How The Pandemic Is Changing Stock Volatility Calculations

By Andrew Roper and Clifford Ang
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Law360 (September 15, 2020, 8:34 PM EDT) --
Andrew Roper
Andrew Roper
Clifford Ang
Clifford Ang
The COVID-19 pandemic is causing betas — or the sensitivity of a stock to market movements — to change. The challenges posed by these changes in beta can affect litigation requiring expert analysis of value or damage, including appraisals actions, damage claims related to business interruption, valuations of portfolios of illiquid assets, and damages claims of lost profits. This change in beta heightens the need for attorneys and valuation experts to support their estimate of beta with credible expert analysis.

The Issue With Beta Exposed

Beta is a critical component used by valuation experts when determining the discount rate in valuation and damages. Even small changes in betas can cause large changes in the discount rate and, consequently, can cause large changes in the valuation or damages conclusion.

Because beta is not directly observable, experts commonly estimate beta using historical data. While there is no consensus on how much historical data to incorporate in estimating beta, they are commonly estimated using five years of monthly returns, two years of weekly returns, and in some cases using one to two years of daily returns. How much historical data is used can impact the effect that the COVID-19-related price volatility has on the estimated beta.

To illustrate the impact the COVID-19 crisis is having on betas, we estimated monthly, weekly and daily betas for each of the members of the S&P 500 as of Feb. 19 and again on July 31.[1] On Feb. 19, the S&P 500 Index peaked at a historic high of 3,386.15. Between Feb. 19 and July 31, the S&P 500 Index fell 34% to 2,237.40 on March 23 before rallying 46% to reach 3,271.12 on July 31. We refer to this period of Feb. 19 to July 31 as the COVID-19 era. Betas estimated as of Feb. 19 are labeled pre-COVID-19 beta. Betas estimated as of July 31 are labeled COVID-19 betas.

We found that betas estimated using the COVID-19 era data have changed relative to betas estimated prior to COVID-19 regardless of the sampling frequency used. For example, 53% to 60% of the companies listed in the S&P 500 Index experienced an increase in beta when we incorporated the COVID-19 era data into the sample period.[2] Conversely, 40% to 54% of betas decreased or stayed the same.

Next, we used a commonly accepted test to understand whether these documented changes were meaningful in a statistical sense. Our research indicates that the outcome of these tests can vary depending on the sampling frequency chosen by the expert. Betas estimated using monthly data are less likely to show evidence of a change compared to daily data. This result is intuitive, because the impact of the COVID-19 era data in the monthly data is limited to five out of 60 or 8% data points whereas the COVID-19 era data impacts 46% of the data in the one-year daily regression.

We also examined the potential impact of these changing betas on valuations to illustrate the challenges facing experts performing valuation impacted by the COVID-19 era data. We performed discounted cash flow valuations on each of the members of the S&P 500 as July 31.[3] We found that valuations estimated using the COVID-19 and pre-COVID-19 data differ, sometimes dramatically, regardless of whether one uses a monthly, weekly or daily sampling frequency to estimate beta.

For example, using monthly data to estimate betas, we found that the COVID-19 beta valuation was at least 16% larger or at least 14% smaller than the pre-COVID-19 beta valuation in more than half of the firms. For daily betas, the COVID-19 beta valuation was at least 19% larger or at least 22% smaller than the pre-COVID-19 beta valuation for more than half of the firms. That is, the choice of COVID-19 or pre-COVID-19 beta results in a swing in the discounted cash flow valuation of about 15% or more in roughly half of the firms on the S&P 500 Index.

The Challenges Facing Attorneys and Experts

Ultimately, the question facing experts is: "Should I incorporate this changed beta into my valuation?" The challenge facing valuation experts is that there may not be a one-size-fits-all answer to this question.

To illustrate the challenge facing experts, we compared our discounted cash flow valuations as of July 31 using pre-COVID-19 beta and COVID-19 beta for firms listed on the S&P 500 Index to their actual closing stock price on July 31. We found that discounted cash flow valuation using COVID-19 beta resulted in estimate of stock price that was closer to the company's actual stock for the typical stock.

For example, using monthly beta, the median pricing error (the percentage difference between the July 31 discounted cash flow implied stock price and the exchange reported closing stock price on July 31) was 5% across all firms when using COVID-19 beta and 12% when using the pre-COVID-19 beta. The median pricing error from our weekly regression betas was 0% using the COVID-19 beta and 13% using the pre-COVID-19 beta. The median pricing error of using daily betas equaled approximately 10% using either the COVID-19 or pre-COVID-19 beta.

Despite this lower pricing error for the typical stock, the individual firm by firm results varied greatly. For example, we found that the pre-COVID-19 beta produced a discounted cash flow valuation that was closer to the actual stock price than the COVID-19 beta in 45% of the firms when we estimated beta using monthly data. Using daily data, 36% of firms had discounted cash flow valuations closer to their actual stock prices using pre-COVID-19 betas.

This variation in the ability of pre-COVID-19 or COVID-19 betas to explain current stock prices suggests that there is not likely a one-size-fits-all solution to the question of whether to use the pre-COVID-19 or COVID-19 betas in valuation.

While we are unaware of any commonly used bright-line test to make such a determination, the peer-reviewed literature has examined several techniques that may be useful for making such a determination. For example, rather than relying on historical measures of volatility, some have proposed using forward-looking measures of volatility extrapolated from option prices.

In 1983, Dan W. French, John C. Groth and James W. Kolari proposed using option prices to incorporate a forward-looking volatility component into beta.[4] In 2007, Peter Christoffersen and Kris Jacobs extended that framework to include a forward-looking correlation and volatility component using option prices.[5] These forward-looking betas use information embedded in option prices to estimate beta instead of using the historical stock price history.

In 2013, Rainer Baule, Olaf Korn and Sven Sassning found that the information embedded in option prices can provide a better estimate on average beta in the future than can estimated betas using a limited sample of just 19 stock. However, results varied stock by stock.

Alternatively, experts may attempt to develop a forward-looking estimate of beta by explicitly estimating beta in a way that incorporates the changing volatility experienced in markets into the estimation process.

For example, Tim Bollerslev, Robert Engle and Jeffrey Wooldridge in 1988 derived a way for beta to change in the estimation sample period based on observed changes in volatility using historical data.[6] In 2009, Turan G. Bali, Nusret Cakici and Yi Tang found that these conditional beta models, commonly referred to as GARCH betas, can help to explain firm returns as predicted under the capital asset pricing model.[7] However, Fabian Hollstein, Marcel Prokopczuk in 2015 found that GARCH betas can produce inferior estimates of beta across several dimensions relative to simple estimated betas using historical price data found in this paper.

While informative, this literature on beta does not explicitly examine the information content in different beta estimates (historical betas, forward-looking betas or GARCH betas) in markets experiencing large swings in prices and dynamically changing volatility. We are currently looking into this important question in our research. In the meantime, we caution experts and litigants from arguing that their method for estimating beta has been commonly accepted as the best method. At present, we know of no authoritative source that permits this conclusion for all stocks.

Additional sources of market information may be useful in helping an expert determine which beta was most likely used by market participants. Analyst reports can allow experts to consider multiple pieces of information which when combined contribute to the total mix of information available about a company. For example, analyst forecast of cash flow can be used to control for the change in expected cash flows caused by COVID-19.[8] Evidence that actual market participants incorporated a changed beta may provide a reliable indication of a changed beta when examined in the total mix of information.


When ignored, the credibility of the valuation expert's analysis could be called into question by the finder-of-fact. Courts have shown a willingness to dig into the details of beta estimates to prod the credibility of experts, as seen in the Delaware Chancery Court's 2010 decision in Global GT LP and Global GT Ltd. v. Golden Telecom Inc.:

Both experts are well qualified generally in the literature of valuation. ...

As in the prior debate, [petitioner's expert] claims that he is using the best forward-looking, academically and professionally sound approach while [the respondent's expert] is using a backward-looking, outdated approach. Again, the petitioners overstate their case and, in this instance, also fail to put forward reliable academic and professional support for their position. ...

This battle of the experts is one that I [the finder-of-fact] am poorly positioned to resolve, and it appears unlikely that a finance professor would fare any better. Even after asking the parties to go back and submit relevant literature on beta, and even after doing an independent review, I admit to finding no literature that sheds reliable light on this question of whether to use a historical or the supposedly forward-looking Barra beta.[9]

In the end, this battle of the experts may come down to who is most credible. We argue that credibility can be established by demonstrating a persuasive argument for an expert's choice of beta. Experts risk losing the battle for credibility without this persuasion, even if their choice of beta was reasonably informed.

Andrew Roper, Ph.D., is the CEO. and founder of Catalyst Economic Consulting LLC.

Clifford Ang is a senior vice president at Compass Lexecon.

The opinions expressed are those of the author(s) and do not necessarily reflect the views of the firm, its clients, or Portfolio Media Inc., or any of its or their respective affiliates. This article is for general information purposes and is not intended to be and should not be taken as legal advice. 

[1] S&P CapitalIQ reports there were 505 stocks in the S&P 500 Index as of 8/1/2020. We eliminated 140 stocks from our analysis because (1) CapitalIQ reported no available consensus analyst forecast of positive levered free cash flows for FY2020 to FY2029 or (2) CapitalIQ reported an estimated Beta outside the range 0.20 to 2.00.

[2] Using monthly data, the Pre-COVID-19 Beta was larger than the COVID-19 Beta in 53% of the 365 firms examined. The Pre-COVID-19 Beta was smaller in the remaining 47%. Using weekly data, the Pre-COVID-19 Beta was larger in 60% and smaller in 40%. Using daily data, the Pre-COVID-19 Beta was larger in 56% and smaller or equal in 54%.

[3] The purpose of these valuations is not to give our expert estimate of the fair value of each company but instead to illustrate how the disparity in Betas can result in large swings in valuations.

[4] French, Dan, John Groth, and James Kolari (1983), "Current Investor Expectations and Better Betas", The Journal of Portfolio Management, January 1983, pp. 12-17.

[5] Christoffersen, Peter and Kris Jacobs (2007), "Forward-Looking Betas", CREATES Research Paper 2007.

[6] Bollerslev, Tim, Engle, Robert and Wooldridge, Jeffrey, (1988), A Capital Asset Pricing Model with Time-Varying Covariances, Journal of Political Economy, 96, issue 1, p. 116-31.

[7] Bali, Turan G., Nusret Cakici, and Yi Tang. "The Conditional Beta and the Cross-Section of Expected Returns." Financial Management 38, no. 1 (2009): 103-37.

[8] See, for example, Landier, Augustin and David Thesmar (2020), "Earning Expectations in the COVID Crisis", National Bureau of Economic Research Working Paper 27160, May 2020. 

[9] Opinion of Vice Chancellor Strine dated April 23, 2010 in the Matter of GLOBAL GT LP and GLOBAL GT LTD vs GOLDEN TELCOM, INC, C.A. No. 3698-V accessed at Expert names removed as they are not relevant to the analysis.

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