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 original guidance set forth in FAS123, followed by FAS123R (now ASC718), and guidance in SEC in Staff Accounting Bulletin #107 and the PCAOB, does not clearly define what definition of stock price should be used when gathering stock price data. Companies have generally used “Closing Price” (appropriately adjusted for splits and dividends) for this purpose, likely because it has historically been the most accessible data point from external data providers. Over time, virtually all companies have used this definition, probably for computational ease.
However, there is academic research that illustrates that using the Volume Weighted Average Price (VWAP) is a better representation of market volatility. 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.
Research shows that using the “closing price” volatility can be 5.4% higher than using a more appropriate VWAP volatility, which is consistent with our experience. Below we summarize key considerations related to this interesting development.
- The VWAP price includes all transactions for a given day, rather than arbitrarily choosing only the closing price, which ignores virtually all transactional data throughout the day
- The closing price includes expectations for future news after the market close, but also may skew the closing price to an extreme rather than what was available during the day
- VWAP is a more theoretically pure representation of an actual transaction in an efficient market
- VWAP is supported with published academic articles
- VWAP 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 FAS123, as written in 1995, paragraph 401 states that “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 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 this statement is important for two reasons. First, the second approach described – the average value of the daily high and low – does not capture the magnitude of data as compared to the VWAP price and does not refine the calculation as significantly (and confirmed in Table 1 of Padungsaksawasdi and Daigler). Second, the statement clearly outlines an expectation for future new developments in methodology, and an objective 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 Infinite Equity at www.VWAPVolatility.com.
 Which Daily Price is Less Noisy, Christopher Ting, Financial Management, September 2006
 Volume Weighted Volatility: empirical evidence for a new realized volatility measure, Chaiyuth Padungsaksawasdi and R. Daigler, 2018