The Treynor ratio is a percentage that measures the reward to risk of a portfolio and when I say risk here I'm referring only to systematic risk. So it's actually a distinction between the Treynor ratio and the Sharpe ratio. They both measure reward from the risk of portfolios and so in that sense, they can each be used to rank portfolios and see which ones give you the most reward for the amount of risk you're taking on. But the Sharpe ratio is actually looking at the excess return of the portfolio divided by volatility and if you remember, volatility measures total risk. When we think about the beta that is just measuring systemic risk so when we calculate the Treynor ratio we're not going to be using volatility like we did with the Sharpe ratio, we're actually going to be using beta we're gonna look at the excess return of the portfolio and then we're gonna divide that by the beta of the portfolio.
We're gonna divide that by the beta of the portfolio because the Treynor ratio just focuses on systematic risk. We only want to use it if we're looking at a well-diversified portfolio where all of the non-systematic risks have already been diversified away. So when we calculate this Treynor ratio the excess return of the portfolio is going to be the expected return of the portfolio minus the risk-free rate and then we divide that by the beta of the portfolio. Again beta is measuring systematic risk so we've got our excess return divided by the systematic risk measure which is beta. Let me do a quick example and just show you how it works.
We've got,
The expected return of the portfolio = 14%
The risk-free rate of return = 2%
The beta of the portfolio = 3
So now we know everything we need to know to be able to calculate the Treynor ratio. We say ok what's the expected return of the portfolio? Well, that's 14% minus the risk-free rate which is 2% so (14% - 2%) and then we divide that by the beta of the portfolio and that is a beta of 3. Then we'd have 12% divided by 3 is equal to 4%.
So the Treynor ratio of this portfolio would be 4% and then we could compare that to another portfolio. Let's say there was some other portfolio that had a Treynor ratio of 3% we have compared these two and we say "This portfolio of our example gives you more reward per unit of systematic risk."
