A Better Way to Calculate Volatility

Have you ever suddenly come to the realization that something you’ve done thousands and thousands of times over the last 20 years could be done better?  That happened to me last year, and instantaneously I thought, “why/how have I never thought of this before?”  The origin of my epiphany was on how to calculate historical volatility.

Most practitioners (myself included) have done this by calculating the standard deviation of lognormal price movements using the closing price (adjusted for dividends and splits). But after reading two academic journals (Which Daily Price is Less Noisy and Volume Weighted Volatility: empirical evidence for a new realized volatility measure), and brainstorming it with anybody who had the patience to listen (special thanks to Jon Burg, Andy Restaino, and countless others). I have come to the conclusion that there is a more refined way to calculate historical volatility, which is no more onerous to perform. And conveniently, I believe there to be empirical evidence that proves it is a better estimate of realized volatility. 

What's Wrong with the Closing Price?

To quickly summarize, many academics and practitioners believe that the closing price is skewed by significant noise in the final spot price, such as end-of-day portfolio re-balancing, investors anticipating post-close news, social media and meme stock volatility. All these contributing factors have led to the closing price to be an extreme price (either on the low or high end).

How Do Closing Prices Compare to Average Prices?

In Infinite Equity research, we found that 37% of closing prices were in the bottom or top decile of all prices (much more than the anticipated 20%). One potential solution is to calculate historical volatility using the intraday volume weighted average price (“VWAP”) rather than the close, which represents the single weighted average price during the day. Intuitively, it makes sense: this is the price an employee could possibly exercise an option at. But through using the VWAP Volatility, Which Daily Price is Less Noisy states, “at-the-money options are 15% more expensive” (p. 91), which is alluding to the fact that the closing price is creating valuations that are 15% higher.

Consistent with this, Infinite Equity studied the S&P 500 and estimated that the closing price overstates the value of a stock option by ~10%. This was pretty profound and awesome for someone like myself, who has built his entire career around valuing employee equity and stock options. After all the diligence and scrutiny on option pricing models ranging from Black-Scholes, to binomials, to lattices, the CRR, the Hull-White—and now to find that one of my basic premises had a 10% overstatement?  Wow! 

How Does VWAP Play Out in Option Pricing Models?

I felt I needed to dig deeper and understand better, starting with one of the underlying theories of the Black-Scholes model, which assumes a normal distribution of stock price returns. One statistical measure to analyze distributions is the kurtosis. The statistic kurtosis is a descriptor to help understand the distribution of stock returns and whether the empirical data is normally distributed. Further, it can help distinguish which stock prices should be used.

Infinite Equity studied the kurtosis of returns using closing prices, as compared to the kurtosis of returns using VWAP prices. We found that 82% of the time, the VWAP returns had an improved kurtosis—a better distribution of returns—which would better match the underlying theory of option pricing models. Although VWAP prices/returns didn’t always have a better kurtosis, they did so much more often than not.

What Are the Implications of Improving Volatility Estimates?

At this point, it became very clear to me that VWAP Volatility is a more refined estimate of historical volatility and needs to be seriously considered in the range of reasonable alternatives for developing volatility estimates. The selection of a process for developing expected volatility is very subjective, and requires considerable deliberation including implied volatility, peer volatility, debt leverage adjustments, and many more. But based upon the empirical data, VWAP volatility needs to be high on this list or receive some significant weighting combined with other reasonable alternatives. There are several areas where this new refined methodology can have huge implications: 

• Total Stock Based Compensation Expense: In any pricing model, expected volatility has a significant impact on option fair value. Using a better volatility estimate will lower option fair values. For many companies, even reducing the option valuation by 5% could have a meaningful effect on compensation expense.

• Grant Sizing: The NASPP/Deloitte survey on stock plan design found that 87% of companies determine the number of options to grant based upon the ASC 718 valuation. If the ASC valuation were to decrease by 5%, then that would mean the grant size would increase by 5%, offering significantly more value to the participant. (Although increasing grant size by 5% would also increase the expense by 5%, neutralizing the expense reduction I discuss above.)  Option usage varies by sector, but Fidelity Stock Plan Services tells me that Healthcare and IT are most likely to be granting options. These are also sectors where the war for talent rages. Valuation methodology that could increase grant sizes could be another tool in that war for talent. 

• Plan Design: Since the beginning of 2006 (when FAS 123(R)/ASC 718 was implemented), the NASPP/Deloitte survey notes that the prevalence of stock options has decreased from approximately 90% in 2006 to 47% presently. There are lots of reasons on why stock options have decreased in prevalence. However, one of the drivers may have been that the perception of value (as compared to the accounting valuation) is low. A change like this could help re-balance the equation; the perception of value would increase, and potentially more companies could shift back into granting new stock options.

More Information

Infinite Equity continues to do significant research on VWAP volatility. We have collected a portal of research at www.VWAPVolatility.com, including a complimentary calculator for you to estimate your own VWAP Volatility as compared to closing price volatility. I hope my epiphany blows your mind too!