Treynor ratio explained

The Treynor ratio adjusts excess return for systematic risk which is computed by dividing a portfolio's excess return by its Beta.  

The formula for calculating this ratio is : 

Treynor ratio = (Rp - Rf) / Bp  

Where, Rp = portfolio return,  

Rf = riskless return, 

Bp = portfolio beta.  

As the Treynor ratio indicates return per unit of systematic risk, it is a useful method to measure the performance when investors evaluate and compare various options of portfolios for investment. During comparison, a fund with a higher Treynor ratio is preferable as it indicates that the fund has a higher risk premium for every unit of market risk.  

Difference between Treynor and Sharpe ratio?  

The numerator in the formula remains the same as in the case of Sharpe ratio too. The only change is in the denominator where the standard deviation is replaced by Beta. The Sharpe ratio uses the standard deviation of return as the measure of risk, whereas the Treynor performance measure uses Beta which measures systematic risk. 

To know about Sharpe ratio, refer to -  

https://www.dsij.in/DSIJArticleDetail/ArtMID/10163/ArticleID/20228/Know-more-about-Sharpe-ratio  

When a portfolio is completely well-diversified then both Sharpe and Treynor ratios provide identical ranking as total risk and systematic risk would be the same. However, when a portfolio is not properly diversified, then the Treynor ratio's ranking could be higher than that of the Sharpe ratio as Treynor ratio measures systematic risk and ignores unsystematic risk. Thus, any difference in rankings based on Sharpe Ratio and Treynor ratio is due to the difference in the portfolio's diversification levels.  

To sum it, Sharpe ratio is a more suitable and useful measure when portfolios under evaluation are not adequately diversified whereas the Treynor ratio is suitable when investors hold well-diversified portfolios.