Treynor Ratio

A metric that determines how much excess return a portfolio has generated for every unit of risk it has taken

Author: Gilbert Monrouzeau
Gilbert Monrouzeau
Gilbert Monrouzeau
I have a BS in Mathematics and an MBA in Finance. I am currently teaching as an adjunct professor at Lourdes University.
Reviewed By: Parul Gupta
Parul Gupta
Parul Gupta
Working as a Chief Editor, customer support, and content moderator at Wall Street Oasis.
Last Updated:February 29, 2024

What Is The Treynor Ratio?

The Treynor Ratio is a metric that determines how much excess return a portfolio has generated for every unit of risk it has taken. In this sense, excess returns refer to returns that exceed those earned by risk-free investments.

It measures the efficiency with which the portfolio manager utilizes the fund's assets to generate returns in relation to the level of systematic risk. It's a risk-adjusted measure of portfolio beta relative to market index proxy.

The Treynor ratio, named after economist Jack Treynor, is particularly useful for evaluating the performance of individual investments within a diversified portfolio.

It helps investors assess whether the returns generated are adequate compensation for the systematic risk taken on relative to the broader market.

A higher Treynor ratio indicates better risk-adjusted performance, as it suggests that the portfolio generates higher returns for each unit of systematic risk compared to the market.

Key Takeaways

  • Treynor Ratio assesses a portfolio's excess return per unit of systematic risk, comparing returns to the market's performance.
  • It is calculated as the difference between portfolio return and risk-free rate, divided by portfolio beta.
  • The ratio is useful for comparing portfolio managers based on risk-adjusted performance, offering insight into efficient asset utilization.
  • A higher Treynor Ratio signifies superior risk-adjusted returns, indicating better performance relative to market risk.
  • While intuitive, the ratio focuses solely on systematic risk and may not provide a comprehensive assessment of portfolio performance when used in isolation.

Treynor Ratio Formula

It can be calculated as follows.

​Treynor Ratio = (rp ​− rf)/ βp​

  • rp= portfolio rate of return
  • ​rf​ = risk-free rate of return
  • ßp beta of the portfolio

The Treynor Ratio compares portfolio managers based on the excess return per unit of systematic risk. A higher ratio suggests better risk-adjusted performance but should be interpreted alongside other measures for a comprehensive assessment.

However, the ratio's adequacy in representing performance is determined by comparing it to the Security Market Line (SML), which illustrates the relationship between risk and return for diversified portfolios.

Note

The security market line (SML) is the line that reflects the relationship between risk and return of systematic, non-diversifiable risk. Thus, a ratio above the SML indicates superior risk-adjusted performance, while a ratio below it signifies inferior performance relative to the market's risk-return relationship.

Components

As seen in its formula, calculating the Treynor Ratio requires knowing the Rf, Rp, and β. But what if we needed to figure out any of these values? Since they're required for calculating the ratio, it might be necessary to calculate these first.

To calculate the risk-free rate (Rf), use the following formula:

Rf = [(1 + US gov security yield rate)/ (1 + inflation rate)] - 1

If one needs to calculate a portfolio's rate of return (Rp), it can be calculated as follows.

Rp = [(End Value + Dividends - Fees)/ (Initial Investment)] -  1

If one needs to calculate a portfolio's beta (β), it is the sum of all of the weighted beta values of a portfolio. The weighted beta value of a stock is the product of its proportion in the portfolio and its beta value.

Note

A portfolio's beta measures its sensitivity to market movements compared to a benchmark. A lower beta indicates lower volatility relative to the market. Diversified portfolios typically aim for a beta close to that of a chosen benchmark, such as the S&P 500.

To calculate the portfolio beta (βp), use the following formula:

ßp = Σ(Pißi)

  • ß= Beta of the portfolio
  • i = each stock in the portfolio (i = 1,2,3,...,n)
  • P =  proportion of the portfolio taken up by the stock
  • ß= Beta of the stock

Treynor Ratio Example

Let's take an example to find out the Treynor Ratio.

Assume the following portfolios and their betas:

Portfolios And Their Betas
Stock Purchase Price Current Price Proportion Beta
Boeing $8,000 $12,000 0.1 1.41
Amazon $18,000 $22,000 0.2 1.22
Pfizer $28,000 $34,000 0.3 0.58
BP $18,000 $22,000 0.2 0.64
Nintendo $38,000 $48,000 0.2 0.36

Therefore, the Beta would be:

ßp =  (0.1 * 1.41) + (0.2 * 1.22) + (0.3 * 0.58) + (0.2 * 0.64) + (0.2 * 0.36) = 0.759

Using the data from the previous table and assuming the investor received $1,000 in dividends and incurred $200 in fees for that period, with a pertinent US Treasury Security yield of 4.15% and an inflation rate of 2.25%, we can determine the portfolio's Treynor Ratio as follows.

ROI = [($12,000 + $22,000 + $34,000 + $22,000 + $48,000 + $1,000 - $200)/ ($8,000 + $18,000 + $28,000 + $18,000 + $38,000)] - 1

≈ 0.2618 = 26.18%

RFR = [(1 + 0.0415)/ (1 + 0.0225)] - 1

≈ 0.0186 = 1.86%

TR = [(0.2618 - 0.0186)/ 0.759] ≈ 0.3204

Note

Current stock market values can be found here.

Treynor ratio Vs. other ratios

Let's understand how the Treynor Ratio is different from other ratios.

Treynor Ratio and Sharpe Ratio

Jack Treynor provided this ratio, expanding William Sharpe's contributions to modern portfolio theory. The Sharpe ratio (SR) measures the fund's ability to generate returns against its overall risk, whereas the Treynor ratio (TR) assesses portfolio performance only in light of economic troubles.

The Sharpe Ratio (SR) measures a fund's risk-adjusted return based on its total risk, represented by the portfolio's standard deviation. In contrast, utilizing its beta, the Treynor Ratio evaluates portfolio performance relative to market risk.

Since the Treynor Ratio considers the relative market risk, it's applicable for determining a portfolio's diversification. Thus, it measures forward-looking performance. SR measures historical performance.

    Note

    TR and SR provide similar performance rankings in fully diversified portfolios where total and systematic risks align. However, their differences emerge due to variations in portfolio diversification levels.

    Any difference in these ratios comes from a difference in the portfolio's level of diversification.

    This should be clear by looking at the formula for SR and noting that it is the same as calculating TR. The only difference is being divided by the portfolio's standard deviation instead of its beta. Here is the formula for calculating SR.

    SR = ROI - RFR/ σp

    • ROI = portfolio rate of return
    • RFR = risk-free rate of return
    • σp = standard deviation of the portfolio

    Treynor Ratio and Jensen's Alpha

    Another portfolio evaluation measure, Jensen's alpha (𝞪), is a risk-adjusted performance measure that measures the average return on an investment or portfolio based on its beta and the market's average return, calculated as follows.

    α = ROI - (RFR + β(RMI - RFR))

    • ROI = portfolio rate of return
    • RFR = risk-free rate of return
    • RMI = realized return of the appropriate market index
    • β = beta of the portfolio

    Jensen's measure indicates that the portfolio's realized return should correspond to the risk-free rate plus a risk premium proportional to the portfolio's systematic risk relative to the market.

      Note

      If a portfolio manager has a positive alpha, they have earned beyond what was required to compensate for the investment's risks. Here's an example.

      Treynor Ratio and Information Ratio

      Another performance measure is the information ratio (IR). The ratio assesses a portfolio's ability to generate excess returns relative to a benchmark, adjusted for the risk captured by the tracking error, which represents the standard deviation of the excess return., calculated as follows.

      IR = (ROI - RMI)/ σER

      • ROI = portfolio rate of return
      • RMI = realized return of the appropriate market index
      • σER = standard deviation of the excess return

      Treynor Ratio Pros And Cons

      The ratio carries both the pros and cons. Let's understand them below.

      Pros

      Now that ratio has been compared to the other three, we can discuss its benefits as an evaluative statistic:

      1. Intuitive benefit-cost comparison of the risk-return trade-off: As seen in the first example, it's evident that the ratio represents how units of return for every unit of market risk are assumed.
      2. Conceptually tied to CAPM
      3. Simple to calculate
      4. They are widely used in practice
      5. It's one of the four main portfolio evaluation tools used frequently. Specifically, it measures the efficiency with which the portfolio manager utilizes the fund's assets to compensate for a given level of risk.

      Cons

      All that being said, the Treynor Ratio does have its limitations. Here are some of its disadvantages:

      1. Provides comparative performance assessments among different portfolios rather than absolute evaluations
      2. "Focuses primarily on systematic risk, represented by the portfolio's beta, while overlooking other aspects of risk diversification
      3. May yield ambiguous interpretations in certain scenarios

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