The impact of the market portfolio on the valuation,incentives and optimality of executive stock options

This paper examines the effect on valuation and incentives of allowing executives receiving options to trade on the market portfolio. We propose a continuous time utility maximization model to value stock and option compensation from the executive's perspective. The executive may invest non-option wealth in the market and riskless asset but not in the company stock itself, leaving them subject to firm-specific risk for incentive?purposes. Since the executive is risk averse, this unhedgeable firm risk leads them to place less value on the options than their cost to the company.

By distinguishing between these two types of risks, we are able to examine the effect of stock volatility, firm-specific risk and market risk on the value to the executive. In particular, options do not give incentive to increase total risk, but rather to increase the proportion of market relative to firm-specific risk, so executives prefer high beta companies. The paper also examines the relationship between risk and incentives, and finds firm-specific risk decreases incentives whilst market risk may decrease incentives depending on other parameters. The model supports the use of stock rather than options if the company can adjust cash pay when granting stock-based compensation.     

SIX CHALLENGES IN DESIGNING EQUITY-BASED PAY

The past two decades have seen a dramatic increase in the equitybased pay of U.S. corporate executives, an increase that has been driven almost entirely by the explosion of stock option grants. When properly designed, equity‐based pay can raise corporate productivity and shareholder value by helping companies attract, motivate, and retain talented managers. But there are good reasons to question whether the current forms of U.S. equity pay are optimal. In many cases, substantial stock and option payoffs to top executives–particularly those who cashed out much of their holdings near the top of the market–appear to have come at the expense of their shareholders, generating considerable skepticism about not just executive pay practices, but the overall quality of U.S. corporate governance. At the same time, many companies that have experienced sharp stock price declines are now struggling with the problem of retaining employees holding lots of deep‐underwater options. This article discusses the design of equity‐based pay plans that aim to motivate sustainable, or long‐run, value creation. As a first step, the author recommends the use of longer vesting periods and other requirements on executive stock and option holdings, both to limit managers' ability to “time” the market and to reduce their incentives to take shortsighted actions that increase near‐term earnings at the expense of longer‐term cash flow. Besides requiring “more permanent” holdings, the author also proposes a change in how stock options are issued. In place of popular “fixed value” plans that adjust the number of options awarded each year to reflect changes in the share price (and that effectively reward management for poor performance by granting more options when the price falls, and fewer when it rises), the author recommends the use of “fixed number” plans that avoid this unintended distortion of incentives. As the author also notes, there is considerable confusion about the real economic cost of options relative to stock. Part of the confusion stems, of course, from current GAAP accounting, which allows companies to report the issuance of at‐the‐money options as costless and so creates a bias against stock and other forms of compensation. But, coming on top of the “opportunity cost” of executive stock options to the company's shareholders, there is another, potentially significant cost of options (and, to a lesser extent, stock) that arises from the propensity of executives and employees to place a lower value on company stock and options than well‐diversified outside investors. The author's conclusion is that grants of (slow‐vesting) stock are likely to have at least three significant advantages over employee stock options:

• ? they are more highly valued by executives and employees (per dollar of cost to shareholders);
• ? they continue to provide reasonably strong ownership incentives and retention power, regardless of whether the stock price rises or falls, because they don't go underwater; and
• ? the value of such grants is much more transparent to stockholders, employees, and the press.

     

IRC Section 162(m) and the law of unintended consequences

In 1993, Section 162(m) of the U.S. Internal Revenue Code was passed into law with the intent to reign in outsized executive compensation by eliminating the tax-deductibility of executive compensation above $1 million unless the excess compensation was performance-based. An unintended consequence of the legislation was that executives' total compensation actually increased in the post-1993 period, largely due to a dramatic increase in employee stock options. Employee stock options have unintended consequences of their own. The economic value of stock options may be influenced by executive decision-making when the options are valued using the Black-Scholes model or some variant thereof. Our findings suggests an unintended consequence that executives used their discretion to positively impact the performance-based component of their compensation through actions increasing share price volatility and reducing dividend yields, assumptions implicit in option valuation models.     

Dilution,anti-dilution and corporate positions in options on the company's own stocks

Abstract

In this paper, we analyse options that are bought or sold by the company on whose stocks these options are written, leading to dilution and anti-dilution effects. We provide valuation equations for the European versions of such options, and discuss conditions for existence and uniqueness of their prices. Option prices to be paid or received for these options by the company are shown to be different from those that apply for standard options (which are bought and sold by outside investors). Since the options become part of the company's assets/liabilities, the stochastic process followed by the stock price changes. We demonstrate how the new stock price process can be derived, and discuss economic implications of our results. Numerical examples illustrate our findings.     

Optimal exercise of executive stock options

Valuing executive stock options is a challenging problem, because the standard risk-neutral valuation of those options is not appropriate; the executive is not allowed to trade the stock of the firm, so is not operating in a complete market. As this paper shows, an executive holding many American-style call options on his firm’s stock will optimally exercise the options bit by bit, whereas a risk-neutral valuation of the options would assume that all are exercised at the same time. Comparative statics of the optimal exercise policy show many surprising features.      

Managerial Risk-Taking Incentives and Executive Stock Option Repricing: A Study of US Casino Executives

I examine the relation between managerial incentives from holdings of company stock and options and stock option repricing. Because options provide incentives to increase both risk and stock price, firms must realize that as options go underwater, executives might face incentives to invest in risky, negative NPV projects. Repricing may alleviate such incentives. I examine repricing activity by firms in the US gaming industry and find that risk-taking incentives from options are positively related to the incidence of executive option repricing. The results support the hypothesis that repricing assists firms in alleviating excessive risk-taking incentives of senior management.     

Fair Terms and Fair Pricing for Multiple Warrant Issues

Abstract

Some firms utilize one or more tranches of warrant issues to supplement their capital base. Unlike exchange-traded options, the exercise of warrants requires the issuance of stock by the company, resulting in a form of dilution. Some previous studies of warrant valuation relied on “the value of the firm,” which is nonobservable, making it difficult to apply the corresponding valuation formula. This paper derives closed-form formulas to value single and multiple tranches of warrants based on the underlying stock price, its volatility, and other known parameter values. The paper first establishes the equivalence of the Black-Scholes formula for both call options and warrants in the case of a single tranche. Thereafter, it considers the impact on the value of previously issued warrants that results when a new tranche of warrants is subsequently issued, showing in each case that fair treatment of the first-issued warrant holders requires an adjustment (due to dilution) in the terms of those warrants and a corresponding modification in the warrants’ value once a second tranche of warrants is issued. To promote such fair treatment, terms of a warrant indenture would specify the nature of the adjustment required when future warrants are issued or exercised, analogous to the antidilution terms related, for example, to stock dividends. Unlike multiple issues of traded options, which are valued independently of one another, multiple warrant issues will be shown to have prices dependent on other warrants outstanding. Also examined is the sensitivity of the fair-value adjustment to changes in the underlying variables, and the theoretical fair-value prices are compared with Black-Scholes prices and with market prices of warrants in the case of two publicly traded companies, each with two warrant issues outstanding. As warrant issues modify the equity structure of a firm, the methodology of valuing warrants presented here will be useful to investment actuaries in situations in which a comprehensive market value for all of a firm’s securities is called for. In addition, risk management practices may sometimes include the use of warrant transactions to hedge stock positions similar to the way that call options are used for that purpose. This may include hedging the risk in equity-linked insurance contracts when the equity position includes stock in companies that have one or more warrant issues that are traded. The methods developed here are also applicable to multiple issues of executive stock options (ESOs) or to combinations of warrant issues and ESOs.     

American-style Indexed Executive Stock Options

This paper develops a new pricing model for American-style indexed executive stock options. We rely on a basic model framework and an indexation scheme first proposed by Johnson and Tian (2000a) in their analysis of European-style indexed options. Our derivation of the valuation formula represents an instructive example of the usefulness of the change-of-numeraire technique. In the paper's numerical section we implement the valuation formula and demonstrate that not only may the early exercise premium be significant but also that the delta of the American-style option is typically much larger than the delta of the otherwise identical (value-matched) European-style option. Vega is higher for indexed options than for conventional options but largely independent of whether the options are European- or American-style. This has important implications for the design of executive compensation contracts. We finally extend the analysis to cover the case where the option contracts are subject to delayed vesting. We show that for realistic parameter values, delayed vesting leads only to a moderate reduction in the value of the American-style indexed executive stock option.     

Valuation and incentive effects of hurdle rate executive stock options

Traditional executive stock options are often criticized for inherently weak links between pay and performance. Hurdle rate executive stock options represent a viable improvement. However, valuing these options presents extraordinary analytic difficulties. With a constant dividend yield the strike price becomes a path-dependent function of the stock price and exact analytic valuation is intractable. To solve this problem, we apply the Monte Carlo valuation approach developed by Longstaff and Schwartz (Rev Financ Stud 4:113–147, 2001) to estimate the value of path-dependent American options. We also extend the methodology to incorporate the theoretical framework by Ingersoll (J Bus 79:453–487, 2006) to permit subjective valuation influenced by an executive’s risk aversion.

Valuation of a Repriceable Executive Stock Option

We introduce a path-dependent executive stock option. The exercise price might be reduced when both the firm’s stock price and a stock market index fall greatly. The repriceable executive stock option has a simple payoff that may be used for realistic executive rewards. We show the valuation formula, and compute the probability of the repriceable executive stock option expiring in-the-money. Both price and probability are important pieces of quantitative information when choosing an executive compensation package.     

Expensing options solves nothing

The use of stock options for executive compensation has become a lightning rod for public anger, and it's easy to see why. Many top executives grew hugely rich on the back of the gains they made on their options, profits they've been able to keep even as the value they were supposed to create disappeared. The supposed scam works like this: Current accounting regulations let companies ignore the cost of option grants on their income statements, so they can award valuable option packages without affecting reported earnings. Not charging the cost of the grants supposedly leads to overstated earnings, which purportedly translate into unrealistically high share prices, permitting top executives to realize big gains when they exercise their options. If an accounting anomaly is the problem, then the solution seems obvious: Write off executive share options against the current year's revenues. The trouble is, Sahlman writes, expensing option grants won't give us a more accurate view of earnings, won't add any information not already included in the financial statements, and won't even lead to equal treatment of different forms of executive pay. Far worse, expensing evades the real issue, which is whether compensation (options and other-wise) does what it's supposed to do--namely, help a company recruit, retain, and provide the right people with appropriate performance incentives. Any performance-based compensation system has the potential to encourage cheating. Only ethical management, sensible governance, adequate internal control systems, and comprehensive disclosure will save the investor from disaster. If, Sahlman warns, we pass laws that require the expensing of options, thinking that's fixed the fundamental flaws in corporate America's accounting, we will have missed a golden opportunity to focus on the much more extensive defects in the present system.     

Underwater Options and the Dynamics of Executive Pay-to-Performance Sensitivities

We empirically analyze the dynamics of executives' pay‐to‐performance sensitivities. Option pay‐to‐performance sensitivities become weaker as options fall underwater, often leading to pressures to reprice options or restore pay‐to‐performance sensitivity in other ways. Building a detailed data set on executives' portfolios of stock and options, we find that the responsiveness of pay‐to‐performance sensitivities (created by all executive holdings of stock and options) to changes in stock price is large. The elasticity of pay‐to‐performance sensitivities with respect to stock price decreases is about 0.7 and is larger for high‐option executives and for executives with high percentages of options already underwater. The dominant mechanism through which companies offset declines in option pay‐to‐performance sensitivities is larger option grants following stock price declines; on average, these larger grants restore approximately 40% of the stock‐price‐induced pay‐to‐performance sensitivity declines. Option repricings are inconsequential in this regard, despite the attention they have attracted. In looking at positive returns, we find the reverse: higher returns both directly increase pay‐to‐performance sensitivities and lead to larger option grants, which raise pay‐to‐performance sensitivities further. Thus, option grants to executives tend to be largest following large stock price increases or large stock price decreases.     

Executive Option Repricing, Incentives, and Retention

While many firms grant executive stock options that can be repriced, other firms systematically restrict or prohibit repricing. This article investigates the determinants of firms' repricing policies and the consequences of such policies for executive turnover and retention. Firms that have better internal governance, that use more powerful stock-based incentives, or that face less shareholder scrutiny are more likely to maintain repricing flexibility. Firms that restrict repricing are more vulnerable to voluntary executive turnover following stock price declines. When share price declines are severe, restricting firms appear to award unusually large numbers of new options.     

Companies' Modest Claims About the Value of CEO Stock Option Awards

This paper analyzes company disclosures of CEO stock option values in compliance with the SEC's regulations for reporting executive compensation data to stockholders. Companies appear to exploit the flexibility of the regulations to reduce the apparent value of managerial compensation. Companies shorten the expected lives of stock options and unilaterally apply discounts to the Black-Scholes formula. Theoretical support for these adjustments is often thin, and companies universally ignore reasons that the Black-Scholes formula might underestimate the value of executive stock options. The findings not only cast light upon how corporations value executive stock options, but also provide a means of forecasting compliance with controversial new FASB requirements for firms to disclose the compensation expense represented by executive stock options.     

Option Awards for Australian CEOs: The Who, What and Why

The compensation structure for Australian CEOs, and especially the extent to which they receive executive stock options, is explored. Evidence suggests that the award of executive stock options is common in Australia, but not in as systematic a manner as has been documented for US CEOs. Where ESOs are awarded, they form a significant component of total compensation, even allowing for limitations in the way we approximate their value. Modelling the use of ESOs shows relatively few empirical regularities, other than a positive association between firm size and ESO use. This is consistent with a view that ESOs are a form of "rent extraction" by CEOs, but it may also reflect a bias towards their use created by accounting rules.     

Exercises of Executive Stock Options on the Vesting Date

We investigate the motives for executives to exercise executive stock options on the options’ vesting date versus a later early exercise. We find that executives frequently exercise on the vesting date, executives with a greater need for portfolio diversification and riskier underlying stocks are more likely to exercise their options on the vesting date versus a later early exercise, and private information appears less relevant to vesting date exercises.     

Valuación de opciones de tipo de cambio asumiendo distribuciones α-estables

This paper aims to present the valuation of options using the Black-Scholes method assuming α-stable distributions as an alternative option valuation in the Mexican market. The use of α-stable distributions for modelling financial series allows to overcome the classical valuation main weakness which assumes normality, by capturing the presence of heavy tails and asymmetry in financial time series. One of the main results is the price differential between the two models and the effect of alpha and beta parameters on prices; to show the difference valuation is made of a call option and a put option for the peso-dollar exchange rate. Likewise, basic sensitivity measurements of options (delta, gamma, and rho) were made and the effect of the stability parameter (α) was made on the implied volatility of options assuming the α-stable price as the market price.     

Managing Pension Risks: A Corporate Finance Perspective

Defined benefit (DB) pension plans of both U.S. and European companies are significantly underfunded because of the low interest rate environment and prior decisions to invest heavily in equities. Additional contributions and the recovery of stock markets since the end of the crisis have helped a bit but pension underfunding remains significant. Pension underfunding has substantial corporate finance implications. The authors show that companies with large pension deficits have historically delivered weaker share price performance than their peers and also trade at lower valuation multiples. Large deficits also reduce financial flexibility, increase financial risk, particularly in downside economic scenarios, and contribute to greater stock price volatility and a higher cost of capital. The authors argue that the optimal approach to managing DB pension risks relates to the risk tolerance of specific companies and their short and long‐term strategic and financial priorities. Financial executives should consider the follow pension strategies:

• Voluntary Pension Contributions: Funding the pension gap by issuing new debt or equity can provide valuation and capital structure benefits—and in many cases is both NPV‐positive and EPS‐accretive. The authors show that investors have reacted favorably to both debt‐ and equity‐financed contributions.
• Plan de‐risking: Shifting the pension plan's assets from equity to fixed income has become an increasingly popular approach. The primary purpose of pension assets is to fund pension liabilities while limiting risk to the operating company. The pension plan should not be viewed or run as a profit center.
• Plan Restructuring: Companies should also consider alternatives such as terminating and freezing plans, paying lump sums, and changing accounting reporting.

     

Dividend taxes and stock volatility

How do dividend taxes affect stock volatility? If a risk-averse executive faces price risk through his incentive contract, changes in stock volatility due to dividend taxes may increase agency costs and therefore decrease overall welfare. In this paper, I use a decrease in dividend taxes as a natural experiment to identify their effect on the firm’s idiosyncratic stock return volatility. Stock volatility decreased after the tax cut for firms at which executives have larger sensitivity to stock price in their incentive compensation package relative to firms at which executives have a smaller sensitivity. Therefore, with risk-averse executives and risk-neutral shareholders, dividend taxes may exacerbate agency costs. The increase in agency costs will decrease shareholder welfare, which can be partially offset by the use of options in the employment contract.     

Options with Constant Underlying Elasticity in Strikes

Closed-form solutions are derived and interpreted for European options, with stochastic strike prices, that maintain constant elasticity of the strike with respect to the price of the underlying asset. We refer to such options as CUES. CUES preserve the relative shares of exercise price risk for both the buyer and writer of the option, regardless of whether the price of the underlying asset moves up or down. The relevance of the CUES concept is established through applications in two distinct fields. First, it is established that CUES-like options are embedded in private equity investments. This concept is then used in a novel application to determine the equity share of a private company corresponding to a given level of investment. Secondly, the advantages that CUES would provide over traditional executive stock option grants are considered and it is shown that CUES can provide enhanced incentive-alignment without increasing options expense to the company. JEL Classification: G130