The Treynor reward to volatility model (sometimes called the reward-to-volatility ratio or Treynor measure), named after

Jack L. Treynor Jack Lawrence Treynor (February 21, 1930 – May 11, 2016) was an American economist who served as the President of Treynor Capital Management in Palos Verdes Estates, California. He was a Senior Editor and Advisory Board member of the ''Journal of ...

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

investment Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance, the purpose of investing i ...

that has no diversifiable risk (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 an alternative to taxation. Since 2012, U.S. gov ...

or a completely diversified portfolio), per unit of market risk assumed. The Treynor ratio relates

excess return Alpha is a measure of the active return on an investment, the performance of that investment compared with a suitable market index. An alpha of 1% means the investment's return on investment over a selected period of time was 1% better than the ...

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 The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free ra ...

\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 ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labiod ...

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 its ...

, 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, which quantifies the added return as the excess return above the

security market line Security market line (SML) is the 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. The risk of an individual risky security re ...

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 well-diversified portfolio. The model takes into accou ...

. 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