Question

1. Assume you are calculating both averages for the same series of observations. Which of the two averages (geometric or arithmetic) is usually the highest? When would they be equal? What situation creates more dispersion between the two averages? What are two reasons why you might prefer geometric averages over arithmetic averages with respect to financial returns?

Answer 1

Between arithmetic average and geometric average, the former one, ie., arithmetic average is higher usually.

Both the averages will become equal when all the return values considered are equal.

Dispersion between the two averages is dependant on the variability of the distribution and is directly proportional. In other words, the more the variability, the greater the difference between arithmetic and geometric averages.

Arithmetic average is the simple average of the values of returns during the period analyzed. This gives the central tendency of the series of returns, and not an indicator of the return actually earned over the period. On the other hand, geometric average gives the compounded rate of return that has been actually earned during the period spread over multiple time slots. Another reason for preferring geometric average is that it takes into account, time value of money.