Question

To estimate the Sharpe ratio of a portfolio from a history of asset returns, we use the difference between the simple (arithmetic) average rate of return and the T-bill rate. Why not use the geometric average?

Short answer

The geometric average will artificially inflate the annual performance of the portfolio.

Step-by-step solution

Given information

For estimating Sharpe ratio from a history of asset returns is the difference between the simple average rate of return and the T-bill rate.

Definition

Arithmetic average is the quarterly returns which are calculated by summing up returns and dividing it by the number of quarters.

Explanation

Since arithmetic return ignores compounding, it is not likely to artificially inflate the annual performance of the portfolio. On the other hand, geometric return represents a compounding growth number and will artificially inflate the annual performance of the portfolio.