# Treynor ratio

July 27, 2023
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The Treynor Ratio is a figure that calculates the extra earnings a business might have made on certain of its assets if there were no variable risks, given the existing market risk. The Treynor ratio statistic assists managers in relating the extra earnings gained above the risk-free rate of return to the additional risk that has been accepted. The Treynor ratio is a volatility/return metric that enables traders to account for systematic risk in portfolio returns. A more substantial Treynor ratio indicates that a portfolio is a better investment. The Treynor ratio is identical to the Sharpe ratio, except that the Sharpe ratio adjusts portfolio returns based on a portfolio's standard deviation.

## What is the Treynor ratio?

The Treynor ratio, or the reward-to-volatility ratio, is an indicator of performance used to calculate how much extra return a portfolio created for each unit of risk it took. In this context, extra earnings refer to the return gained over what would have been generated in a risk-free investment. Although there is no risk-free investment, treasury bills are frequently utilized in the Treynor ratio to approximate the risk-free return. Volatility in the Treynor ratio is defined as the systematic risk assessed by a portfolio's beta. The propensity of a portfolio's return to alter in reaction to changes in the broader market return is measured by beta. Jack Treynor, an American economist and co-inventor of the Capital Asset Pricing Model (CAPM), devised the Treynor ratio.

### The Treynor ratio formula

Treynor ratio = (r p ​– r f) / β p​

Where;

• rp ​= Portfolio return
• rf = Risk-free rate
• βp ​= beta of the portfolio​

Portfolio return and systematic risk are the subjects of the Treynor ratio calculation. It quantifies, quantitatively speaking, how much more return above the risk-free rate may be earned per unit of systematic risk. It is a measure of return relative to risk, like the Sharpe ratio.

The formula calls for three variables: the beta of the portfolio, which is the weighted sum of the betas of all the investments in the portfolio. The risk-free rate is the return rate on a hypothetical investment with zero risk of monetary loss over a particular duration and the average return on the portfolio.

A negative beta would render the ratio meaningless. In any case, a greater ratio indicates that the portfolio is likely a smart investment. A more substantial ratio outcome is desired and indicates that a specific portfolio is probably a better investment. However, since the Treynor ratio is based on historical data, it cannot predict future results, and investors should never use it alone to make important financial decisions.

### Perceiving the Treynor ratio concept

The Treynor ratio is calculated by assuming an investment's beta to represent its risk. The worth of any investment indicates the unpredictability of the investment in the present stock market position. The more the unpredictability of the securities in the holdings, the greater the worth of that investment.

The value may be measured using one as a reference point. The value for the whole market is set at 1. A portfolio containing a high proportion of volatile equities will have a beta value higher than one. If, on the other hand, an investment only contains a few volatile stocks, its value will be less than one.

Equities with a higher beta value are more likely to rise and fall than those with a lower beta value in the stock market. Consequently, an average comparison of beta values cannot provide a realistic result in the market. As a result, comparing investments using this metric is impractical. So, the Treynor ratio is useful since it allows you to compare investments or companies that have nothing in common to obtain a clear performance report.

### Negative Treynor ratio

The Treynor index is seldom used with negative integers since it becomes more difficult to comprehend. It is typically associated with positive earnings and betas. A Treynor ratio may be negative in two ways: an adverse earning or a negative beta. We cannot simply state that one ratio is superior in any situation. Logically, a lower negative number is preferable if we wish to get the ratio positive and rise upward. It may not necessarily indicate the greatest investment since if two equities' returns are negative (-15%), the one with a greater beta will have a smaller negative Treynor ratio. The investor must select whether to make deals on a riskier stock with a lower Treynor or a less unstable stock with a higher Treynor.

### Treynor ratio application in mutual fund investments

Mutual funds are regarded as an excellent investment choice, and determining a risk-free return is a phenomenon you should examine before investing in a mutual fund. Mutual funds, like all other investment alternatives, entail risks and are a long-term investment option; you ought to carefully evaluate all risks and always choose a mutual fund with a lower risk tolerance to deliver a reasonable rate of return on investment.

### Market risk

Market circumstances are constantly shifting, and market risks significantly impact mutual funds. Market changes may influence how an investment produces income, which applies to mutual funds. The following are the most prevalent risks associated with mutual funds:

#### i. Interest rate risk

Interest rates and bond prices are inextricably linked. Bond prices may fall as interest rates rise, and bond prices can rise when interest rates fall. As a result, the risk associated with interest rates must be considered.

#### ii. Credit risks

Failure to make timely payments on debts or loans taken out by the investor might result in credit risks. Credit dues might have a negative impact on the investor's company.

#### iii. Industry risk

Industry hazards are prevalent in the market. Any investment in a sector that experiences a decrease or a piece of negative news will alter how the market reacts. As a result, the number of returns may be affected.

#### iv. Nation risk

The nation in which the investment is made affects the country-based risks. Any events that occur in that nation may have a substantial impact on how the investments perform. Elections, changes in government norms, and natural calamities may all affect the rate of return on investment in that nation.

#### v. Currency risk

Changes in currency exchange rates have a significant impact on the financial market. Business entities do transactions in a variety of nations and currencies. As an outcome, changes in the exchange rate of a currency in which commerce is conducted might impact how the market works. As a result, currency risk must be included when computing the Treynor ratio.

#### vi. Principal risk

Any drop in pricing, such as that of the firm's equipment, might impact the company.

#### vii. The risk associated with fund managers

The fund manager's task must be done flawlessly. Any miscalculation in the fund manager's job might have a negative impact on the funds. It is known as fund manager risk, and it is critical that the workers in the investment business operate well to acquire a decent Treynor ratio and hence a good rate of return.

As depicted above, traders must identify mutual funds that assist them in fulfilling their investing goals while taking the appropriate risk. Furthermore, you should be aware that assessing the risk of a mutual fund scheme solely based on the NAV of the fund reports may not be a comprehensive evaluation. It is worth noting that in a rapidly rising market, it is not impossible to get better growth provided the fund manager is ready to take on more risk. Many comparable occurrences have occurred, including the 1999 and early 2000 rallies and other mid-cap stock rallies. As a result, evaluating the mutual fund's previous results in isolation would be misleading since it would not reveal the degree of risk you have been subjected to as an investor.

Keep the following in mind while using the Treynor ratio:

·       The ratio fails to offer significant values for negative Beta values.

·       The ratio fails to account for the importance of the difference in values when evaluating two portfolios since they are ordinal.

·       The surplus yield above the risk-free rate is the numerator. The denominator is the portfolio's beta, which indicates its systematic risk.

### Constraints of the Treynor ratio

Although the Treynor ratio is considered an ideal way to analyze and determine the best-performing investment in a group of assets, it does not work in all instances. The Treynor ratio does not consider any values or metrics obtained via portfolio or investment management. As a result, the Treynor ratio is only a ranking criterion with multiple limitations that render it ineffective in certain contexts.

Furthermore, the Treynor ratio can only be utilized efficiently for assessing several portfolios if they are a portion of a larger portfolio. In circumstances when the portfolios have varied total risks but comparable systematic risks, they will be rated the same, rendering the Treynor ratio worthless in such portfolio performance study.

Another drawback of the Treynor ratio is from the metric's evaluation of the past. The Treynor ratio emphasizes how portfolios performed in the past. Investments or holdings are always shifting. We cannot assess one based on historical performance since portfolios may behave differently in the future due to changes in market patterns and other factors.

The Treynor ratio formula possesses an intrinsic flaw: it is designed backwards. It is feasible, and perhaps even more probable, that an investment will perform differently in the future than it has in the past. For example, an asset with a beta of 3 may not have the market's volatility thrice permanently. Similarly, you should not anticipate a portfolio to produce money at an 8% rate of return over the next ten years just because it did so in the previous ten.

Furthermore, some may object to using beta as a risk indicator. According to some experienced investors, beta cannot provide a realistic picture of the risk involved. For a long time, Warren Buffett and Charlie Munger have maintained that an investment's instability is not a meaningful risk indicator. They may claim that risk is the possibility of permanent, rather than temporary, capital loss.

### The Sharpe ratio versus the Treynor ratio

The Sharpe ratio is a statistic similar to the Treynor ratio used to examine the productivity of various investments while considering risk.

The primary distinction between the Sharpe ratio and the Treynor ratio is that, unlike the Treynor ratio, the Sharpe ratio uses absolute risk or standard deviation rather than systematic risk. The Sharpe ratio measure applies to all portfolios instead of the Treynor ratio, which only applies to well-diversified portfolios. The Sharpe ratio measures how effectively a portfolio outperforms a risk-free investment. US Treasury bills or bonds are the most often used references to symbolize a riskless investment.

The Sharpe ratio estimates the anticipated or actual return on investment for an investment holding (or even an individual equity investment), subtracts the return from the riskless investment, and divides the result by the investment portfolio's standard deviation.

The Sharpe ratio's initial objective is to establish if you are getting a significantly higher return on your investment in exchange for incurring the greater risk inherent in equities investing instead of investing in risk-free products. Both techniques seek to determine a "better-performing portfolio" by considering risk, making it more appropriate than raw performance evaluation. As a result, both ratios function similarly in certain respects while differing in others, making them suited for distinct scenarios.

## Conclusion

The Treynor ratio is a popular statistic in finance for calculating an organization's earnings. It is also referred to as the Treynor metric or a reward-to-volatility ratio. Ratios employing beta, such as the Treynor ratio, may best contrast short-term outcomes. It should be highlighted that the direct and linear association between greater beta and better long-term returns may not be as strong as previously thought. For years, researchers and traders will undoubtedly disagree on the most effective ways to mitigate activity risk. In reality, there could be no such thing as a perfect risk measure. Regardless, the Treynor ratio will possibly provide you with a technique to compare the efficiency of a portfolio by taking volatility and risk into account, which may produce more useful comparisons than a basic comparison of historical results.