FASB rule change sets off
quest for a better valuation model
» Overstating Value
» Pension Points
Even in the midst of the pension funding crisis, the
actuarial sciences have often seemed to be relegated to the
nether reaches of developing workable solutions. However,
recent directives on stock option expensing from the
Financial Accounting Standards Board (FASB) may bring a new
luster to that expertise.
In a nutshell, FASB's March 2004 ruling said that
all forms of share-based payments to employees would be
treated the same as other forms of compensation by
recognizing the related cost in the income statement (see
"
Out of
Options
," April 2005). The expense of the award generally
would be measured at fair value at the grant date. Then, in
mid-December 2004, any hope of a stay of implementation was
dashed, when FASB announced a new 295-page Statement No.
123. Just as important, FASB's announcement also put a
definitive date on the implementation of the new rule.
Public entities (other than those filing as small business
issuers) will be required to apply Statement 123 as of the
first interim or annual reporting period that begins after
June 15, 2005.
To reach this measurement, FASB will require that the
fair value of share-based options be valued using a
technique that takes into account "various
factors," including:
• exercise price of the option
• expected term of the option
• current price of the underlying share
• expected volatility of the underlying share price
• expected dividends on the underlying share
• risk-free interest rate.
While FASB took no official stance on the appropriate
model to be used for valuation, it seems apparent that the
accounting rulemaker would prefer that public companies use
a binomial model, such as a lattice-based valuation method,
rather than the model typically used to value traded stock
options, a close-form model, such as Black-Scholes-Merton,
which uses a single weighted average expected option term.
Aon Consulting Senior Vice President Phil Peterson says
companies would have to produce a good reason to continue
using Black-Scholes-Merton in lieu of a lattice approach.
"Companies will still have the option to continue to use
Black-Scholes but, where it is at all possible, companies
are going to be directed to use a lattice-based model."
Put in simpler terms, FASB believes the result of an
expense calculated with a lattice model that incorporates
an optionee's expected exercise and expected
post-vesting employment termination behavior renders a more
accurate compensation expense result. However, recognizing
that some firms may have trouble coming up with one or two
variables necessary to properly utilize the preferred
lattice-based model, it allowed both models.
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Overstating Value
In fact, a Towers Perrin study done in 2003 and reprised
in 2004 showed that the Black-Scholes model can overstate
the fair value of employee stock options by 10% to 50%, by
ignoring or misapplying the following criteria:
• Nontransferability—The basic model was designed to
estimate the value of transferable stock options, which
have a greater value than employee stock options, because
transferable options can be bought and sold on the open
market.
• Fixed estimate of volatility and risk-free
rate—Black-Scholes requires a single input for the expected
volatility and risk-free rate during the life of the
option, which are unrealistic expectations when applied to
real-life market conditions.
• Single estimate for the life of the
option—-Black-Scholes requires a single estimate for the
life of an option, even though it is more realistic to
expect the actual exercise to happen at any point between
the option's vested date and the end of the option's
contractual term.
With the lattice-based model, more assumptions may be
incorporated, plus the formula is customizable to the firm
issuing the stock options. Still, it is one thing to tout
the benefits of a lattice-based model, another altogether
to actually find one that is both practical and applicable
to an individual situation. One such model has been
developed by Aon Consulting. As explained by Vice
President, Compensation Consulting, Terry Adamson and his
colleague Peterson, to derive their proprietary model, Aon
started with the generalized American binomial model, which
requires the following inputs:
• Stock price at grant
• Stock price at a particular node
• Exercise price
• Expected life of the option
• Continuously compounded risk-free rate of return over
the expected life of the option
• Continuously compounded expected continuous rate of
dividend yield
• Volatility of the stock
With the foundation laid, Aon continued to build,
pulling constructs from the Cox, Ross, Rubinstein model—a
binomial option pricing method commonly used to price all
manner of complex options due to its flexibility—that
includes the following additional calculations:
• Probability of an upward price movement
• Magnitude of upward price movement
• Probability of a downward price movement
• Magnitude of downward price movement
Lattice-based models do not require many more data
inputs than Black-Scholes. The main difference lies in the
accounting for the possibility of option exercises, a
variable the previous Black-Scholes formula, designed for
other purposes altogether, did not accommodate.
To fully illustrate this variable in the lattice model,
Aon's model takes some probability of exercise at each
"node" along the way. Simply stated, at each measurable
point in time, there are exactly two actions that can take
place—the stock price moves either up or down. From this,
actuaries can determine probabilities of exercise at each
node. To determine these probabilities, Adamson and his
team built a matrix of probabilities for option exercise
across a 10-year term, producing 120 measurement periods.
With these basic premises, Aon went on to construct its Aon
Consulting Actuarial Binomial Model, which takes even more
variables into consideration (remember the binomial model
is infinitely flexible):
• Current stock price relative to the strike price
• Time elapsed since vesting
• Time to expiration
• Risk tolerance of the option holder
• Wealth diversification of the option holder
• Turnover and other decrements affecting the employment
of the option holder
• Gender of the option holder
• Age of the option holder.
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Pension Points
Interestingly enough, Aon turned to another benefit
calculation to find the answer for its lattice model:
pension assumptions. When called upon to construct a
specific lattice-based model, Aon will ask to see the
company's pension plans (if applicable) to determine the
post-separation option exercises—-those exercises that
result from events such as termination, retirement, death,
or disability. Using the same expectations of a terminating
event from a pension plan as in stock options, Aon starts
layering active employment exercises onto that.
Even with rocket scientists and supercomputers, though,
the idea of active employment option exercise remains an
elusive one for practitioners. Adamson states, "There are
many variables and not enough data to understand active
employment exercises…yet." Hope springs eternal, though, as
the Aon team is taking this opportunity to develop standard
tables for voluntary exercises. "The goal is to have tables
for exercises during active employment similar to other
actuarial decrement tables used for pension plans."
For all their differences, the binomial and the
Black-Scholes models are still remarkably similar,
particularly when it comes to the single largest variable
driving valuation results: expected volatility, the
statistical measure of the amount by which a stock price is
expected to fluctuate during a period. "Volatility is the
most sensitive driver of these results," states
Adamson.
The reason for this is simple—FASB left a specific
approach for calculating volatility out of its official
guidance, leaving companies to their own devices on the
topic of volatility, so long as the company provides a
reasonable rationale for its calculations—and the proof is
in the fiscal pudding. In 2004, Aon prepared a valuation
report for a client, showing different levels of
expenditures based on a variety of assumptions using Aon's
proprietary binomial model. Part of this modeling required
different alternatives for volatility, measurements that
ranged from 45.25% (based on the long-term mean for the
company) to 23.41% (the implied volatility for a call
option found in the public marketplace). While this may not
be music to a compliance officer's ears, it illustrates
how, with expanded flexibility, a true binomial model can
produce compensation expenses lower than Black-Scholes.
With the impetus on employers to craft a workable
solution to the expensing dilemma, it is still surprisingly
difficult to get "inside" most lattice models. "Financial
statements are intended to be transparent. As actuaries, we
believe that these calculations need to be replicable by
other firms, and the only way to do that is to open up the
black box for the world," Adamson states.
Does the new valuation method mean the end of
Black-Scholes as we know it? Not quite, says Adamson, who
says Black-Scholes will continue to be used as an option
valuation tool only, instead of using it for financial
reporting purposes, plan sponsors now turn to Black-Scholes
as a way of determining the amount of options to grant.
"Black-Scholes is brilliant, and will always be the
quickest and most efficient tool for planning purposes,"
Adamson states. "When looking at alternative plan designs,
incremental changes in valuation on a Black-Scholes basis
will be comparable to incremental changes using a
binomial."
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