# TRV: Introducing A New Coefficient For Comparing Stock Return Volatility

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by: Anton Tyumin

## Summary

When analyzing particular stocks, I am always paying much attention to the volatility of its daily returns.

Alpha, beta, correlation and annualized volatility values have certain deficiencies and should be used with caution when one is weighing the risks and benefits of investing into a particular stock.

Trading volumes and price changes during the most volatile sessions can sometimes demonstrate a much broader picture when it comes to assessing the actual quality of a holding's performance.

Focusing on the volume impact

Trading volume data can always shed light on the quality of the stock price movements.

• Sustainability of a low-volume rally should always be viewed with a certain degree of skepticism.
• High-volume sell-off might be viewed as a strong short-term negative catalyst since the security is subject to significant capital outflows.

Focusing on the most volatile trading days

Putting more emphasis on the outlier daily changes in the stock price can help investors avoid the securities that tend to frequently overshoot their average daily performance. What if a particular stock's tendency of demonstrating an exceptionally volatile performance on particular days gets smoothed out when calculating average values? How can one adjust for that?

TRV: a coefficient capable of complementing the volatility analysis

Since one cannot always rely on charts when analyzing the stock's performance, I have decided to come up with a mathematical formula which could make the process of assessing the trading volumes and outlier performance values more convenient.

In addition, the goal was also to create a coefficient that could easily outline the securities that tend to experience outlier performance values on low trading volumes, which can be viewed as a rather negative sign. I would appreciate that if the readers could come up with a better name for the indicator. Meanwhile, I will be referring to it as TRV (which stands for Tyumin's Return Volatility).

The formula and its practical implications

The mathematics behind the calculations of the coefficient are rather simple. It can also be decomposed into 3 main parts which shed more light on the quality of the stock's performance:

• Average performance outlier - by which extent does the stock's performance deviate from the historical averages during particular days of extraordinary performance?
• Frequency of outliers - how often does the stock strongly deviate from its normal (average) daily performance?
• Volume impact - does the stock tend to experience the most significant run-ups or decreases in price with lower- or higher-than-average trading volumes?

The coefficient is being calculated as follows:

As the formula suggests, the larger the coefficient is, the more dangerous the stock might be for the one who is holding it.

TRV Coefficient in action

For the demonstration purposes, I am selecting 3 securities:

• Helen of Troy Ltd. (NASDAQ:HELE) - a stock which is often rising and falling on low volume. I was covering HELE in one of my recent articles.
• The Coca-Cola Company (NYSE:KO) - a low-volatility stock.
• Valeant Pharmaceuticals International, Inc. (NYSE:VRX) - a volatility champion.

The results are not surprising.

Made by the author using Yahoo Finance data.

Valeant's stock demonstrates a significant (as well as reasonably frequent) difference between the average and outlier values (3x average) of daily changes in stock prices. Even though number of outliers is significantly lower than that of the two other stocks due to the large absolute value of average daily change in the stock price over the last 250 trading days, the coefficient is being increased by the high absolute value of the average outlier. Outliers are more frequent on the downside, with volume complementing the bearish thesis for the stock. The stock has the highest TRV coefficient among the three. As mentioned before, Valeant is an absolute volatility champion, with its annualized volatility accounting for 96.42%.

Speaking of Coca-Cola, the stock with the lowest TRV, it is important to mention the stock's tendency to surprise on the upside more often than it does on the downside. In addition, it tends to experience outlier performance with a reasonably low increase in overall trading volume, for which the coefficient awards the stock with a relatively low number in the third part of the formula. The company has the largest number of common shares outstanding among the 3, which corresponds with average trading volume accounting for only a fraction of the total float of KO.

Helen of Troy's stock is one of those that might occasionally catch its investors off-guard. With 233 outliers during the last 250 trading days, average outlier performance is nearly 35 times higher than the average daily change in the stock price, which I view as an argument in favor of assessing the stock's daily performance values using the TRV. The coefficient gets a boost both from the high absolute outlier values and their overall frequency, which is viewed as negative for the holders of the stock. The stock has a relatively low average volume-to-float ratio, which might prove my previous conclusions regarding the stock's tendency to experience the most important spikes and falls on low volume. HELE's TRV is 87% higher than that of the KO, which corresponds with the stock's annualized volatility accounting for 28.17%, which is nearly twice as much as the value of KO (14.9%).

Conclusion

The TRV coefficient complements the analysis of the stock's daily volatility and is capable of rating the quality of its daily performance over the period. It cannot replace any other financial metric and is by no means capable of being used as a 100%-reliable tool when assessing a particular stock's dynamics, as extensive due diligence is of paramount importance when performing any type of security analysis.

Nevertheless, I am going to use the coefficient in my future analyses as it can (1) either prove or reject hypotheses regarding the volume impact on particular stocks and (2) demonstrate the relative risk of holding certain stocks on a daily basis. Even when it comes to stocks with solid fundamentals, timing is everything, and investors can be occasionally surprised by the other, negative side of the stocks that have demonstrated a decent run-up and relatively low volatility values in the past.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.