Treynor Ratio

The Treynor Ratio, named after Jack Treynor, is a efficiency metric used to evaluate the returns of an investment compared to its risk. It specifically focuses on the relationship between the risk premium (the return above the risk-free rate) and the systematic risk, represented by beta.

Investments (11th Edition, 2018, McGraw-Hill Education) — Zvi Bodie, Alex Kane and Alan J. Marcus Quantitative Investment Analysis (4th Edition, 2020, CFA Institute) — Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto and David E. Runkle

Risk is a part of investing, but the Treynor Ratio helps us measure how well we are compensated for taking that risk.

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How to Calculate the Treynor Ratio

The Treynor Ratio is calculated using the following formula:

\text{Treynor Ratio} = \frac{R_i - R_f}{\beta_i}

Where:

$𝑅_𝑖$ - Return of the investment
$𝑅_𝑓$ - Risk-free rate (often the yield on Treasury bills)
$\beta_i$ - Beta of the investment (a measure of its systematic risk)

Quantitative Investment Analysis (4th Edition, 2020, CFA Institute) — Richard A. DeFusco, Dennis W. McLeavey, Jerald E. Pinto and David E. Runkle

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Perfect for Portfolio Comparison: Use the Treynor Ratio to compare portfolios with similar market exposure. It helps uncover which strategy delivers the most return per unit of beta.

Importance of the Treynor Ratio in Trading

The Treynor Ratio is important in trading because it helps investors understand how much return they are receiving for the amount of risk they are taking. It is particularly useful for comparing the performance of different investments or portfolios that have different levels of market risk.

Comparing Two Portfolios

Let’s consider two hypothetical portfolios: Portfolio A and Portfolio B. We’ll compare their performance using the Treynor Ratio. The relevant data for these portfolios is as follows:

Metric	Portfolio A	Portfolio B
$Annual Return (R_p)$	12%	15%
$Beta (β_p)$	1.2	1.5
$Risk-Free Rate (R_f)$	2%	2%

For Portfolio A:

\text{Treynor Ratio}_A = \frac{0.12 - 0.02}{1.2} = \frac{0.10}{1.2} = 0.0833

For Portfolio B:

\text{Treynor Ratio}_B = \frac{0.15 - 0.02}{1.5} = \frac{0.13}{1.5} = 0.0867

Analysis: Based on the Treynor Ratio, Portfolio B has a higher value (0.0867) compared to Portfolio A (0.0833), indicating that Portfolio B has a better risk-adjusted return.

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Focus on Systematic Risk: Unlike the Sharpe ratio, the Treynor Ratio ignores unsystematic risk, making it ideal for diversified portfolios where systematic risk dominates.

Combining Treynor Ratio with Other Tools

The Treynor Ratio can be combined with other performance metrics to gain deeper insights:

Sharpe ratio: While the Treynor Ratio focuses on systematic risk (beta), the Sharpe ratio considers total risk (standard deviation). Comparing both can provide a comprehensive view of an investment’s risk-adjusted performance.
Alpha: Alpha measures the excess return of an investment relative to the market. Combining Treynor Ratio with Alpha helps in understanding both the relative performance and the skill of the investment manager.
Sortino ratio: This ratio adjusts for downside risk, giving more context to the Treynor Ratio by highlighting returns relative to negative volatility.

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Risk Management: Remember that a higher Treynor Ratio doesn’t always mean a better investment; it should be part of a broader risk management strategy.

Key Points

Risk-Adjusted Performance: The Treynor Ratio measures returns earned above the risk-free rate per unit of market risk (beta), emphasizing systematic risk.
Market Risk Focus: Unlike the Sharpe Ratio, the Treynor Ratio evaluates performance based on beta, making it suitable for diversified portfolios where only market risk is relevant.
Higher is Better: A higher Treynor Ratio indicates better risk-adjusted returns, reflecting efficient use of market exposure to generate excess returns.
Applicable to Well-Diversified Portfolios: Most effective for portfolios or investments where unsystematic risk is negligible due to diversification.
Benchmarking Tool: Use the Treynor Ratio to compare different portfolios or funds to determine which delivers higher returns for the same level of market risk.
Dependence on Beta: The ratio assumes beta is a reliable measure of market risk; this can be less accurate for investments with non-linear or asymmetric risk profiles.
Risk-Free Rate Sensitivity: The choice of the risk-free rate affects the Treynor Ratio, emphasizing the importance of using an appropriate benchmark.
Dynamic Over Time: The ratio changes with market conditions and portfolio beta, requiring regular updates to stay relevant.
Strategic Insight: Helps investors identify whether a manager or strategy effectively utilizes market exposure to achieve outperformance.
Complementary Analysis: Combine the Treynor Ratio with other metrics like the Sharpe Ratio to evaluate both systematic and total risk-adjusted performance.

Conclusion

By understanding and applying the Treynor Ratio, investors can make more informed decisions and better manage the risk-return profile of their portfolios. This metric helps quantify the performance of an investment relative to its market risk, enabling a more precise evaluation of whether the returns justify the risk taken. While it should not be used in isolation, the Treynor Ratio provides valuable insights when combined with other performance measures, such as the Sharpe Ratio or Jensen’s Alpha.

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