Treynor Ratio Pass Node

Treynor Ratio — Series Input

StatisticalRisk-Adjusted ReturnPass

Overview

The Treynor Ratio Pass Node computes the rolling Treynor ratio — excess return per unit of systematic risk (beta). Unlike Sharpe, which divides by total volatility, Treynor divides by beta, making it appropriate for portfolios that are part of a larger, already-diversified allocation.

A higher Treynor ratio indicates better compensation per unit of market exposure taken. It is most meaningful when comparing fully-diversified strategies or components within a larger portfolio.

Formula

Rolling Treynor:
β = cov(portfolio, benchmark) / var(benchmark) [rolling]
Treynor = (mean(returns) − riskFreeRate) / β
Returns null when β ≈ 0 (denominator near zero).
Warm-up: period bars.

Parameters

ParameterDefaultDescription
period20Rolling window in bars
riskFreeRate0Per-bar risk-free rate subtracted from returns

Inputs & Outputs

SlotDirectionTypeDescription
inputInput{ values, timestamps }Portfolio returns series
valuesOutput(number | null)[]Rolling Treynor ratio per bar; nulls during warm-up or β ≈ 0
timestampsOutputnumber[]Unix timestamps aligned to input

Use Cases

Portfolio Component Ranking

Rank strategies or assets by Treynor ratio to identify which delivers the most excess return per unit of systematic risk contributed to the overall portfolio.

Market-Neutral Evaluation

For fully hedged or market-neutral strategies (β ≈ 0), Treynor is undefined. Use Sharpe or Jensen's Alpha instead for such strategies.

Complement to Sharpe

Treynor is optimal for portfolios in a larger allocation context; Sharpe is optimal for standalone strategy evaluation. Use both for a complete picture.

Tips & Best Practices

Requires Benchmark

Beta is computed relative to a benchmark. Ensure your input series and benchmark represent the same time period and bar alignment.

Treynor vs Sharpe

If all idiosyncratic risk is diversified away, Treynor and Sharpe produce the same ranking. Otherwise, Treynor favours high-beta strategies; Sharpe favours low-total-volatility ones.

Negative Beta Strategies

A negative Treynor with negative beta can actually mean the strategy is outperforming — interpret carefully when β < 0 (e.g. short strategies).

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