The Treynor ratio named after Jack L. Treynor

Jack L. Treynor

Jack L. Treynor is the President of Treynor Capital Management, Palos Verdes Estates, CA. He is a Senior Editor and Advisory Board member of the Journal of Investment Management, and is a Senior Fellow of the Institute for Quantitative Research in Finance...

, is a measurement of the returns earned in excess of that which could have been earned on an investment

Investment

Investment has different meanings in finance and economics. Finance investment is putting money into something with the expectation of gain, that upon thorough analysis, has a high degree of security for the principal amount, as well as security of return, within an expected period of time...

 that has no diversifiable risk (e.g., Treasury Bills or a completely diversified portfolio), per each unit of market risk assumed.

The Treynor ratio relates excess return over the risk-free rate to the additional risk taken; however, systematic risk is used instead of total risk. The higher the Treynor ratio, the better the performance of the portfolio under analysis.

Formula

where:
Treynor ratio,
portfolio is return,
risk free rate
portfolio is beta

Beta coefficient

In finance, the Beta of a stock or portfolio is a number describing the relation of its returns with those of the financial market as a whole.An asset has a Beta of zero if its returns change independently of changes in the market's returns...

Limitations

Like the Sharpe ratio

Sharpe ratio

The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...

, the Treynor ratio (T) does not quantify the value added, if any, of active portfolio

Portfolio (finance)

Portfolio is a financial term denoting a collection of investments held by an investment company, hedge fund, financial institution or individual.-Definition:The term portfolio refers to any collection of financial assets such as stocks, bonds and cash...

 management. It is a ranking criterion only. A ranking of portfolios based on the Treynor Ratio is only useful if the portfolios under consideration are sub-portfolios of a broader, fully diversified portfolio. If this is not the case, portfolios with identical systematic risk

Systematic risk

In finance, systematic risk, sometimes called market risk, aggregate risk, or undiversifiable risk, is the risk associated with aggregate market returns....

, but different total risk, will be rated the same. But the portfolio with a higher total risk is less diversified and therefore has a higher unsystematic risk which is not priced in the market.

An alternative method of ranking portfolio management is Jensen's alpha

Jensen's alpha

In finance, Jensen's alpha is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return....

, which quantifies the added return as the excess return above the security market line

Security market line

Security market line is the graphical representation of the Capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk .-See also:...

 in the capital asset pricing model

Capital asset pricing model

In finance, the capital asset pricing model is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk...

. As these two methods both determine rankings based on systematic risk alone, they will rank portfolios identically.

See also

• Bias ratio (finance)
  Bias ratio (finance)
  The bias ratio is an indicator used in finance to analyze the returns of investment portfolios, and in performing due diligence.The bias ratio is a concrete metric that detects valuation bias or deliberate price manipulation of portfolio assets by a manager of a hedge fund, mutual fund or similar...
  
  
• Hansen-Jagannathan bound
• Jensen's alpha
  Jensen's alpha
  In finance, Jensen's alpha is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return....
  
  
• Modern portfolio theory
  Modern portfolio theory
  Modern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...
  
  
• Modigliani Risk-Adjusted Performance
  Modigliani Risk-Adjusted Performance
  Modigliani risk-adjusted performance or M2 or M2 or Modigliani–Modigliani measure or RAP is a measure of the risk-adjusted returns of some investment portfolio. It measures the returns of the portfolio, adjusted for the deviation of the portfolio , relative to that of some benchmark...
  
  
• Sharpe ratio
  Sharpe ratio
  The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...
  
  
• Sortino ratio
  Sortino ratio
  The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target, or required rate of return, while the Sharpe ratio penalizes both upside and downside...
  
  
• Upside potential ratio
  Upside potential ratio
  The Upside-Potential Ratio is a measure of a return of an investment asset relative to the minimal acceptable return. The measurement allows a firm or individual to choose investments which have had relatively good upside performance, per unit of downside risk....