1 = 5 years. If Year 1 return is r1, Year 2 return is r2 and so on, then geometric average return = [(1+r1) x (1+r2) x ......x (1+rn)]^(1/n) - 1.

Investment returns are measured in terms of geometric average and not arithmetic average because the former incorporates the impact of yearly return volatilities in investment return measurement. Arithmetic average ignores annual return volatilities and compounding of returns and hence is inaccurate. Therefore, geometric average is the appropriate measure of a fund's return. Since Alpaca's geometric average return is lower than that of Conquistador's, the former did not outperform the latter as originally claimed.