Six Challenges in Designing Equity-Based Pay

This paper analyzes why the primary goal of the equity-pay explosion--creating long-run ownership incentives for top executives--has often been difficult to achieve in practice. More generally, I describe six challenges in the design of equity-based pay plans and discuss potential solutions. The six challenges involve: 1. mismatched time horizons; 2. gaming; 3. the value-cost wedge'; 4. the leverage-fragility tradeoff; 5. aligning risk-taking incentives; and 6. avoiding excessive compensation. The paper also discussed the merits of stock versus options and concludes that restricted stock is often a superior form of compensation.

The Segal--Bargmann transform for odd-dimensional hyperbolic spaces

We develop isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.Comment: To appear in Mathematic

Coherent states for a 2-sphere with a magnetic field

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on Coherent State

Stock Options for Undiversified Executives

We employ a certainty-equivalence framework to analyze the cost and value of, and pay/performance incentives provided by, non-tradable options held by undiversified, risk-averse executives. We derive Executive Value' lines, the risk-adjusted analogues to Black-Scholes lines, and distinguish between executive value' and company cost.' We demonstrate that the divergence between the value and cost of options explains, or provides insight into, virtually every major issue regarding stock option practice including: executive views about Black-Scholes measures of options; tradeoffs between options, stock and cash; exercise price policies; connections between the pay-setting process and exercise price policies; institutional investor views regarding options and restricted stock; option repricings; early exercise policies and decisions; and the length of vesting periods. It also leads to reinterpretations of both cross-sectional facts and longitudinal trends in the level of executive compensation.

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L^2 space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an "unwrapped" version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi

Property and Casualty Solvency Funds as a Tax and Social Insurance System

When a Property and Casualty (P&C) insurance company becomes insolvent, solvent insurance companies are forced to pay assessments (a form of taxation) to state guarantee funds ('solvency funds') in order to protect the policyholders of the failed companies. We produce estimates of the costs to the guarantee funds of resolving P&C insurance company insolvencies. We find that the total net costs (payments by the fund less recoveries by the fund) of resolving insolvencies are remarkably high. We estimate that the mean ratio of net costs to assets is approximately one, implying that insolvent companies have liabilities that are roughly twice as large as assets when they fail. Our cost estimate for resolving insurance company insolvencies is roughly three times higher than similar estimates for banks. We also find that the ratio of net costs to assets tends to be higher for small firms, poorly capitalized firms, firms writing significant premiums in long tail lines, and firms that fail because of disasters. Our findings also indicate that the resolution of insolvencies is typically quick. More than 60 percent of all costs to the fund for a given insolvency occur within two years, and more than three-quarters of total costs occur within three years. However, we find that firms with a high proportion of premiums in long tail lines take much longer to resolve.

The Taxation of Executive Compensation

Over the past 20 years, there has been a dramatic increase in the share of executive compensation paid through stock options. In this paper, we examine the extent to which tax policy has influenced the composition of executive compensation, and discuss the implications of rising stock-based pay for tax policy. We begin by describing the tax rules for executive pay in detail and analyzing how changes in various tax rates affect the tax advantages of stock options relative to salary and bonus. Our empirical analysis leads to three conclusions. First, there is little evidence that tax changes have played a major role int the dramatic explosion in executive stock option pay since 1980. Although the tax advantage of options has approximately dounbled since the early advantage of options has approximately doubled since the early 1980s options currently have only a slight tax advantage relative to cash - approximately $4 per$100 of pre-tax compensation to the executive. A more convincing story for the dramatic explosion in stock options involves changes in corporate governance and the market for corporate control. For example, there is a strong correlation between the fraction of shares held by large institutional investors and the fraction of ececutive pay in the form of stock options, a result that holds both longitudinally and cross-sectionally. Second, we find evidence that the million dollar rule (which limited the corporate deductibility of non-performance-related executive compensateion to $1 million) led firms to adjust the composition of their pay away from salary and toward "performance related pay," although our estimates suggest that substitution was minor. We find no evience that the regulation decreased the level of total compensation. Third, we examine whether there is evidence for significant shifting of the timing of option exercieses in response to changes in tax rates. After replicating the Goolsbee (1999) result regardin tax-shifting with our data for the 1993 tax reform, we show that no such shifting occurred in either of the two tax reforms of the 1980s. Moreover, we find evidence that much of the unusually large level of option exercises in 1992 was the result of the rising stock market rather than the change in marginal tax rates.

Managing Option Fragility

We analyze and explore option fragility, the notion that option incentives are fragile due to their non-linear payoff structure. Option incentives become weaker as options fall underwater, leading to pressures to reprice options or restore incentives through additional grants of equity-based pay. We build a detailed data set on executives' portfolios of stock and options and find that executive options are frequently underwater, even when average stock returns have been high. For example, at the height of the bull market in 1999, approximately one-third of all executive options were underwater. We find that, in contrast to the incentives provided by stock, the incentives provided by options are quite sensitive to stock price changes, especially on the downside. Overall, we find that the incentives created by all executive holdings have an elasticity with respect to stock price decreases of about 0.7, and this elasticity is larger for high-option executives and for executives with high percentages of options already underwater. The dominant mechanism through which companies manage option fragility is larger option grants following stock price declines; on average, these larger grants restore approximately 40% of the stock-price-induced incentive declines. Option repricings are far less prevalent, despite the attention they have garnered. Interestingly, we find that for positive stock returns, higher returns lead to larger option grants, which raise incentives further. Thus, option grants are largest when companies do very poorly or very well. Executive exercising behavior also affects option fragility. Since executives are much less likely to exercise options following stock price decreases, the natural declines in incentives due to exercises are attenuated on the downside, leading executives to 'manage their own incentives' in a way that augments company management of option fragility.

Risk-Based Capital Standards and the Riskiness of Bank Portfolios: Credit and Factor Risks

Bank risk-based capital (RBC) standards require banks to hold differing amounts of capital for different classes of assets, based almost entirely on a credit risk criterion. The paper provides both a theoretical and empirical framework for evaluating such standards. A model outlining a pricing methodology for loans subject to default risk is presented. The model shows that the returns on such loans are affected by the complicated interaction of the likelihood of default, the consequences of default, term structure variables, and the pricing of factor risks in the economy. When we examine whether the risk weights accurately reflect bank asset risk, we find that the weights fail even in their limited goal of correctly quantifying credit risk. For example, our findings indicate that the RBC weights overpenalize home mortgages, which have an average credit loss of 13 basis points, relative to commercial and consumer loans. The RBC rules also contain a significant bias against direct mortgages relative to mortgage- backed securities. In addition, we find large differences in the credit riskiness of loans within the 100 percent weight class and potentially large benefits to loan diversification, neither of which are considered in the RBC regulations. We also examine other types of bank risk by estimating a simple factor model that decomposes loan risk into term structure, default, and market risk. One implication of our findings is that although banks have reallocated their portfolios in ways intended by the RBC standards, they may have merely substituted one type of risk (term structure risk) for others (default and market risk), of which the net effect is unknown.