## Treynor Ratio Definition

The Treynor ratio is similar to Sharpe ratio where excess return over the risk-free return, per unit of the volatility of the portfolio, is calculated with the difference that it uses beta instead of standard deviation as a risk measure, hence it gives us the excess return over the risk-free rate of the return, per unit of the beta of the overall portfolio of the investor.

### Explanation

The term Treynor Ratio can be explained as a number which measures the excess returns, which could have been earned by the firm in some of its investments that have no variable risks, assuming the current market risk. The Treynor ratio metric helps managers in relating the returns earned in excess over the risk-free rate of return with the additional risk that has been taken.

**Source**: Yahoo Finance

### Treynor Ratio Formula

In the Treynor ratio formula, we don’t take the total risk into consideration. Instead of that, the systematic risk is considered.

Treynor ratio formula is given as:

**T = R _{i} – R_{f} / β_{i}**

Here, Ri = return from the portfolio I, Rf = risk free rate and βi = beta (volatility) of the portfolio,

The higher the Treynor ratio of a portfolio, the better is its performance. So when analyzing multiple portfolios, the use of the Treynor ratio formula as a metric will help us to analyze them successfully and find the best one among them.

### How Does the Treynor Ratio Work?

Treynor ratio calculation is done by considering the beta of an investment to be its risk. The β value of any investment is the measure of the investment’s volatility in relation to the current stock market position. The more the volatility of the stocks included in the portfolio, the more will be the β value of that investment.

The β value can be measured, keeping the value of 1 as a benchmark. The β value for the whole market is taken equal to 1. If a portfolio has a high number of volatile stocks, it will have a beta value greater than 1. On the other hand, if an investment has only a few volatile stocks, the β value of that investment will be less than one.

Stocks that possess a higher beta value have more chances to rise and fall more easily than other stocks in the stock market, having a relatively lower beta value. So when considering the market, the average comparison of beta values cannot give a fair result. So comparing investments with this measure is not really practical. So here comes the utility of the Treynor ratio because it helps in comparing investments or stocks having nothing common at all among them to get a clear performance analysis.

### Treynor Ratio Calculation

We will now look at a Treynor ratio example to clearly understand how Treynor ratio calculations. Look at the table given below with three investments, their beta values, and the returns in percentage:

Investment |
Beta value |
Percentage of return |

Investment A |
1.00 | 10% |

Investment B |
0.9 | 12% |

Investment C |
2.5 | 22% |

To carry out the Treynor Ratio calculations, we also need the risk free rate of the three investments. Let us assume all the three investments here have a risk free rate of 1.

Now we can carry out the Treynor Ratio calculation by using the Treynor ratio formula, which is as follows: –

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- For investment A, the Treynor ratio formula comes out to be ( 10 – 1 ) / (1.0 * 100) = 0.090
- For investment B, the Treynor ratio comes out to be ( 12 – 1 ) / (0.9 * 100) = 0.122
- For investment C, the Treynor ratio comes out to be ( 22 – 1 ) / (2.5 * 100) = 0.084

Therefore, the Treynor ratio for Investment A is 0.090, for Investment B is 0.122 and for the Investment C is 0.084. We can clearly notice from the obtained Treynor ratio values that Investment B has the highest Treynor ratio, and hence, this is the investment with a relatively lower beta value. So, in this case, Investment B is said to be the investment with the best performance among the three investments that we have analyzed. Similarly, Investment A is the second-best, while Investment C is the lowest-performing investment among the three.

Now, let us consider the raw analysis of the performance of the investments. When we look at the percentages of return, Investment C is supposed to perform best with a percentage of return of 22% while the Investment B must have been chosen to be the second-best. But from the Treynor ratio calculation, we have understood that Investment B is the best among the three, while Investment C, despite having the highest percentage, is the worst-performing investment among the three. This difference in the results came because of the use of the measure of the risk in Treynor ratio calculation.

### Limitations of Treynor ratio

Although the Treynor ratio is considered a better method to analyze and find out the better performing investment in a group of investments, it does not work in several cases. Treynor ratio does not consider any values or metrics calculated by means of the management of portfolios or investments. So this makes the Treynor ratio just a ranking criterion with several drawbacks, making it useless in different scenarios.

Further, the 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 Treynor ratio useless in performance analysis of such portfolios.

Another limitation of the Treynor ratio occurs because of the past consideration did by the metric. Treynor ratio gives importance to how the portfolios behaved in the 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 the future due to changes in market trends and other changes.

For example, if a stock has been giving the firm a 12% 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 is not considered by the Treynor ratio.

The Treynor ratio formula has an inherent weakness, which is its backward-looking design. It’s quite possible, maybe even more likely, for an investment to perform in a different manner in the coming periods from how it has done in the past. A stock with a beta of 3 might not essentially have the volatility of the market thrice forever, for instance. Likewise, you should not expect a portfolio to make money at an 8% rate of return over the coming ten years just because it did so over the past ten years.

In addition, some might take 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. For many years, Warren Buffett and Charlie Munger have argued that the volatility of an investment isn’t the true measure of risk. They might argue that risk is the likelihood of a permanent, not temporary, loss of capital.

### Treynor Ratio vs 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 main difference between the Sharpe ratio and the Treynor ratio is that unlike the use of systematic risk used in the case of Treynor ratio, the total risk or the standard deviation is used in the case of the Sharpe ratio. The Sharpe ratio metric is useful for all portfolios, unlike the Treynor ratio that can only be applied to well-diversified portfolios. The Sharpe ratio reveals how well a portfolio performs in comparison to a riskless investment. The common benchmarks, which are used to represent a riskless investment, are the U.S. Treasury bills or bonds.

The Sharpe ratio 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.

The first purpose of the Sharpe ratio is to find out whether or not you’re creating a considerably bigger return on your investment in exchange for accepting the extra risk inherent in equity investment, as compared to investing in riskless instruments. Thus, both the ratios work similarly in some ways while being different in others, making them suitable for different cases. Both the methodologies work for determining a “better performing portfolio” on considering the risk, making it more suitable than raw performance analysis.

### Application of Treynor ratio in Mutual Funds

Mutual funds are considered to be a good option to invest in, and determination of the risk-free return is something you should surely consider before deciding to invest in a mutual fund. Like all other investment options, mutual funds also carry risks, and is a long-term investment option; you should seriously consider all risks associated with it and always consider a mutual fund with less risk tolerance to provide a good rate of return from the investment.

The common risks involved in mutual funds are the following:

**Market risk:**Market scenarios are ever-changing, and mutual funds are largely affected by market risks. The change in market trends can affect the way an investment is returning income, and this is true for mutual funds too.**Industry risk:**Industry-based risks are common in the market. Any investment is made in the industry, in which a decline or a piece of bad news occurs, will change the way the market behaves. And therefore, it may affect the number of returns made.**Country risk:**The particular country where the investment goes, make them affected by the country based risks. Any scenarios taking place in that country can have significant effects on the way the investments behave. Things like election, government norm changes, and natural disasters can change the rate of return investment in that country provides the investors.**Currency risk:**The change in the exchange rate of currencies also affects the financial market greatly. Business organizations do business in different countries, which makes the inclusion of multiple currencies. So the change in an exchange rate of a currency in which business is done can affect the way the market behaves. So the currency risk is an important thing to be considered while calculating the Treynor ratio.**Interest rate risk:**The interest rates and the bond prices are greatly related to each other. An increase in interest rate can cause a decline in bond prices, and a reduction in the same can increase bond prices. So the risk related to the interest rate is important to consider.**Credit risks:**Timely payment against the debts or loans taken by the investor is important, and a failure in this can give rise to credit risks. The credit dues can inversely affect the business of the investor.**Principal risk:**Any fall in prices, like that of the equipment used by the firm, can affect the business too.**Fund manager risk:**The fund manager’s job has to be done perfectly. Any error in the fund manager’s work can adversely affect the funds. This is called the fund manager risk, so the proper working of the worker in the investment firm is an important thing in order to obtain a good Treynor ratio and hence a good rate of return.

As we have seen, it’s imperative for investors to find out mutual funds, which will help them meet their investment objectives at the required risk level. And you should realize that gauging the risk involved in a mutual fund scheme just on the basis of the NAV of the fund reports might not be the holistic assessment. It is noteworthy that, in a fast-rising market, it’s not altogether tough to clock higher growth if the fund manager is willing to take up a higher risk. There have been many such occasions in the past, like the rally of 1999 and early 2000, as well as many mid-cap stock rallies of the past. Therefore, assessing the past returns clocked by the mutual fund in isolation would be inaccurate because they will not give you any indication of the extent of risk you have been exposed to as an investor.

### Conclusion

Treynor ratio is a metric widely used in finance for calculations based on returns earned by a firm. It is also known as a reward-to-volatility ratio or the Treynor measure. The metric got its name from Jack Treynor, who developed the metric and used it first.

Ratios that use the beta, the Treynor ratio being one of those, could also be best fitted to compare short-term performance. There have been a lot of studies on the long-term stock market performance, and a study of Buffett’s record at Berkshire Anne Hathaway has shown that low beta stocks have really performed better than high beta stocks, whether on a risk-adjusted basis or in terms of raw, unadjusted performance basis.

It must be noted here that the direct and linear relationship between higher beta and higher long-term returns might not be as robust as it is believed to be. Academics and investors will invariably argue about the most effective strategies for activity risk for years to come. In truth, there may be no measure to be regarded as the perfect measure of risk. However, despite this, the Treynor ratio will at least offer you some way to match the performance of a portfolio on considering its volatility and risk, which can create more helpful comparisons than just a simple comparison of past performances.

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