Treynor Ratio : Meaning, Calculation and Examples

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treynor ratio

What is Treynor Ratio?

The Treynor ratio is basically used by the investors to measure the performance of their investments or to know how their investments are performing.

As, of Treynor Ratio definition is stated as a measure by which the additional returns which is produced by a fund and is over and above the risk-free returns.

Treynor Ratio Formula

Treynor Ratio is calculated by taking into account the difference between portfolio returns as well as the risk free rate and dividing them both. So, the formula for Treynor Ratio can be stated as follows:

Treynor Ratio Formula 1:

Treynor Ratio = Portfolio Return-Risk free rate/portfolio’s Beta

Here, the Treynor formula can also be represented as follows:

Treynor Measure = βPR – RFR / β

​Where in the above Treynor Ratio formula:

  • PR = is the portfolio return
  • RFR = is the risk-free rate
  • Β = refers to beta​

In the treynor ratio formula the numerator represents the risk premium, whereas the denominator represents the portfolio risk. And the result obtained by dividing both the numerator and the denominator or say the risk premium and the portfolio risk depicts the portfolio’s return per unit of the risk.

Read Here:- Understand the Full Definition of Per Stirpes

Treynor Ratio Formula 2:

The formula can also be represented as follows:

Treynor Ratio = Ri – Rf / B

Where, in the above Treynor Ratio formula:

  • Ri = return of the investment
  • Rf = the risk free rate of return
  • B = the beta of the portfolio

How to calculate Treynor Ratio?

The Treynor Ratio revolves around striking the balance between the return and risk of the portfolio. Whereas, the fund’s beta depicts the sensitivity of the fund returns. So, the higher the value of the beta the higher or lower will be the returns of the portfolio or investments as it eventually depends upon the market.

What is good treynor ratio?

A good treynor ratio is the one that holds up the higher value. As, it depicts the relationship between the portfolio’s return and risk. So, a higher Treynor ratio means the better or good the treynor ratio.

Treynors ratio examples:

Example 1: Let us assume that we are given the following figures:

Actual Return of the Portfolio ({367c01af22dc6c3a8611ff25983b0f0a247ed9fc1c45fd9103ad49b47a0c5f39}): 6.5

Risk-free Rate of Return ({367c01af22dc6c3a8611ff25983b0f0a247ed9fc1c45fd9103ad49b47a0c5f39}): 20

Beta of the Portfolio ({367c01af22dc6c3a8611ff25983b0f0a247ed9fc1c45fd9103ad49b47a0c5f39}): 3

Applying the treynor formula as:

Treynor Ratio = Portfolio Return-Risk free rate/portfolio’s Beta
= 6.5 – 20 / 3

The calculated Treynor Ratio is -4.5

Example 2: Let us assume that we are given the following figures:

Actual Return of the Portfolio ({367c01af22dc6c3a8611ff25983b0f0a247ed9fc1c45fd9103ad49b47a0c5f39}): 4

Risk-free Rate of Return ({367c01af22dc6c3a8611ff25983b0f0a247ed9fc1c45fd9103ad49b47a0c5f39}): 2

Beta of the Portfolio ({367c01af22dc6c3a8611ff25983b0f0a247ed9fc1c45fd9103ad49b47a0c5f39}): 10

Applying the treynor formula as:

Treynor Ratio = Portfolio Return-Risk free rate/portfolio’s Beta
= 4 – 2 / 10

The calculated Treynor Ratio is 0.002

Treynor ratio calculator:

For calculation of treynor ratio, we can use treynor ratio calculator that depicts the actual value of the ratio.

Treynor ratio vs sharpe ratio:

The Treynor ratio explores the surplus return which is produced for each unit of the risk in the given portfolio, whereas the Sharpe ratio assists the investors in recognizing an investment’s return as compared to its risk. So, both the Treynor ratio and the Sharpe ratio works towards measuring the risk free rate or the risk adjusted rate from the return.

Treynor ratio formula in mutual fund:

The Treynor ratio formula in mutual fund can be stated as: The difference of the fund returns and the risk free rate divided by its beta factor.

Example: Suppose the return on the investments be 20{367c01af22dc6c3a8611ff25983b0f0a247ed9fc1c45fd9103ad49b47a0c5f39} and the risk free rate is 10. Whereas, the beta factor is 2. So, the Treynor ratio formula in mutual fund will be calculated as follows:
treynor ratio formula in mutual fund = return – risk free rate / Beta
= 20 – 10 / 2
= 5

So, the treynor ratio for mutual funds will be 5.

Black Treynor Ratio:

The Treynor-Black model ratio is used for the purpose of exploiting or maximizing the Sharpe ratio by adding some adjusted and non adjusted portfolios together. Therefore, here the non systematic risk is involved and the ratio of alpha with the non systematic risk is termed as the black Treynor ratio.

Conclusion:

As performance of the portfolio is must, in any investment process. And the Treynor ratio helps us in measuring the performance of an investment by providing the information related to investor, risk free return. So, by analysing the treynor ratio we know how profitable an investment will prove out. As, higher the treynor ratio, the more profitable will be the investment.

FAQ

The systematic risk is the main point of difference that lies between the sharpe ratio and the treynor ratio. As, the Treynor ratio explores the surplus return which is produced for each unit of the risk in the given portfolio, whereas the Sharpe ratio assists the investors in recognizing an investment's return as compared to its risk.

No, the treynor ratio is not a percentage. In fact, it is a ratio that depicts the performance of an investment or the portfolio.

By A negative ratio we come to know that the investment or the portfolio has performed not as good as expected, as compared to a risk free instrument.

A Treynor ratio provides us information about the return on investment, portfolio of stock, the exchange rate, mutual funds being traded, etc. By comparing the return and the risk free rate.

Having a beta of 0 mean, eventually means that there exist some risk free assets like cash and treasury bonds. Moreover, the value of Beta can also be 0 when there exists correlation of the item's returns with the market's returns.

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