Principle:Avhz RustQuant Risk Reward Metrics

Knowledge Sources	Sharpe - Mutual Fund Performance Sortino and Price - Performance Measurement in a Downside Risk Framework Treynor - How to Rate Management of Investment Funds
Domains	Risk_Management, Portfolio_Management
Last Updated	2026-02-07 21:00 GMT

Overview

Risk-reward metrics for evaluating portfolio performance, including Sharpe ratio, Sortino ratio, Treynor ratio, Burke ratio, Jensen's alpha, and Return on VaR.

Description

Risk-Reward Metrics in RustQuant are encapsulated in the PortfolioMeasures struct, which holds the key inputs needed to compute various performance ratios. The struct contains the following fields:

r_p -- The average return of the portfolio.
r -- The risk-free return over the same period.
beta_p -- The beta of the portfolio (systematic risk).
sigma_p -- The standard deviation of portfolio returns.
sigma_down -- The downside standard deviation (semi-standard deviation).
var -- The Value-at-Risk.
r_m -- The expected market return.

The following metrics are implemented:

Sharpe ratio (1966) -- Measures excess return per unit of total risk.
Treynor ratio (1965) -- Measures excess return per unit of systematic risk.
Sortino ratio (1994) -- Measures excess return per unit of downside risk.
Burke ratio (1994) -- Measures excess return relative to the sum of squared drawdowns.
Return on VaR -- Measures the average return relative to Value-at-Risk.
Jensen's alpha -- Measures the excess return above the CAPM-predicted return.

Usage

Use Risk-Reward Metrics when evaluating the risk-adjusted performance of a portfolio or investment strategy. The Sharpe ratio is the most widely used general-purpose metric; the Sortino ratio is preferred when downside risk is the primary concern; the Treynor ratio is appropriate for diversified portfolios where systematic risk dominates; and Jensen's alpha measures a manager's ability to generate returns above the market-predicted level.

Theoretical Basis

Sharpe Ratio (Sharpe, 1966):

$Sharpe = \frac{r_{p} - r_{f}}{σ_{p}}$

Treynor Ratio (Treynor, 1965):

$Treynor = \frac{r_{p} - r_{f}}{β_{p}}$

Sortino Ratio (Sortino and Price, 1994):

$Sortino = \frac{r_{p} - r_{f}}{σ_{down}}$

Burke Ratio (Burke, 1994):

$Burke = \frac{r_{p} - r_{f}}{\sum_{i = 1}^{n} d_{i}^{2}}$

where $d_{i}$ are the drawdowns.

Return on VaR:

$RoVaR = \frac{r_{p}}{VaR}$

Jensen's Alpha:

$α = r_{p} - [r_{f} + β_{p} (r_{m} - r_{f})]$

Related Pages

Implemented By

Implementation:Avhz_RustQuant_Risk_Reward

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