The Treynor ratio is a measure of risk-adjusted return, similar to the Sharpe ratio and the Sortino ratio. It is used to evaluate the performance of a portfolio by adjusting for the risk taken to generate the return. The higher the Treynor ratio, the better the portfolio’s return relative to the risk it is taking on. It is calculated by dividing the portfolio’s excess return (the portfolio return minus the risk-free rate of return) by the portfolio’s beta. Beta is a measure of a portfolio’s volatility in relation to the market. A beta of 1 indicates that the portfolio’s returns are in line with the market, while a beta greater than 1 indicates that the portfolio’s returns are more volatile than the market, and a beta less than 1 indicates that the portfolio’s returns are less volatile than the market.

The formula for the Treynor ratio is:

### Treynor ratio = (portfolio return – risk-free rate of return) / portfolio beta

For example, let’s say a portfolio has a return of 8%, a beta of 1.5, and the risk-free rate of return is 2%. The Treynor ratio would be:

### (8 – 2) / 1.5 = 4

A Treynor ratio of 4 indicates that the portfolio is generating a return that is 4 times higher than the level of market risk (beta) it is taking on. A Treynor ratio greater than 1 indicates that the portfolio is generating a return that is higher than the level of market risk it is taking on, while a Treynor ratio less than 1 indicates that the portfolio is generating a return that is lower than the level of market risk it is taking on.

The Treynor ratio is useful for evaluating the performance of a portfolio in relation to the market. It can be used to compare the risk-adjusted performance of different portfolios, and is particularly useful for portfolios that have a high beta.

However, as with the Sharpe ratio and Sortino ratio, it is important to consider the Treynor ratio in the context of the investor’s risk tolerance and investment goals. Additionally, it is also important to note that the Treynor ratio also does not account for skewness or kurtosis of the return distribution.