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Treynor Ratio as a Portfolio Performance Benchmark

Article Quant Q&A · Author: chichi
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Summary

The document explains how to interpret the Treynor ratio, which measures a portfolio’s excess return per unit of beta, alongside the CAPM market risk premium. Under CAPM with zero alpha, a portfolio’s expected Treynor ratio equals the market risk premium. This explains why the two expressions can appear identical when CAPM assumptions hold.

The ratio is presented as a portfolio appraisal measure: an observed value above the market premium can indicate performance beyond the CAPM benchmark, while the market premium serves as a reference for judging the result. The discussion is conceptual and provides no empirical tests or detailed calculation example. Its comparison depends on the CAPM framing, so the equality is not a universal identity for realized portfolio returns; observed ratios can differ from the benchmark.

Key ideas

  • Under CAPM with zero alpha, expected excess return divided by beta equals the market risk premium.
  • The Treynor ratio evaluates a portfolio’s excess return relative to its market risk exposure.
  • The market risk premium can serve as a benchmark for interpreting a portfolio’s Treynor ratio.
  • A higher observed Treynor ratio may indicate performance beyond the CAPM benchmark.

Tags

StatisticsPortfolio constructionRisk management
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# Difference between Treynor ratio and market premium


# Difference between Treynor ratio and market premium












The definition of Treynor ratio is given by $$ T = \frac{r_i-r_f}{\beta_i}, $$ where $r_i$ is the portfolio $i$'s return, $r_f$ is the risk-free rate and $\beta_i$ is the portfolio $i$'s beta. I am stunned after reading this definition. Isn't it exactly the market premium?

The CAPM model says that $$ E[r_i] - r_f = \beta_i (E[r_m] - r_f). $$ Compare the above two equations we then conclude that $T$ is universal for all $i$ as $T$ is nothing but the market premium $r_m - r_f$. Could you point out what I missed? thank you guys

## Answer by nbbo2 (score 2, accepted)

https://quant.stackexchange.com/a/71773

So, the Treynor Ratio $T_p$ is intended to be used for the appraisal of portfolios (not only individual securities). If all securities in the portfolio satisfy the CAPM (with $\alpha = 0$) then indeed the Treynor Ratio achieved will be equal the the Risk Premium on the Market. But Treynor thought if someone really smart comes along (George Soros, Warren Buffet, chici, etc.) they will achieve a TR higher than this. So "superior performance" is $\alpha > 0$ if you are using the CAPM or $T_p > R_{PM}$ if you are using Treynor's model.

You could say the Market Risk Premium serves as a reference point for whether a particular Treynor ratio you observe for a given portfolio is "good" or "bad" or "average".

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.