1. Insights
from Human Resource Services
www.pwc.com
PwC study on estimating stock
compensation volatility
December 15, 2014
In brief
This Insight describes the findings of a recent PwC study on stock compensation volatility, and the
potential implications for companies that develop volatility estimates for use in stock compensation
valuations. Our study found that stock compensation volatility estimates are predicted just as well by
using historical volatility as by blending historical with implied volatility. Further, longer-term windows
of up to 15 years were shown to outperform the comparable-window forecasts typically in use.
In detail
Background
Fair value measurements
involving modelling are
required both for employee
stock options and performance
share plans (those with TSR or
other ‘market condition’
targets). The most important
and judgmental assumption in
valuing these types of awards is
the volatility of stock prices for
the company making the grants.
The most common source for
public companies in estimating
volatility is their own stock price
history. This is usually analyzed
over a historical window equal
to the forecast period (the
expected term for options, or
the performance period for TSR
plans). However, a growing
number of companies have been
using forecasts based on both
historical price data and
‘implied volatility’ data, typically
blended with equal weights.
Implied volatility is determined
using the price of publicly
traded options — so, it’s a
‘market-generated’ forecast of
volatility. Some believe it to be a
superior measure since it
theoretically incorporates all
available market information.
While there is broad consensus
among academic researchers
that implied volatility contains
useful information, at least for
shorter-term volatility forecasts,
differing approaches have been
published on the question of
how to best use implied
volatility.
The SEC staff also notes that
‘implied volatility can be useful
in estimating expected volatility
because it is generally reflective
of both historical volatility and
expectations of how future
volatility will differ from
historical volatility.’1 The SEC
staff goes on to say ‘a company
with actively traded
options…generally could place
greater (or even exclusive)
reliance on implied volatility.’
New volatility study
PwC recently completed a study
to examine the use of stock
compensation volatility
estimates.2 The study was based
on historical and implied
volatility data for 189 large
public companies that were part
of the S&P 100 index during the
period 1990 through 2009.
Volatility data over various
windows from 1980 through
2009 was analyzed.
Study results showed two major
findings.
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Length of historical windows
The first finding was that volatility
calculated over a longer-term
historical window of up to fifteen
years was more accurate than shorter
windows in predicting volatility over
the next five to seven years. That is,
accuracy of volatility predictions was
significantly higher for these longer-
term forecasts, when compared to
using the ‘comparable window’
forecasts going back over five- or
seven-year windows, as companies
commonly do in calculating historical
volatility for share-based
compensation accounting today.
For companies with limited public
history (e.g., for a company with ten
years’ history), our results suggested
that lengthening the look-back from a
comparable window (five- or seven-
years) to the full available window up
to 15 years still improved forecast
accuracy. On the other hand, we found
that using even longer data-windows
than 15 years, over periods as long as
available up to 30 years, did not
appear to improve accuracy beyond
the use of data up to 15 years old.
FASB guidance directs companies in
setting their volatility assumptions to
consider historical volatility over ‘the
most recent period generally
commensurate with’ an option’s
expected or contractual term (or, by
extension, with the performance
period associated with a TSR-type
award), along with other factors,
including implied volatility.3
While common practice is accordingly
to use a look-back period roughly
equal to the forecast period, the SEC
staff has acknowledged that use of
longer periods is acceptable. The SEC
staff notes that a company ‘could
utilize a period of historical data
longer than the expected or
contractual term…if it reasonably
believes the additional historical
information will improve the
estimate.’4
Our study shows that use of longer
periods will likely improve the
estimate for most large public
companies, and possibly for other
companies as well.
Historical versus implied
Our second finding is that use of
implied volatility did not significantly
improve forecasts over five- to seven-
year horizons. And somewhat
surprisingly, applying different
weightings on the historical and
implied volatility components used in
blended forecasts also didn’t
significantly impact forecasting
performance.
A blend of about 65% historical and
35% implied (again, basing the
historical component on the longest
available window up to 15 years)
slightly outperformed all the other
forecasts tested; however, the
improvement over forecasts based on
‘longest available’ historical data alone
was not statistically significant.
Observation
There were indications of problems
with implied volatility when used as a
forecast in our dataset, which were
not present when considering
historical data alone. Specifically,
patterns of forecasting errors over
time were more apparent when
analyzing implied volatility forecasts
than when using historical volatility
forecasts. These patterns can be
interpreted as ‘forecast bias.’ See our
full technical report for details.
Our study did not provide conclusive
evidence as to whether implied
volatility should be used or
discontinued in order to improve
accuracy of companies’ volatility
estimates in valuing stock
compensation.
However, in view of the lack of
significant improvements in accuracy
given blended forecasts, as well as the
risk of introducing greater forecast
bias, companies that use implied
volatility might consider applying a
minority weighting (for example, 75%
historical / 25% implied), in
preference to the common practice
today of using equally-weighted (50%
historical / 50% implied) forecasts.
Putting the findings to use
Our principal study finding was that
historical forecasts based on longer
windows, up to 15 years,
outperformed comparable-window or
shorter forecasts. One way for
companies to use this finding might
therefore be to incorporate a longer
window in estimating historical
volatility.
There is no specific prohibition in
FASB guidance of looking backward
beyond the forecast period (i.e., over a
longer historical window), and as
noted, the SEC staff has explicitly
approved it in circumstances where
the company reasonably expects it to
improve the estimate.
Observation
It might not be always appropriate to
use older data, based on individual
facts and circumstances. For
example, if a company had a
historical volatility at a given level
over the most recent period (say, five
years), and there were business-
specific reasons why volatility may
have differed over the period between
five and 15 years ago, as compared to
volatility over the past five years, the
company should likely not use the
older data in a forward-looking
forecast.
Another alternative approach
companies might consider is using a
blend of comparable-window
historical volatility (i.e., five-year
volatility for an award with a five-year
expected term) and longer-term
volatility (up to 15 years). Implied
volatility, if available and significantly
different from historical volatility,
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might also be incorporated with a
minority weighting.
This alternative approach above of
combining comparable-window and
long-term historical volatilities could
be interpreted as a ‘mean reversion’
technique, relying on the well-
documented phenomenon of mean
reversion, or the tendency of volatility
to return to a long-run average.
Observation
While FASB guidance refers to mean
reversion, it is only a shorter-term
form of mean reversion that is
intended, since the FASB guidance
specifically refers to subdividing the
historical window equal in length to
the expected or the contractual term.
The argument needed to support
using a blend of 15-year and
comparable-window volatility would
involve a longer-term form of mean
reversion. In other words, while the
FASB has referred to models
involving reversion of volatility to
average levels over historical
intervals stretching back five to ten
years, our research suggests possible
mean reversion toward even longer-
term average levels.
Finally, companies looking to our
findings in supporting volatility
development methods should bear in
mind that the population for our study
was composed only of companies
included in the S&P 100 index over
the past 30 years, selected from the
largest U.S. public companies with
listed options. Companies that do not
meet these criteria or that have
limited public history will need to
evaluate the degree to which our
findings may be expected to apply to
them.
The takeaway
Companies should consider the use of
longer-term historical data (up to 15-
year windows) in developing their
volatility forecasts. Longer-term
volatility could also be averaged with
comparable-window volatility, and
possibly with implied volatility, to
contribute as well to a blended
volatility forecast.
We have worked with many
companies to provide guidance in
setting policies for valuing stock based
compensation, as well as on related
issues such as compensation plan
design and general compensation and
benefits accounting matters.
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1 SAB Topic 14, Section D.1, Q&A #1. The SEC staff's guidance outlines certain factors that companies should consider
when evaluating the extent of its reliance on the implied volatility derived from traded options, including the volume of
market activity, the ability to synchronize the variables used to derive implied volatility, the similarity of the exercise
prices, and the similarity of length of terms.
2 Results of the study are available on-line (a full technical report is posted at
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2046192).
3 ASC 718-10-55-37a
4 SAB Topic 14, Section D.1, Q&A #2
5 ASC 718-10-55-37a
