What is the Treynor Ratio?
The Treynor Ratio is a measure of a portfolio’s excess return per unit of systematic risk, or the market volatility of the portfolio.
Often referred to as the “reward-to-volatility ratio”, the Treynor ratio attempts to gauge the risk attributable to a portfolio (and the expected returns) in the context of the total non-diversifiable risk inherent to the market.
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How to Calculate Treynor Ratio
The Treynor ratio captures the difference between a portfolio’s total return and the risk-free rate, which is subsequently adjusted for the amount of risk undertaken on a per-unit basis.
Designed by economist Jack Treynor, who also created the capital asset pricing model (CAPM), the ratio is used by investors to make informed decisions regarding asset allocation and portfolio diversification.
In particular, the Treynor ratio is used to perform comparative analysis among different funds to compare the historical track record of a specific portfolio manager (and investment fund).
From the perspective of an investor, the insights derived from comparing the risk-adjusted fund returns contributes toward the selection of which funds to allocate their capital to.
Calculating the Treynor ratio requires three inputs:
- Portfolio Return (Rp) → Usually, the portfolio return is based on a backward-looking average, such as the portfolio returns in the past five years. If the returns from one year of performance were to be used, the chance of misinterpreting the ratio would be very high since returns can fluctuate substantially, especially for firms that utilize riskier strategies.
- Risk-Free Rate (Rf) → In the U.S., the risk-free rate is most often the yield on Treasury bonds since the default risk is essentially zero, i.e. if the government were at risk of defaulting, it could technically print more money to avoid default.
- Beta of the Portfolio (β) → The last variable is the beta of the portfolio, which is a frequently criticized — yet commonly used — measure of risk in investing and portfolio management. Since a portfolio is a collection of assets, a weighted average must be taken of each asset’s sensitivity to movements within the broader market.
Treynor Ratio Formula
The formula for calculating the Treynor ratio is as follows.
Where:
- rp = Portfolio Return
- rf = Risk-Free Rate
- βp = Beta of the Portfolio
Note: In order for the ratio to be meaningful, all the figures in the numerator must be positive.