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# Treynor Ratio

## Definition

The Treynor Ratio, named after economist Jack Treynor, is a performance metric for investment funds or portfolios. It measures returns earned in excess of that which could have been earned on a risk-free investment per each unit of market risk. The ratio is calculated by subtracting the risk-free rate from the portfolio’s return, then dividing the result by the portfolio’s beta.

### Phonetic

The phonetics of the keyword “Treynor Ratio” is: Trey-nor Ray-shee-oh

## Key Takeaways

<ol><li>Treynor Ratio, also known as the reward-to-volatility ratio, is a performance metric for determining how well an investment has compensated for each unit of systemic risk. It is calculated by taking the excess return over the risk-free rate divided by the portfolio’s beta.</li><li>It is predominantly used to evaluate the performance of a portfolio or fund manager. A higher Treynor Ratio implies that the portfolio or fund manager achieved higher returns while managing systemic risk effectively.</li><li>The Treynor Ratio is most useful when comparing funds or portfolios that are composed of diversified investments. However, it only takes into consideration systemic risk (represented by beta) and ignores unsystemic risk. Therefore, it works best for well-diversified portfolios.</li></ol>

## Importance

The Treynor Ratio is important in business and finance because it is a performance metric for determining how well an investment has been when taking into consideration the systematic risk involved. Named after Jack Treynor, it is also known as the reward-to-volatility ratio. It is particularly useful in comparing the risk-adjusted performance of different portfolios or funds. A higher Treynor Ratio indicates a more desirable portfolio performance, demonstrating a superior risk-reward balance, and vice versa. Thus, it provides valuable insights for financial analysts and investors in their decision-making process to opt for more profitable and less risky investments.

## Explanation

The purpose of the Treynor Ratio, a financial metric, is to assist investors and analysts in determining the level of risk undertaken to produce a certain level of return. By relating the risk premium (the difference between the average return of a portfolio and the risk-free rate) to “systematic risk” , this ratio gauges the reward efficiency – that is, how much return is generated per unit of risk. This ratio, developed by Jack L. Treynor, is particularly useful for comparing portfolios that have disparate risk levels.The Treynor Ratio evaluates the effectiveness of the portfolio’s risk management strategy and guides investment decisions. It assesses whether the risk undertaken was justified by the returns, aiding investors in balancing their risk-return preferences. It is crucial to note that the higher the Treynor Ratio, the more desirable the portfolio is, as it suggests that the portfolio is earning more return per unit of risk. This metric therefore plays an integral part in optimizing portfolio performance and decision-making in financial management.

## Examples

The Treynor Ratio, developed by Jack Treynor, is a performance metric for determining how well an investment has done in comparison to the risk-free rate of return, given its level of market risk. Here are three real-world examples:1. Index Mutual Fund: Consider an index mutual fund that over the past year has yielded a return of 8%, while the risk-free rate (such as a 3-year U.S. Treasury Bill) has yielded 2%. If the beta value of the fund (the measure of market risk) is 1.2, then the Treynor ratio would be (8%-2%)/1.2 = 5.2. Large-cap Stocks: An investment portfolio is heavily invested in large-cap stocks. Over a specific period, the portfolio gives a return of 12%. Meanwhile, the risk-free rate for the same period is 3%. The beta value, a measure of the portfolio’s relative volatility, is 1.5. The Treynor ratio is then calculated as (12%-3%)/1.5 = 6.3. Pension Funds: A pension fund has achieved an average return of 10% over the last five years, while the returns on risk-free investments like T-bills over that same period is 4%. The beta of the pension fund is found to be 1.3. The Treynor ratio is then (10%-4%)/1.3 ≈ 4.62.In all of these cases, the Treynor ratio provides a measure of the excess return earned above the risk-free rate, per unit of market risk, which helps investors assess the performance of their investments in relation to the risks involved.

What is the Treynor Ratio?

The Treynor Ratio, named after Jack Treynor, is a performance metric for determining how well an investment has performed considering market risk. It compares the risk-adjusted performance of an investment portfolio or a fund to the market as a whole.

How is the Treynor Ratio calculated?

The Treynor Ratio formula is (Portfolio Return – Risk-Free Rate) / Beta. Beta in this context is a measure of the investment’s volatility against the market. The Risk-Free Rate is typically the return on a 3-month Treasury bill.

What does a higher Treynor Ratio indicate?

A higher Treynor Ratio indicates that the investment or portfolio is more efficient or provides a better return for each unit of market risk taken.

Is a negative Treynor Ratio good or bad?

A negative Treynor Ratio indicates that the investment’s risk-adjusted returns are less than the risk-free rate, suggesting a poor investment decision when considering the level of risk taken.

How does Treynor Ratio differ from Sharpe Ratio?

While both these ratios are used to evaluate the risk-adjusted return of an investment, the key difference lies in how they measure risk. The Sharpe Ratio considers total risk (systematic and unsystematic risk) of a portfolio, while the Treynor Ratio only looks at systematic risk (market risk).

Can the Treynor Ratio be used to compare different investment portfolios?

Yes, the Treynor Ratio can effectively compare the performance of different funds or portfolios on a risk-adjusted basis, allowing investors to assess which investments are giving the best return for the level of market risk taken.

What are the limitations of using the Treynor Ratio?

A key limitation of the Treynor Ratio is that it assumes that the investment portfolio is well-diversified and therefore, only considers market or systematic risk. In real-life scenarios, all portfolios carry some level of unsystematic risk, hence results can be misleading.

What kind of investors typically use the Treynor Ratio?

The Treynor Ratio is often used by risk-averse investors or those focused on maximizing returns while minimizing their exposure to market volatility.

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