## Definition of Treynor Ratio and comparison with Sharpe Ratio

#### introduction

The Treynor Ratio, also known as Rewards-to-Volatility Ratio, is a performance metric to determine how much excess return is generated for each unit of the risk taken by a portfolio. In other word, it tries to measure how well an investment has compensated its investors at its given level of risk.

#### Definition : Treynor ratio

- Treynor Ratio was developed by Jack Treynor, an American economist who was one of the inventors of the Capital Asset Pricing Model (CAPM).
- The ratio measures the excess return generated per unit of risk taken by the portfolio. Excess return here means the return earned above the return that could have been earned in a risk-free investment.
- There is no true risk-free investment. So Treasury Bills are often used to represent the risk-free return in the ratio. Risk in the ratio refers to the systematic risk which is measured by the portfolio’s Beta. Beta measures the tendency of a portfolio’s return to change in response to changes in return for the overall market.
- It is a risk assessment tool that calculates the value of an investment adjusted risk by measuring the volatility in the market. In other words, it is a financial equation that investors use to calculate the risk of certain investments taking into account the volatility of the market.
- It aims to adjust all the investment for the market volatility and the risk associated with it, in order to compare investments based on their performance instead of market factors.

#### formula

- Treynor Ratio = [Average Portfolio Return – Average Risk Free Rate] / Beta of the Portfolio
- TR = [ Rp – Rf ] / B

Where,

- TR = Rp = Return of the Portfolio
- Rf = Risk-Free Rate of Return
- B = Beta of the Portfolio
- Rp represents the actual return of the stock or investment. Rf represents the rate that a risk free investment like Treasure bills is willing to pay. B represents the volatility of the investment portfolio in comparison to the market as a whole.

#### What does the treynor ratio tell?

- 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.
- The higher the Treynor ratio of a portfolio the better is its performance. So when analyzing multiple portfolios, the use of it as a metric will help us to successfully analyze them and find the best one among them.
- In a portfolio with a negative beta, however, the ratio result is not meaningful. A higher ratio result is more desirable. It means that a given portfolio is likely a more suitable investment.
- Since, the ratio is based on the historical data, it does not necessarily indicate future performance. Therefore, one should not solely rely upon it for investing decisions.

#### Treynor ratio v/s sharpe ratio

- Sharpe Ratio is a metric, similar to the Treynor ratio, used to analyze the performance of different portfolios, taking into account the risk involved. The equation for calculating Treynor Ratio is similar to the method of Sharpe Ratio for assessing the risk and volatility in the market with one exception.
- The main difference between the Sharpe ratio and the Treynor ratio is that the Treynor Ratio uses the systematic risk, while the Sharpe ratio uses the total risk or the standard deviation.
- The Sharpe ratio metric is useful for all portfolios, while the Treynor ratio can only be applied to well-diversified portfolios.
- The Sharpe ratio reveals how well a portfolio performs in comparison to a riskless investment. It first calculates either the expected or the real return on investment for an investment portfolio (or even a personal equity investment), subtracts the riskless investment’s return on investment, and then divides that result by the standard deviation of the investment portfolio.
- Both the methodologies work for determining a “better performing portfolio” on considering the risk, making it more suitable than raw performance analysis.

#### limitations

- The main drawback of the Treynor ratio is that it is backward-looking. It relies on using a specific benchmark to measure beta. A stock with a beta of 2 might not essentially have thrice the volatility of the market forever.
- Treynor ratio gives importance to how the portfolios behaved in past. In reality, the investments or portfolios are ever changing and we can’t analyze one with just past knowledge as the portfolios may behave differently in future due to change in market trends and other changes.
- For example, if a stock has been giving the firm a 10% rate of return for the past several years, it is not guaranteed that it will go on doing the same thing in the years to follow. The rate of return can go either way, which the Treynor ratio don’t consider.
- Treynor ratio can be effectively used for analyzing multiple portfolios only if it is given that they are a subset of a larger portfolio. In cases where the portfolios have a varying total risk and similar systematic risks, they will be ranked the same, making the ratio useless in performance analysis of such portfolios.
- There is an issue with the utilization of beta as a measure of risk. Several accomplished investors would say that beta can’t give you a clear picture of involved risk. Also, aacording to them the volatility of an investment isn’t the true measure of risk.

#### summary

- The Treynor ratio is a risk/return measure that allows investors to adjust a portfolio’s returns for systematic risk.
- The higher the Treynor ratio of a portfolio the better is its performance. A higher ratio result means a portfolio is a more suitable investment.
- The Sharpe ratio is similar to the Treynor ratio. But the Sharpe ratio uses a portfolio’s standard deviation to adjust the portfolio returns, while the latter one uses portfolio’s Beta for the same.

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