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# Treynor Ratio Definition, Quiz and Tutorial

While not as popular as the Sharpe Ratio, it provides performance analysts another view of the historical reward-to-risk trade off.
1. Define - Learn how an when to apply the Treynor Ratio.
2. Context - Use Treynor Ratio in a sentence.
3. Video - See the video for the concepts.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself. by Paul Alan Davis, CFA
Updated: February 23, 2021
If you consider Beta a more important risk measure than standard deviation, the Treynor Ratio may be more relevant for you. Keep reading to learn why.

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## Interpreting the Treynor Ratio for Portfolio Analysis

Intermediate

Treynor Ratio is a risk-adjusted-return measure for historical portfolio evaluation named after Jack Treynor. It is similar to the Sharpe Ratio except instead of total risk, it is the return per unit of market-related risk. A higher ratio represents higher portfolio performance.

Synonym: Treynor Measure

Treynor's measure is calculated by subtracting the risk-free return from the portfolio return, then dividing by the portfolio beta.

• Treynor Ratio = (Portfolio Return - Risk Free Return) / Portfolio Beta

For context, think a moment about the Treynor Ratio interpretation here. Since portfolio beta refers to the exposure to the market for a portfolio the Treynor Ratio is similar to the Sharpe Ratio, except that it measures the return per unit of systematic risk.

So a mutual fund with a beta of 1.00 generated from a linear regression of say 60 monthly returns would be compared directly with the benchmark because the denominator is 1.00, and the risk-free rate is the same.

The analyst has to be careful about changes in beta over time due to changes in portfolio structure. Also, every regression will generate a slope coefficient (beta) even if beta is insignificant. For a scatterplot that looks like a shotgun pattern the beta demonstrates low significance. Finally, the selection of measurement periods is important because outliers can skew the beta coefficient materially.

### In a Sentence

Doc:  Interpreting the Treynor Ratio is difficult when your beta has a low R-squared.
Ali:  Got it, so look at them in tandem.

### Video

This video can be accessed in a new window or App , at the YouTube Channel or from below.

Treynor Ratio definition for investment modeling (4:48)

### Video Script

The script includes two sections where we visualize and demonstrate the concept of the Treynor Ratio.

#### Visualize

Here we are focused on portfolios and specifically evaluating the historical performance of portfolios.

There are two types of performance calculations: returns-based and holdings-based. For the Treynor Ratio we will use returns-based performance analysis, meaning the input is monthly returns. Holdings-based performance analysis uses holdings and provides more detail, but is a bit too complex to cover here.

##### The Steps

First, we need to create a portfolio. In this section we have a Market portfolio, like an index or benchmark, with these weights to four stocks. And another portfolio, called Portfolio, which is actively managed, with these weights. Active weights refer to the differences.

Here we have returns calculated over a 60-month period, totals and averages, based on data on the Returns tab. Let's focus on the second row, average arithmetic. The Portfolio beat the Market by 0.08% per month.

Next, we have the standard deviation of monthly returns, so the Portfolio had higher monthly volatility, but we won't use that for the Treynor.

Because for beta, we need to run a regression as shown on this chart, the 60 monthly returns on the Market plotted on the x-axis, with the Portfolio return on the y-axis. So from the regression we get the measures: alpha and beta here, and the slope of this line is beta.

And last, in this section we have the formula for the Treynor ratio, the risk-free rate of 0.24% and a table for the calculation of several ratios.

Next, let's focus on this cell in blue an demonstrate.

#### Demonstrate

This is one way to calculate the Treynor Ratio in Excel, using monthly data, but it is very common to use annual figures.

Ok, we have all the data we need. Using this formula, let's take the Portfolio return of 0.79% minus the risk-free of 0.24%, then divide by beta of 1.10 to get 0.005. This basically matches the market, or benchmark.

So to interpret, the Portfolio had higher risk as measured by standard deviation and beta. Net-net, active returns started positive but after adjusting for market-related risk using Treynor, were on par with the benchmark.

### Quiz

The Treynor Ratio is typically used in holdings-based performance analysis. | True or False?

False. It is more commonly used in a returns-based analysis.

The denominator in the Treynor Ratio is a measure of a stock's sensitivity to systematic risk. | True or False?

True. This explains why it is commonly used to evaluate portfolios.

Still unclear on the Treynor Ratio? Check out the Quant 101 Series, specifically Analyze portfolio performance with linear regression in Excel.

### Related Terms

Our trained humans found other terms in the category risk-adjusted performance you may find helpful.

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