Developing volatility assumptions is a common practice in the financial community, where many sophisticated techniques have been developed that go beyond simply calculating volatilities based on historical stock prices. The Black-Scholes, Monte Carlo, and lattice models all use a volatility input, which may come from a variety of sources – for example the use of a historical price, an implied market volatility, or peer group volatilities are all common approaches in ASC718.
However, the guidance set forth in the original FAS123, and followed by FAS123R (now ASC718), as well as guidance from SEC in Staff Accounting Bulletin #107 and the PCAOB, does not clearly define what definition of stock price should be used when gathering the stock price data. More typically than not, companies have used “Closing Price” (appropriately adjusted for splits and dividends) for this purpose, which has historically been the most accessible from external data providers. Over time, virtually all companies have used this definition for calculating historical volatility, probably for computational ease.
However, we have become aware of academic research that illustrates that using the Volume Weighted Average Price (VWAP) is a better representation of market volatility (as opposed to closing price). The VWAP is a weighted intraday average of all transactions from a given trading day. It represents the price that market participants generally received in a transaction and better represents the activity during the course of the day for the average participant.
The research indicates that the “closing price” volatility can be 5.4% higher than using a more appropriate VWAP volatility. Intuitively, this makes sense in our experience and we want to highlight the following considerations of this important development.
- The VWAP price includes all transactions for a given day, rather than arbitrarily choosing only the closing price, which ignores virtually all of the transactional data during the day
- The closing price includes expectations for future news after the market close, but also may skew the closing price to the extremes rather than what was available during the day
- VWAP is a more theoretically pure representation of an actual transaction in an efficient market
- Supported with published academic articles
- Continues to be computationally possible in a scalable way
Accounting History & Background
The regulatory guidance listed above does not prescribe any specific methodology for gathering stock prices. In the original FAS123 as written in 1995, it says in Paragraph 401“the time intervals between price observations should be as uniform as possible; for example, the weekly stock closing price could be used for all observations. It would not be appropriate to use the weekly closing price for some observations and, for example, the average weekly price for other observations in the same calculation.” We agree that it is critically important to follow a consistent and uniform process for gathering stock prices, and VWAP prices should not be mixed with closing prices, as whatever historical price in a calculation should be used consistently in a single calculation. Further, since each VWAP price is ‘independent’ of any other day VWAP price, the approach does not mathematically bias the calculation in any single direction.
All of the subsequent written guidance regarding assumption selection and expected volatility (FAS123, FAS123R (now ASC718), SEC in Staff Accounting Bulletin #107 and Auditing The Fair Value of Share Options Granted to Employees by the PCAOB) allow for significant flexibility in the estimation of expected volatility. On December 5, 2005, at the 2005 AICPA National Conference on Current SEC and PCAOB Developments, the following was said regarding the selection of expected volatility,
“We have become aware of two methods for computing historical volatility that we believe will not meet this expectation. The first method is one that weighs the most recent periods of historical volatility much more heavily than earlier periods. The second method relies solely on using the average value of the daily high and low share prices to compute volatility. While we understand that we may not be aware of all of the methods that currently exist today and that others may be developed in the future, we would like to remind companies to keep in mind the objective in Statement 123R when choosing the appropriate method.”
We believe that this speech is important in a couple of ways. First off, the second approach described – the average value of the daily high and low – does not capture the magnitude of data as captured in a VWAP price and does not refine the calculation as significantly (and confirmed in Table 1 of Padungsaksawasdi and Daigler). Further, the statements clearly outline the expectation for future new developments in methodology, and that the objective is to develop the best estimate of expected volatility.
We believe that the calculation of a VWAP Volatility is a refined estimate of historical volatility. Given some of the extreme volatility seen in the marketplace today due to influences like algorithmic trading, social media, the rebalancing of institutional investor portfolios, we believe that the closing price can no longer be seen as the most reliable approach for calculating historical volatility. Further, with advances in computational capabilities, we believe that the VWAP volatility should be one of the considered alternatives in selecting your process for estimating volatility.
For an estimate of how the VWAP Volatility compares to a traditional historical volatility or to know if VWAP Volatility is better for you, please reach out to your Infinite Equity consultant. Please see more research from Morgan Stanley and Infinite Equity at www.VWAPVolatility.com.
 Volume Weighted Volatility: empirical evidence for a new realized volatility measure, Chaiyuth Padungsaksawasdi and R. Daigler, 2018