What is the Treynor Index in stock market

November 28, 2009

A measure of a portfolio's excess return per unit of risk, equal to the portfolio's rate of return minus the risk-free rate of return, divided by the portfolio's beta. This is a similar ratio to the Sharpe ratio, except that the portfolio's beta is considered the measure of risk as opposed to the variance of portfolio returns. This is useful for assessing the excess return from each unit of systematic risk, enabling investors to evaluate how structuring the portfolio to different levels of systematic risk will affect returns.

The Treynor index offers a more nuanced analysis of an investment’s success over simply looking at the bottom-line financial returns on a stock. Prior to the Treynor index, stock market investors had known how to measure risk and compare returns, but it wasn’t until the advent of the Treynor index, and latterly the Sharpe and Jensen ratios, that investors were able to discern the correlations between risk and returns on their investments clearly.

The Treynor index works on the notion of risk posited by Treynor in his understanding of the two-sided nature of market risk. These two elements of risk are integral to the Treynor Index and comprise the risk arising from the fluctuations of individual securities and the risk produced by fluctuations in the market.

A stock investment yield calculated according to the Treynor index assumes that the portfolio of the investor is suitably diversified, as it only takes into consideration systematic risk. Unsystematic risk is not accounted for and therefore the results of a Treynor Index calculation for an undiversified portfolio are misleading.

As an example of the Treynor Index in operation; if we say that the ten year annual return of the S&P 500 index is 10% and over the same period the average annual return on risk-less Treasury bills is 5%, then we have a scenario where the relative risks and yields of three stock portfolios over the predictable Treasury bills can be calculated and compared:

Portfolio A 10% Beta, 0.90 Portfolio B 14% Beta, 1.03 Portfolio C 15% Beta 1.20

The Treynor Index for the market calculates as (0.10-0.05)/1.00 = 0.050. For the three respective stock portfolios we have Treynor indices of:

T(manager A) = (0.10-0.05)/0.90 = 0.056 T(manager B) = (0.14-0.05)/1.03 = 0.087 T(manager C) = (0.15-0.05)/1.20 = 0.083

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