> ## Documentation Index
> Fetch the complete documentation index at: https://kalpi.ai/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Treynor Ratio

> Calculate risk-adjusted returns based on systemic market risk rather than total absolute volatility.

The **Treynor Ratio** is an efficiency metric closely related to the Sharpe Ratio. However, while the Sharpe Ratio penalizes a strategy for its *total* volatility (Standard Deviation), the Treynor Ratio only penalizes a strategy for its *systematic* risk (**Beta**).

This makes the Treynor Ratio exceptionally useful for evaluating portfolios that are part of a broader, well-diversified investment ecosystem.

## The Mathematical Formula

The ratio divides the portfolio's excess return over the risk-free rate by its Beta:

$T = \frac{R_p - R_f}{\beta_p}$

**Where:**

* $R_p$ = The return of the portfolio.
* $R_f$ = The risk-free rate.
* $\beta_p$ = The Beta of the portfolio.

## When to Use the Treynor Ratio

* **Use the Sharpe Ratio** when you are evaluating your entire net worth or a standalone strategy in isolation, as you need to account for every ounce of specific idiosyncratic risk.
* **Use the Treynor Ratio** when evaluating a specific "sub-basket" or algorithmic sleeve within a larger, fully diversified portfolio, where idiosyncratic risk has already been diversified away.

A higher Treynor Ratio indicates that the strategy is generating superior returns for the amount of broader market risk it is forced to endure.