Treynor Ratio
The Sharpe ratio measures risk by 'total swings.' But for a well-diversified portfolio, how much it is tossed around by the market's overall movement (beta) can matter more. That's what the Treynor ratio measures.
What is the Treynor ratio?
The Treynor ratio is the excess return divided by beta (β). The formula is (portfolio return - risk-free rate) ÷ beta.
The numerator is the excess return over a safe deposit, and the denominator is beta, which shows 'when the market moves 1%, how many % does this portfolio move.' In other words, it looks at 'how much excess return you get per unit of market risk (systematic risk).'
The difference from the Sharpe ratio — what counts as risk
The Sharpe ratio uses 'total volatility (standard deviation)' as the denominator for risk. This includes both the idiosyncratic risk that can be removed through diversification and the market risk that cannot.
The Treynor ratio uses only 'beta,' that is, market risk, as the denominator. It assumes the idiosyncratic risk has already been removed through diversification. That's why the Treynor ratio is especially well suited to evaluating a 'well-diversified portfolio.' If you have piled everything into a single stock, the idiosyncratic risk is large, but because only beta is considered, the risk can be underestimated.
For a well-diversified portfolio, the Sharpe and Treynor rankings come out similar. If the two rankings differ greatly, it may be a signal that the portfolio is not well diversified.
Limits of the Treynor ratio
Because the Treynor ratio depends on beta, if the beta estimate is inaccurate, the result wobbles too. This is because beta changes depending on which index you use to represent the market.
Also, beta is calculated from past data and changes over time. And for an asset that has almost no relationship with the market (when beta is close to 0), the denominator becomes small and the figure becomes unstable. The Treynor ratio is also just one of several risk-adjusted measures, so it should be viewed together with others rather than alone.
Frequently Asked Questions
Q. Which should I look at, the Sharpe ratio or the Treynor ratio?
If the portfolio is well diversified, the Treynor ratio is more appropriate; if it is poorly diversified and idiosyncratic risk is large, the Sharpe ratio is. If an individual investor holds only a few stocks, the Sharpe ratio, which reflects total volatility, is generally the safer choice.
Q. What if the Treynor ratio is negative?
A negative value comes out if you earned less than the risk-free rate (negative excess return) or if beta is negative. If the negative value is because the excess return is negative, it means the risk you took on was not rewarded.
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📋 Results are based on historical data; past returns do not guarantee future returns.
📋 This service is provided for educational purposes to help you understand investing, not as investment advice.