The Treynor index or Treynor ratio, also referred to as the reward-to-volatility ratio, is an investment measurement index invented by Jack Treynor that indicates how much an investment that involves some level of risk has earned over a risk-less investment per unit of market risk (given in the following calculation as the beta coefficient):
(Average Return of the Portfolio - Average Return of the Risk-Free Rate) / Beta coefficient
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
If we were to simply consider the annual return as the index of profitability, we would view Portfolio C as the best of the three. However, according to the Treynor index, Portfolio B has been the most profitable when the relative risks involved in the investments have been taken into account.
