Hvass Laboratories
Blog on Investment Finance

All this was made by a single person without any grant-money.
If you find it useful then please donate securely using PayPal.
Even a few dollars are appreciated. Thanks!


Investing
Books
Services
Blog
S&P 500

Video Talks
Investing
Deep Learning
Optimization

Source Code
GitHub
SwarmOps
RandomOps
ArrayOps
NeuralOps

Author
Publications
Thesis
Citations
Schoolwork
Contact

Hvass Labs

The Deception of Stock Options

by Magnus Erik Hvass Pedersen, April 9, 2014

Stock options are granted to employees as part of their compensation in an effort to align the interests of employees and shareholders.

But if the stock is underpriced when the options are granted and the stock is overpriced when the options are exercised, then the employee is overcompensated at the expense of shareholders. A recent example of this occurred with the company Best Buy.


Market-Cap: September 2011-2012

In September 2011 the company's market-cap was about USD 9b (market-cap = 362m shares x USD 25 per share). In September 2012 the company's market-cap had decreased to about USD 6b (337m shares x USD 18 per share). This was a decrease of USD 3b or about 33%.

Stock Options

A new CEO was appointed in September 2012 and was granted 700,935 stock options with an exercise price of USD 18.02 as part of the compensation package.

A year after, on September 6, 2013, the CEO exercised 350,467 options (the maximum allowed at that time) and sold the shares at USD 37.01 for a profit of USD 18.99 per share and almost USD 6.7m in total.

A new CFO (who also has other roles in the company) was granted 383,142 stock options on December 10, 2012 with an exercise price of USD 12.39.

Market-Cap: September 2012-2013

In September 2012 the company's market-cap was around USD 6b. In September 2013 the market-cap had increased to almost USD 13b.

But in the 12 months ending February 1, 2014 the company's net income was only USD 532m while Free Cash Flow was USD 753m (FCF, defined here as Operating Cash Flow minus Capital Expenditures plus proceeds from asset sales).

So the increase in market-cap of USD 7b was clearly due to a change in perceived value of the company amongst market participants, rather than an actual increase in intrinsic value which could at most be the FCF net of dividends and share buybacks.

Market-Cap: January 2014

After the company released an earnings report on January 17, 2014, the company's share-price decreased 33% from USD 37 to USD 25, and the market-cap went from around USD 13b (347m shares x USD 37) to below USD 9b.

Recall that the CEO had exercised options at USD 37 per share only months before this large decrease in share price.

Accounting Value

Accounting for stock option compensation is complicated and highly inaccurate. It is based on an assumption that the company's stock price evolves randomly according to the historical volatility and performance of the stock. A popular formula for estimating the value of a stock option is known as the Black-Scholes formula.

The Black-Scholes estimate of "fair value" of the CEO's 700,935 stock options was USD 3.75m on the date of grant. The exercise price was USD 18 but a year later the stock price was USD 37. So the options were actually worth more than USD 13m which is 355% of the Black-Scholes estimate of "fair value".

The Black-Scholes estimate of "fair value" of the CFO's 383,142 stock options was USD 1.3m on the date of grant. The exercise price was USD 12.39 but a year later the stock-price was USD 41.50. So the stock options were actually worth more than USD 11m which is about 836% of the Black-Scholes estimate of "fair value".

Not all these stock options were exercisable after one year but the conclusion still holds: Black-Scholes is grossly incorrect at estimating the option value when the underlying stocks are greatly mispriced.

Intrinsic Value

To determine if a stock is mispriced we must know the so-called intrinsic value which is the present value of future earnings that can be paid out as dividends. As the future earnings are uncertain we cannot determine the intrinsic value with certainty but we can estimate it in different ways, e.g. by assuming past earnings will continue in the future.

During 2005-2011 the average net income was around USD 1.2b per year. Assuming this average continues indefinitely in the future and the discount rate is 10% gives a present value of USD 12b (USD 1.2b divided by 10%), and dividing by 337m shares gives a present value of USD 36 per share.

However, in 2012 the company reported a net loss of USD (1.2b) with positive FCF of about USD 1b (calculated somewhat differently than above because of a divestment). In 2013 the company reported a net loss of USD (441m) with positive FCF of USD 743m. So perhaps the estimate of present value was too high as it assumed average earnings of USD 1.2b.

The market was evidently also unsure of the long-term value of the company's shares as they were trading below USD 12 for a while (market-cap around USD 4b). The CFO was awarded stock options around this time at an exercise price of USD 12.39. If the intrinsic share value was really higher than this, then the difference between the exercise price and intrinsic value would constitute overcompensation as the value was not added by the CFO but due to a temporary mispricing of the stock.

For example, if the intrinsic value was USD 36 per share as estimated above, then the CFO would be awarded USD 9m in undue compensation ((USD 36 - USD 12.39) x 383,142 options). A more conservative estimate of intrinsic value of USD 25 per share would still give a large undue compensation of almost USD 5m, which far exceeds the compensation estimate of USD 1.3m calculated with the Black-Scholes formula.

Other Stock Grants

Furthermore, the new CEO was also granted 499,446 shares and the new CFO was granted 107,614 shares, subject to certain restrictions. These shares were believed to have a value of USD 9m and USD 1.3m, respectively, based on the low share prices at the time of grant. But the actual values were far greater. After a year of the grant date, the CEO's shares were worth almost USD 18m and the CFO's shares were worth almost USD 4.5m.

Conclusion

The Black-Scholes formula for estimating the "fair value" of options is grossly inaccurate and stock options can severely over- or under-compensate employees for their work. Stock options misalign the interests of shareholders and employees. Stock grants have similar problems.

Data Sources


Hvass Laboratories