Performance
Treynor Ratio
The Treynor Ratio is excess return over the risk-free rate divided by market beta — risk-adjusted return where the relevant risk is systematic, not total.
Also known as: Reward-to-volatility ratio
The Treynor Ratio, introduced by Jack Treynor in 1965, is one of the founding measures of risk-adjusted return. Where Sharpe uses total volatility in the denominator, Treynor uses market beta. The implicit assumption: the portfolio is already well-diversified, so idiosyncratic risk is negligible and the relevant risk is systematic.
Formula
Treynor = ( R_p − R_f ) / β_pwhere R_p is the annualised portfolio return, R_f the risk-free rate, and β_p the portfolio's beta against the chosen benchmark. By construction the benchmark has Treynor = R_b − R_f.
Treynor vs Sharpe
- ·Sharpe: relevant for the whole portfolio decision. Penalises idiosyncratic risk because the investor will bear it.
- ·Treynor: relevant for ranking sleeves within an already-diversified portfolio. Idiosyncratic risk is diversified away at the total level.
- ·For a well-diversified portfolio the two ratios rank strategies similarly. For a concentrated portfolio they can disagree sharply.
How MEDGE Capital uses Treynor
Treynor is reported in the Compare module alongside Sharpe, Sortino and Information Ratio when a benchmark is selected — surfacing where a portfolio earns its return from market exposure vs alpha.
See also
Sharpe Ratio
The Sharpe Ratio measures a portfolio's excess return over the risk-free rate per unit of total volatility, annualised.
Beta
Beta (β) is the slope of the regression of a portfolio's returns on a benchmark's returns — the sensitivity of the portfolio to the benchmark.
Alpha
Alpha (α) is the excess return of a portfolio relative to the return predicted by its market beta, typically estimated via regression.