Understanding the Treynor Ratio for evaluating Mutual Funds…

It is now understood that Sharpe ratio is a good measure of return per unit of risk. The problem stems from the issues associated with using standard deviation as a measure of risk. The SD focuses more on volatility of returns around the mean. This creates a problem because the mean for a stable series and a volatile series can be almost similar and the SD in both cases will be measured with respect to that mean. Let us understand that more clearly.

The problem with mean, stable returns and external factors…

Since Sharpe uses the Standard Deviation (SD) as the denominator, it is essential to understand the two basic drawbacks of SD as a measure of risk. Let us assume a series of numbers (33, 32, 30, 31, and 34) and another series of numbers (18, 9, 72, 41, and 20). Both these series of numbers have a mean of 32. But obviously, the second series is more volatile and the first series is more predictable and stable. But then in both cases, the SD uses the mean and calculates the deviation around the mean. While SD may be relevant in the first case, it is not so relevant in the second case.

The second issue is that SD focuses too much on stability of returns rather than on quality of returns. If one fund has been growing by 1% each month and another fund has been falling by 1% each month, then the SD of both the funds will be the same. This is obviously not a reflection of the real picture. This focus on stability makes SD a fairly rigid measure.

The third issue pertains to the fact that the SD is internal to the series of numbers. For example, SD is always calculated with respect to the mean. Hence it does not capture any external factors and hence does not capture the external risk. So what is an improved methodology available to investors?

One can look at the Treynor ratio…

Treynor ratio is a slight improvement over the Sharpe Ratio. It addresses the 3 principal drawbacks of the Sharpe ratio. It does not focus overtly on the mean; it does not focus too much on stability of returns and it considers external factors by using the Beta instead of standard deviation. Beta is a very popular measure and it measures how volatile your fund is with respect to the index. For example if the Beta of the MF scheme is 1.2, then the fund will move 1.2 times the index. So if the index moves up by 10% then the fund will move up by 12% and if the index moves down by 10% then the fund will move down by 12%.

In Treynor ratio, the numerator is the same excess returns as used in the Sharpe ratio. The only difference is in the denominator. Instead of using the Standard Deviation as the denominator, the Treynor ratio uses the Beta as the denominator. Remember, the Standard deviation is a measure of total risk while the Beta is a measure of systematic risk.

Mathematically, the Treynor ratio can be expressed as under:

(Returns on the Fund – Risk Free Returns) / Beta of the Fund

When to use Sharpe Ratio and when to use Treynor ratio…

The big challenge is in knowing when to use the Sharpe ratio and when to use the Treynor ratio. There are some basic rules that you can follow. Since the Treynor ratio uses the Beta as the denominator, it is more suited to well-diversified equity portfolios. Here is why! There are two types of risks in equities. Unsystematic risks focus on company and industry level factors, while Systematic risk focuses on market level factors. Systematic risk is measured by Beta, while Standard Deviation measures the total risk. In a diversified portfolio, the unsystematic risk is diversified away and hence the Treynor ratio is more suitable.

What do fund managers and analysts use more often?

While the Treynor may appear to be a more sophisticated measure of a mutual fund performance, the Sharpe ratio is more popular. There are 2 reasons for the popularity of Sharpe Ratio. Firstly, Sharpe ratio captures the past performance of the fund, whereas Treynor ratio is more useful as an indicator of future performance. Since fund fact sheets are more an evaluation of past performance, they will necessarily disclose the Sharpe ratio but not necessarily the Treynor ratio. Hence Sharpe ratio is more easily available and accessible for investors. Secondly, the Beta is much more intuitive than standard deviation and hence there is a high element of discretion. From a realistic perspective, Sharpe is therefore more popular.

For investors what is important is that both the Sharpe and the Treynor measures give almost similar comparative results over a period of time. What is more essential is that you understand the importance of imputing the risk aspect when evaluating the returns of a fund. That will give you a better handle on how your fund manager is actually performing.

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