A StockOpter White Paper

This white paper explains the concept of volatility and why it is used in StockOpter.com (SO.com).  Selecting a reasonable and appropriate volatility input is paramount to properly estimating the Black-Scholes Value (BSV) and Time Value (TV) of an employee stock option.  It is also used in the estimation of an option holder’s Value-at-Risk (VaR).  Please visit the StockOpter University  for white papers on Black-Scholes, Time Value, VaR and a more detailed discussion on the concept of Stock Price Volatility.

What is volatility?

Volatility, as it is used in SO.com, is an estimate of the future variance from the mean return expected for the stock underlying the client’s employee stock options (ESOs). There is not a “correct” or “ideal” value for this input.  After all, the future price, and therefore volatility, of a stock cannot be known.  As a consequence, when setting up client data, the advisor must make an estimate of the expected future volatility that is appropriate for the stock in question.  Because this input is an estimate, having a reasonable methodology for selecting this input is extremely important.  For a more detailed discussion of how volatility is calculated, please review the introductory and advance sections of this white paper.  This executive summary will focus on the methodology for developing this estimate rather than the specific mathematics for how volatility is calculated.

As with developing any estimate, history can be quite informative.  Thus, a review of the stock’s historical volatility is an excellent starting point.  For example, if it can be determined that the historical volatility of ABC Corp stock has ranged between the 52-week-high of 80% and the 52-week-low of 30%, then a reasonable range of outcomes is established.  Because history is not necessarily indicative of the future, additional research may be appropriate.  This research may include a review of what the option trading markets expect for the near-term volatility of the stock.  This is indicated by the current implied volatility of the stock.  For example, if the current implied volatility for ABC Corp stock is 55%, one might conclude that the market is expecting “average” volatility in the forthcoming period, based on the historical range of 30%-80%.  While this might be an overly simplistic conclusion, it does provide a framework for selecting an appropriate estimate to be used in the SO.com model.  To view this information for a publicly traded stock,  visit www.ivolatility.com and enter the trading symbol of the stock you wish to review (a subscription may be required).  Clicking the “Volatility Chart” provides a visual depiction of both the historical and the implied volatility for the past year.  Viewing this chart is a good way to see the range and to select an appropriate value for SO.com.

Implied volatility will not be available if there are no marketable stock options traded for the stock in question.  However, historical volatility information is usually available for guidance in selecting an appropriate estimate for the future volatility.  In all cases, the advisor should consider including the client in this part of the planning process.  After all, the client’s expectations will be a significant factor in the perceived value of their ESOs.

Another source for determing volatility is the company’s SEC filings since they are now reqired to expense their employee stock options.  Nearly all companies use the Black Scholes formula or a derivation of it which includes a volatility assumption.  So the company’s annual report and other filings will contain the volatility assumption they used.  Company SEC filings can be  found at finance.yahoo.com.

Volatility and the Black-Scholes value:

It is important to bear in mind how this input will affect a SO.com analysis. This is best illustrated through the use of an example.  Sally Sample works for a major US beverage company.  She has ESOs with vested in-the-money value (ITMV) of approximately \$1,690,000.  If a volatility input of 32% is used, the Black-Scholes value (BSV) of these same vested ESOs would be approximately \$1,810,000.  If the volatility input were changed to 85%, the BSV would become \$2,200,000.  As is seen in this example, the volatility input used can have a significant impact on the BSV.  The importance of the BSV is that it provides the advisor and the client with an estimate of the Time Value (TV) remaining in the option.  TV is the amount by which the BSV exceeds the ITMV and is an important criterion in the decision to exercise options.  Therefore, selecting a reasonable and appropriate volatility input is paramount to properly estimating the TV component for the ESO holder.

Volatility and Value-at-Risk (VaR):

When demonstrating VaR to a client, the advisor must remember that volatility is a key component in this calculation.  For example, if we assume the same facts as above, when the volatility is 32%, the VaR of Sally Samples entire company holdings (vested options and stock held) is approximately \$770,000 out of total value of \$4,000,000.  If the volatility is increased to 85%, the VaR becomes \$1,850,000 out of total value of \$4,000,000.  Again, the volatility input used, has a dramatic impact on the estimated outcome.

Conclusion:

Selecting a volatility input is more art than science.  It is a function of the client’s expectations and insights and, the advisor’s intuition and experience.  Most importantly, educating the client on the impact of this input and demonstrating the potential impacts of various inputs is the key to establishing this important input and using StockOpter.com effectively.