# Treynor Ratio

The Treynor ratio, also called the reward-to-volatility ratio, measures how much excess return is produced by a portfolio per unit of risk that comes with it. Excess return is any return an investment makes outside of what it could have earned in the absence of risk.

While no investment is truly risk-free, the Treynor ratio typically uses treasury bills to represent a risk-free return. Risk is determined by the portfolio’s beta, which is a measure of an investment portfolio’s general systematic risk.

The Treynor ratio was created by American economist Jack Treynor, who also developed the Capital Asset Pricing Model (CAPM) in the 1960s. The CAPM is a model that determines an asset’s theoretically suitable minimum rate of return, helping investors make decisions regarding the addition of assets to a well-diversified portfolio.

When understanding the Treynor ratio, its similarity to the Sharpe ratio is worth noting. These two metrics are almost the same in that they both assess a portfolio’s risk and return. Their difference is, while the Treynor ratio determines volatility with a portfolio beta or systematic risk, the Sharpe ratio adjusts returns based on the portfolio’s standard deviation.

## Treynor Ratio Formula

$Treynor\: Ratio = \dfrac{r_{p} - r_{f}}{\beta_{p}}$
• rp   = Portfolio return
• rf    = Risk-free rate
• βp  = Beta of the portfolio

The formula looks more complex than it is because of the beta symbol and the subscript letters, but it can be explained simply:

$Treynor\: Ratio = \dfrac{Average\: Portfolio\: Return - Average\: Risk\: Free\: Rate}{Beta\: of\: the\: Portfolio}$

The Treynor ratio formula deals with portfolio return and systematic risk. Mathematically speaking, it determines how much excess return can be gained from the risk-free rate per unit of systematic risk. Similar to the Sharpe ratio, it is a return/risk ratio.

In the formula, portfolio return refers to the average of multiple returns earned within a certain period; Risk-free rate is a hypothetical investment’s rate of return under zero risk of financial loss over a specific time frame, and the beta of the portfolio is the weighted sum of all the asset betas of the investments in the portfolio.

In the case of a negative beta, the ratio will not mean anything. Otherwise, a higher ratio means the portfolio is probably a good investment. But again, because the Treynor ratio is derived from past performance, it cannot be an indicator of future performance, and one must never rely purely on one ratio when deciding on investments.

## Treynor Ratio Example

A financial analyst has been studying an equity portfolio and wants to use the Treynor ratio to help him decide if it is a better investment than a fixed Income Portfolio with a Treynor ratio of .03. The equity portfolio’s total return is 7%, its beta is 1.25, and the risk-free rate is 2% (based on the U.S Treasury Bills’ return). Given these values, what is the Treynor ratio of the Equity Portfolio?

Let’s break it down to identify the meaning and value of the different variables in this problem.

• Portfolio return (rp)  = 7%
• Risk-free rate (rf)   = 2%
• Beta of the portfolio (βp) =  1.25

We can now apply the values to our variables and calculate the Treynor ratio:

$Treynor\: Ratio = \dfrac{0.07 - 0.02}{1.25} = 0.04$

In this case, the Treynor ratio on the equity portfolio would be 0.04.

Generally speaking, the higher the Treynor ratio, the better the investment’s performance. In the example, it is clear that the equity portfolio is performing more favorably than the fixed income portfolio, whose Treynor ratio is only 0.03. However, it is important to note that since the ratio is based on past performance, it may no longer be duplicated in the future. And just like other metrics, using just one ratio is not advisable. Instead, other financial metrics should be used before making an investment decision.

## Treynor Ratio Analysis

The Treynor ratio is basically a method of measuring return according to systematic risk. It shows how profitable an investment is – for example, a portfolio of stocks, exchange-traded funds and mutual funds – with respect to the level of risk associated with such investment.

Bottom line, the Treynor ratio measures how likely an investor can benefit from an investment despite the associated risk. It is also driven by a portfolio’s beta, or the portfolio’s responsiveness to market movements, in determining risk levels. The concept behind this metric is investors should receive compensation for a portfolio’s accompanying risks, which do not go away with diversification.

As well, like other financial metrics, the Treynor ratio has a few limitations, such as its historical nature. Investments are not likely to do in the future as they did in the past. The ratio’s accuracy mainly depends on using the right benchmarks for beta measurement. For instance, when using the Treynor ratio to assess a domestic large-cap mutual fund’s volatility, the Russel 2000 Small Stock index will hardly be the right basis for measuring the fund’s beta, which would then end up understated since larger-cap stocks are usually less volatile. The beta should instead be based on a large cap-appropriate index, like the Russell 1000.

Moreover, the Treynor ratio could not be ranked on any dimensions. Provided all else is equal, a higher ratio is usually better when comparing similar investments, but it cannot define by how much exactly. In any case, it is important to note that for negative beta values, Treynor ratio values will not be useful. And because these values are ordinal, the significance of their differences could not be determined as portfolios are compared. For instance, while a 0.8 Treynor ratio is definitely better than a 0.4, it’s not automatically twice as good.

## Treynor Ratio Conclusion

• The Treynor ratio is a performance indicator that measures the amount of return that a portfolio generates with every unit of risk.
• The Treynor ratio formula requires three variables: Portfolio Return, Risk-Free Rate, and Beta of the Portfolio.
• The results of the Treynor ratio is usually expressed as a number.
• The Treynor ratio is a measure that enables investors to adjust a portfolio’s returns for systematic risk.
• A higher Treynor ratio result indicates a better investment.
• The Treynor ratio works like the Sharpe ratio, except the Sharpe ratio adjusts portfolio returns using the portfolio’s standard deviation.
• The Treynor ratio is part of the Capital Asset Pricing Model.

## Treynor Ratio Calculator

You can use the Treynor ratio calculator below to quickly how much excess return was generated per unit of risk associated with a portfolio by entering the required numbers.