The Treynor ratio measures how much an investment has earned over a risk-free unit of market risk, using the beta coefficient. The Treynor index considers both individual security and market fluctuations, but assumes adequate diversification. It helps investors discern correlations between risk and returns. A calculation example shows how the Treynor ratio can reveal the best-performing portfolio when relative risks are taken into account.
The Treynor ratio or Treynor ratio, also known as the reward-to-volatility ratio, is an investment measurement ratio invented by Jack Treynor that indicates how much an investment involving a certain level of risk has earned over an investment per risk-free unit of the market risk (given in the following calculation as the beta coefficient):
(Average Portfolio Return – Average Risk-Free Rate Return) / Beta Coefficient
The Treynor Index offers a more detailed analysis of investment success than simply looking at a stock’s bottom line financial returns. Before the Treynor ratio, stock market investors knew how to measure risk and compare returns, but it wasn’t until the advent of the Treynor ratio and, later, the Sharpe and Jensen ratios, that investors were able to discern the correlations between risk. and returns on your investments clearly.
The Treynor index works on the notion of risk raised by Treynor in his understanding of the two-sided nature of market risk. These two elements of risk are an integral part of the Treynor Index and comprise the risk arising from fluctuations in individual securities and the risk arising from fluctuations in the market.
A stock investment return calculated according to the Treynor index assumes that the investor’s portfolio is adequately diversified, since it only takes into account 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 at work; 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-free Treasuries is 5%, then we have a scenario where the relative risks and returns of three stocks Portfolios on 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 is calculated as (0.10-0.05)/1.00 = 0.050. For the three respective stock portfolios we have Treynor indices of:
T (bearing A) = (0.10-0.05) /0.90 = 0.056
T (bearing B) = (0.14-0.05) /1.03 = 0.087
T (bearing C) = (0.15-0.05) /1.20 = 0.083
If we simply considered annual return as the rate of return, we would view Portfolio C as the best of the three. However, based on the Treynor ratio, Portfolio B has performed the best when the relative risks involved in the investments are taken into account.
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