Question

5-what is the difference between arithmetic and geometric return? Which is the correct matrix to measure stock/portfolio performance? why?

Answer 1

Arithmetic returns are the everyday calculation of the average. You take the series of returns , add them up and then divide the total by the number of returns in the series.

Geometric returns is calculated by multiplying all the (1+ returns), taking the n-th root and subtracting the initial capital (1). The result is the same as compounding the returns across the years.

A simple way to explain the difference is by taking the numbers 2 and 8. The arithmetic average is 5, being (2 + 8)/2 = 10/2 = 5. The geometric mean, on the other hand, is 4: exactly 20 per cent lower. This is calculated as ?(2 x 8) = ?16 = 4

There are various matrices to measure portfolio performance -

1. Sharpe Ratio

2. Treynor Ratio

3. Jenson Ratio

However, Sharpe ratio is more appropriate for well-diversified portfolios, because it more accurately takes into account the risks of the portfolio

The Sharpe ratio can be easily defined as:

(Portfolio Return – Risk-Free Rate) / Standard Deviation