finance Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...

, the Treynor reward-to-volatility model (sometimes called the reward-to-volatility ratio or Treynor measure), named after American economist Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an

investment Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broade ...

that has no

risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environ ...

that can be diversified (e.g.,

Treasury bills United States Treasury securities, also called Treasuries or Treasurys, are government debt instruments issued by the United States Department of the Treasury to finance government spending as a supplement to taxation. Since 2012, the U.S. ...

or a completely diversified

portfolio Portfolio may refer to: Objects * Portfolio (briefcase), a type of briefcase Collections * Portfolio (finance), a collection of assets held by an institution or a private individual * Artist's portfolio, a sample of an artist's work or a ...

), per 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

T = \frac

where: :

T \equiv

Treynor ratio, :

r_i \equiv

portfolio ''is return, :

r_f \equiv

risk free rate :

\beta_i  \equiv

portfolio ''is beta

Example

Taking the equation detailed above, let us assume that the expected portfolio return is 20%, the risk free rate is 5%, and the

beta Beta (, ; uppercase , lowercase , or cursive ; or ) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Ancient Greek, beta represented the voiced bilabial plosive . In Modern Greek, it represe ...

of the portfolio is 1.5. Substituting these values, we get the following :

T = \frac = 0.1

Limitations

Like the

Sharpe ratio In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for ...

, the Treynor ratio (''T'') does not quantify the value added, if any, of active portfolio 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 In finance and economics, systematic risk (in economics often called aggregate risk or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggrega ...

, 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 In finance, Jensen's alpha (or Jensen's Performance Index, ex-post alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. It is a version of the standard alpha based on a the ...

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

capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a Diversification (finance), well-diversified Portfolio (f ...

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

References

Financial ratios Investment indicators Statistical ratios {{finance-stub

Formula

Example

Limitations

See also

References