The Treynor ratio, also known as the reward-to-volatility ratio, is a performance metric for determining how much excess return was generated for each unit of risk taken on by a portfolio.
Excess return in this sense refers to the return earned above the return that could have been earned in a risk-free investment. Although there is no true risk-free investment, treasury bills are often used to represent the risk-free return in the Treynor ratio.
Risk in the Treynor ratio refers to systematic risk as measured by a portfolio's beta. Beta measures the tendency of a portfolio's return to change in response to changes in return for the overall market.
Key Takeaways
The Treynor ratio is a risk/return measure that allows investors to adjust a portfolio's returns for systematic risk.
A higher Treynor ratio result means a portfolio is a more suitable investment.
The Treynor ratio is similar to the Sharpe ratio, although the Sharpe ratio uses a portfolio's standard deviation to adjust the portfolio returns.
In essence, the Treynor ratio is a risk-adjusted measurement of return based on systematic risk. It indicates how much return an investment, such as a portfolio of stocks, a mutual fund, or exchange-traded fund, earned for the amount of risk the investment assumed.
If a portfolio has a negative beta, however, the ratio result is not meaningful. A higher ratio result is more desirable and means that a given portfolio is likely a more suitable investment. Since the Treynor ratio is based on historical data, however, it's important to note this does not necessarily indicate future performance, and one ratio should not be the only factor relied upon for investing decisions.
How the Treynor Ratio Works
Ultimately, the Treynor ratio attempts to measure how successful an investment is in providing compensation to investors for taking on investment risk. The Treynor ratio is reliant upon a portfolio's beta—that is, the sensitivity of the portfolio's returns to movements in the market—to judge risk.
The premise behind this ratio is that investors must be compensated for the risk inherent to the portfolio, because diversification will not remove it.
Difference Between the Treynor Ratio and Sharpe Ratio
The Treynor ratio shares similarities with the Sharpe ratio, and both measure the risk and return of a portfolio.
The difference between the two metrics is that the Treynor ratio utilizes a portfolio beta, or systematic risk, to measure volatility instead of adjusting portfolio returns using the portfolio's standard deviation as done with the Sharpe ratio.
Limitations of the Treynor Ratio
A main weakness of the Treynor ratio is its backward-looking nature. Investments are likely to perform and behave differently in the future than they did in the past. The accuracy of the Treynor ratio is highly dependent on the use of appropriate benchmarks to measure beta.
The fund's beta would likely be understated relative to this benchmark since large-cap stocks tend to be less volatile in general than small caps. Instead, the beta should be measured against an index more representative of the large-cap universe, such as the Russell 1000 index.
Additionally, there are no dimensions upon which to rank the Treynor ratio. When comparing similar investments, the higher Treynor ratio is better, all else equal, but there is no definition of how much better it is than the other investments.
The Treynor ratio is an extension of the Sharpe ratio
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 risk.
. Instead of using total risk, Treynor uses beta or systematic risk in the denominator. Treynor ratio=Rp–Rfβp Treynor ratio = R p – R f β p As with the Sharpe ratio, the Treynor ratio requires positive numerators to give meaningful comparative results.
In essence, the Treynor ratio is a risk-adjusted measurement of return based on systematic risk. It indicates how much return an investment, such as a portfolio of stocks, a mutual fund, or exchange-traded fund, earned for the amount of risk the investment assumed.
Both the Sharpe and Treynor Ratios are used to understand an investment's risk-adjusted return. The Sharpe Ratio divides the excess return by the investment's standard deviation.The Treynor Ratio instead divides excess returns by the investment's Beta.
The Appraisal Ratio, also known as the Treynor-Black Ratio, is a measure that quantifies an investment manager's ability to generate excess returns compared to a benchmark, while taking into account the level of risk assumed.
To calculate IR, subtract the total of the portfolio return for a given period from the total return of the tracked benchmark index.Divide the result by the tracking error. The tracking error can be calculated by taking the standard deviation of the difference between the portfolio returns and the index returns.
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.
Given a sequence of returns for an investment or portfolio and its benchmark, tracking error is calculated as follows: Tracking Error = Standard Deviation of (P - B)Where P is portfolio return and B is benchmark return.
In practice, the risk-free rate of return does not truly exist, as every investment carries at least a small amount of risk. To calculate the real risk-free rate, subtract the inflation rate from the yield of the Treasury bond matching your investment duration.
The Sortino ratio is a risk-adjustment metric used to determine the additional return for each unit of downside risk. It is computed by first finding the difference between an investment's average return rate and the risk-free rate.The result is then divided by the standard deviation of negative returns.
Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.
To calculate the Sharpe ratio investors can subtract the risk-free rate of return from the expected rate of return, and then divide that result by the standard deviation (the asset's volatility.)
Therefore, Sharpe is a good measure where the portfolio is not properly diversified while Treynor is a better measure where the portfolios are well diversified.
The Treynor ratio is a measure of the risk-adjusted returns earned from an asset per unit of systematic risk it brings. For this reason, it is also called the reward-to-volatility ratio. The systematic risk of an asset is represented by its beta.
The Sharpe Ratio helps rank and indicate the expected return compared to risk: Usually, any Sharpe ratio greater than 1.0 is considered acceptable to good by investors. A ratio higher than 2.0 is rated as very good. A ratio of 3.0 or higher is considered excellent.
The expected return is calculated by multiplying the weight of each asset by its expected return. Then add the values for each investment to get the total expected return for your portfolio. Hence, the formula: Expected Portfolio Return = (Asset 1 Weight x Expected Return) + (Asset 2 Weight x Expected Return)...
For example, a Treynor Ratio of 0.5 is better than one of 0.25, but not necessarily twice as good. The numerator is the excess return to the risk-free rate. The denominator is the Beta of the portfolio, or, in other words, a measure of its systematic risk.
Treynor, evaluates the excess return of a portfolio per unit of systematic risk, as measured by beta. Unlike the Sharpe Ratio, which considers total risk, the Treynor Ratio focuses solely on systematic risk. This makes it particularly useful when analyzing well-diversified portfolios.
The Sharpe Ratio helps rank and indicate the expected return compared to risk: Usually, any Sharpe ratio greater than 1.0 is considered acceptable to good by investors. A ratio higher than 2.0 is rated as very good. A ratio of 3.0 or higher is considered excellent.
The Jensen's measure, or Jensen's alpha, is a risk-adjusted performance measure that represents the average return on a portfolio or investment, above or below that predicted by the capital asset pricing model (CAPM), given the portfolio's or investment's beta and the average market return.
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