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The Holes in Black-Scholes

Valuing stock-option grants with Black-Scholes may cause some confusion on the income statement.
Tim Reason, CFO Magazine
March 1, 2003

Does the Black-Scholes option-pricing model — the most common method for valuing stock-option grants — accurately forecast how much an option will be worth? Not even close, says a study by Sibson Consulting. "Black-Scholes is not a good predictor of actual gains," says senior vice president Blair Jones, who managed the study.

Sibson tested a broad sample of 1,445 companies during six periods between 1972 and 2002. For each period, the average actual gains as a percent of Black-Scholes value ranged from 95 percent to 910 percent. Only 3 to 5 percent of stocks were within 90 to 110 percent of the price estimated by Black-Scholes.

Odds are high that public companies soon will be required to expense stock options, which generally means Black-Scholes estimates will appear as expenses on the income statement. (The alternative binomial model is rarely used, and so far, no one has figured out how to obtain market-based prices, which are preferred under the current accounting standard.) Both the Financial Accounting Standards Board and its overseas counterpart, the International Accounting Standards Board, are already considering expensing requirements that are likely to pass this year (see our February 2003 cover story "Questions of Value").

Jones is quick to note that FASB doesn't claim Black-Scholes actually predicts future gains — it's simply a way of reporting an estimated cost. But, she adds, "if this cost is going to be perceived as the actual cost to the company, it is somewhat misleading. I'm not sure the average analyst or investor makes the distinction about whether this is the actual economic cost to the company or not."

Companies should be careful how they portray Black-Scholes, says Jones, adding that they "probably shouldn't use it in their communications [with employees]."

Rarely Hitting the Mark

Percent of Black-Scholes estimates that hit an acceptable range. Actual gains were 90­-110% of the Black-Scholes estimated value. "Grant dates" are for hypothetical options exercised within seven years, if they were above water.
Source: Sibson

Grant datesPercent
Stable Markets
January 19734.0
January 19805.4
Declining Markets
January 19824.8
February 19955.6
Bull Markets
September 19804.3
November 19903.3