# Basics of Stock Options ## Definitions - Call option - Gives contract owner right to **purchase** one share of a company's stock, at a fixed strike price, before an expiration date - Put option - Gives contract owner right to **sell** one share of a company's stock, at a fixed strike price, before an expiration date - Exercising - Executing the contract by either: - (For calls) Buying a share at the strike price and then (usually) selling the share on the stock market, at market price. Pocketing the difference - (For puts) Buying a share off the stock market, at market price, and then immediately selling the share to the company at the strike price. Pocketing the difference >[!info] Employee stock options are **always** call options, because put options are betting *against* the growth of the company. ## Stock Option Valuation ### Intrinsic Value >[!info] The difference between the option's strike price and the stock price, if strike price $\gt$ stock price. If strike price is *below* stock price, intrinsic value is $0$ $ \max(0,SP-EP) $ Where: - $SP=$ Stock Price - $EP=$ Exercise/Strike Price ### Black-Scholes Value >[!info] Market value of stock options. It describes how rational (risk-neutral) diversified investors value tradable options. #### Formula: $ \begin{align} BS=&S\times N(d_1)-K\times e^{-rT}\times N(d_2) \\ &Where\\ d_1=&\frac{[\ln(\frac SK)+(r+\frac12\sigma^2)T]} {\sigma\sqrt T}\\ d_2=&d_1-\sigma\sqrt T \end{align} $ Variables: - $S=$ Stock price - $K=$ Exercise/Strike price - $r=$ Risk-free interest rate (Usually federal interest rate) - $T=$ Time to maturity - $\sigma=$ Volatility (Standard Deviation) of stock return - $N=$ Standard Normal cumulative distribution Black-Scholes value is **always** higher than intrinsic value # Employee Stock Options ## Characteristics Compared to Exchange-Traded Options - Vesting period (typically 3–5 years) - Employees cannot exercise the options during the vesting period - Not tradable - Employees cannot freely sell options on the open market - Forfeited if employee leaves - An employee loses the right to their options if they terminate employment Value of stock options to employees $\neq$ market traded options, because: - Employees are more likely to be risk-averse - Compensation options are not diversified - Compensation options are non-tradable - Compensation options are lost if the employee leaves the firm >[!info] Economic costs of options is extremely high, accounting cost of options was very low (and remains low). ### Why Give Employees Options - Financing - Cash that would have been given as a paycheck is freed for reinvestment - Sorting - Attract employees who are willing to take risk - Attract employees who are optimistic about the firm's success - Retention - Incentivizes retention during vesting period # Executive Compensation ## CEO Pay Debate Several views on executive pay - Principal-agent view - Rent-extraction view - Other views ### Principal-Agent View >[!info] Agency Theory >Agency theory is concerned about solving the agency problem that occurs when one party (the principal) delegates work to another (the agent), who performs that work. Agency theory focuses on how to use appropriate incentives to motivate the agent to act int eh best interest of the principal. Applied to modern corporations: - Firms are owned by shareholders - Shareholders delegate the task of operating the firm to the executives. - CEO is the "agent" of the "principals" shareholders. - If the executives' interests in the firm are not identical with those of the shareholders, this leads to an agency problem - Board of directors are elected by shareholders to monitor and compensate the CEO The goal of the shareholders is to maximize firm value. The shareholders task the board of directors with aligning the CEO's interests with those of the shareholders. This usually involves compensation that is heavily dependent on stock performance. #### Incentive Strength A measure of how strong an executive's incentives are relative to a metric. For stock price-based metric, this is usually measured by the payoff to the CEO when shareholder wealth increases by $1,000. $ \begin{align} &=\frac{$1000}{\text{Total shares outstanding}}\times \text{(Number of executive stock options)}\\ &=\frac{\text{Number of executive stock options}}{\text{Total shares outstanding}}\times{$1000} \end{align} $ Incentive strength for CEO pay has increased over time ### Rent-Extraction View The increased use of stock options in executive compensation is because of the stock market boom during the 1990's, and accounting advantage of using stock options. This would require: - CEO's to have undue influence over the board of directors - CEO's to have influence over the consulting firms used to set CEO pay - Shareholders to have little direct influence on pay-setting - CEO's to be paid for good "luck" and not for the effects of good performance This generally does not line up with reality ### Alternative Explanations ### Market Force - Increased competition for managerial talents - Those with the ability to properly manage a large company are extremely rare - Increased market valuation involves larger financial stakes - Larger company $=$ more money at play ### Compensation Disclosure & Wage Comparison - Everyone is above average - Not entirely sure what this is about ## Reforms Potential reforms to "fix" the CEO pay debate - Outside directors - Compensation committee - Better disclosure - Use of compensation consulting firms - Say-on-pay - Institutional investors