Indexing Executive Compensation Contracts

Standard principal-agent theory prescribes that managers should not be compensated on exogenous risks, such as general market movements. Rather, firms should index pay and use contracts that filter exogenous risks (e.g., Holmstrom 1979, 1982; Diamond and Verrecchia 1982). This prescription is intuitive and agrees with common sense: CEOs should receive exceptional pay only for exceptional performance, and “rational” compensation practice should not permit CEOs to obtain windfall profits in rising stock markets. However, observed compensation contracts are typically not indexed. Specifically, stock options almost never tie the strike price of the option to an index that reflects market performance or the performance of peers. Commentators often cite this glaring difference between theory and practice as evidence for the inefficiency of executive compensation practice and, more generally, as evidence for major deficiencies of corporate governance in U.S. firms (e.g., Rappaport and Nodine 1999; Bertrand and Mullainathan 2001; Bebchuk and Fried 2004). This paper therefore contributes to the discussion about which compensation practices reveal deficiencies in the pay-setting process.

In our paper, Indexing Executive Compensation Contracts, recently featured in the Review of Financial Studies, we address the indexation of compensation contracts with a particular focus on indexed options, which link the strike price to an index and are a central theme in the debate about executive pay. We highlight two main contributions. First, we show analytically that indexed options differ from conventional options in three important ways: (i) the underlying asset of indexed options has a lower volatility; (ii) the underlying asset does not earn a risk premium and therefore has a lower drift rate; (iii) indexing increases the strike price of the option. We show that the first effect not only generates the familiar benefits from risk sharing, but also improves incentives; a simple intuition for this effect is that reducing volatility reduces the probability that in-the-money options expire out of the money and therefore increases the option’s utility-adjusted delta. The latter two effects reduce incentives because they implicitly raise the performance benchmark, reduce the probability that the option ends up in the money, and therefore reduce the utility-adjusted deltas of options.

Proponents of indexation often rely on the risk sharing component of the first effect, whereas more critical voices emphasize the third effect. The drift-rate effect is usually neglected. By contrast, our analysis shows that a proper assessment of indexation needs to look at the joint effect of all three factors and weigh the advantages from effect (i) against the disadvantages from effects (ii) and (iii). The efficiency of indexing stock options is theoretically ambiguous and ultimately an empirical question.

Our second contribution is to calibrate the standard model used in the compensation literature individually to each CEO in a large sample of U.S. CEOs. Calibration allows us to quantify the costs and benefits from indexing for each individual CEO, determine how the different effects play out, and identify the cases in which indexing is beneficial. Our calibration approach also reveals to what extent the tradeoffs between the different effects are the same for all CEOs. The central finding from our calibration analysis is that across the many different scenarios we consider, indexing creates either small savings or large costs. In many empirically relevant cases, indexed options provide incentives at a higher cost than conventional options, which is in line with the skepticism expressed by Murphy (2002), but contrary to widely held beliefs that the absence of indexation indicates poor governance. We suggest that the absence of indexation can be explained based on the fundamental tradeoff between risk and incentives.

In our baseline case, we analyze the full indexation of stock options under the assumption that contracting is efficient and managers do not extract rents; in terms of our model, the last condition implies that shareholders have to adjust base salaries to compensate for the loss of value from exchanging conventional options for indexed options, and ensure that managers’ participation constraint remains satisfied. We find that full indexation of stock options increases compensation costs by more than 50% on average in our baseline parameterization. In dollar terms, average CEO pay would increase by $32.5 million ($1.5 million at the median). Only about 15% of firms would benefit from indexing all options of the CEO. The few firms that benefit from indexation are high-beta, high-risk firms that have CEOs with a relatively high level of absolute risk aversion. For these firms the benefits from the reduction in volatility (the first effect of indexed options discussed above), which improves incentives as well as risk sharing, outweigh the costs of reduced incentives from a stricter performance hurdle (the second and third effect). In particular, a higher beta creates a larger scope to reduce risk through indexation.

We extend our baseline setting in several dimensions. We first analyze partial indexation and allow firms to optimally choose the proportion of stock options they wish to index. Then the efficiency gains from indexation are non-negative by construction. For our baseline parameterization, firms would save 2.3% of compensation costs on average, which is less than $1 million for the average CEO. Still, the adverse effects of indexation on incentives imply that three-quarters of the firms in our sample would optimally choose not to index their CEOs’ options at all.

Our analysis shows that the indexation of stock options as proposed in the literature is unwarranted in most cases, but leaves open whether alternative forms of indexation may still be beneficial. We therefore examine two alternative forms of indexation in additional tests. First, we analyze options on indexed stock. Indexed stock is a security that carries only the firm-specific risk of the stock and has an expected return equal to the risk-free rate. At-the-money options on indexed stock improve on indexed options, because options on indexed stock avoid the implicit increase in the strike price (effect (iii) above) and therefore provide incentives more efficiently compared to indexed options, which are out of the money and have a lower delta. We confirm that options on indexed stock are more effective. However, the gains from using them are still limited, because of the adverse effect of the reduction in the drift rate of the underlying asset (effect (ii) above); more than 40% of firms would optimally use only conventional, non-indexed options rather than options on non-indexed stock.

Second, we analyze indexed stock itself. Indexing stock does not involve any of the complications associated with the strike price we encountered with indexed options or with options on indexed stock. Hence, we expect indexed stock to perform better than any of the options we study. Interestingly, this conjecture is confirmed, but the gains are not large: Fully indexing all restricted shares leads to efficiency gains near zero, whereas optimal partial indexation of stock leads to gains that are about 25% to 30% larger than those observed for the partial indexation of options. In absolute terms, savings are always small, because the volatility effect and the drift-rate effect carry over from the case of stock options to shares. The analysis of indexed stock and options on indexed stock allows us to isolate the different effects we highlight above and to compare securities with different exposures to these effects. This comparison is one of the contributions of this paper.

Finally, we adopt the perspective of the rent-extraction view (e.g., Bebchuk and Fried 2004). This step of the analysis is important because proponents of the rent-extraction view may not agree with the presumption that shareholders have to compensate CEOs for the loss associated with exchanging valuable conventional options for much less valuable indexed options. We model rent extraction in our context by dropping the assumption that CEOs’ outside options are binding. Effectively, we ask which contracts would be optimal if firms only want to provide a given level of incentives, but do not need to be concerned about retaining the CEO. In this framework we ask whether indexation is an appropriate strategy for shareholders to recapture rents. The analysis shows that for about half of all CEOs, indexation does not help with recovering rents. Indexation would still increase CEO pay levels by more than 20% on average if firms were required to fully index stock options. Optimal partial indexation leads to cost savings of just under 8% of compensation costs. The intuition for these results is that indexing leads to inefficient incentive provisions for the same reasons as in the efficient contracting case.

We conduct all our analyses for a range of different parameterizations and subject the results to several robustness checks. Specifically, our findings are not driven by our treatment of the CEO’s investment in the stock market as exogenous and are also not attributable to the fact that stock market risk is associated with a risk premium.

The model we use is a standard principal-agent model with constant relative risk aversion (CRRA) utility and lognormal stock prices. This modeling strategy has become standard in much of the compensation literature, and our results can therefore be compared directly with previous work. The impact of the three main effects of indexing options is theoretically ambiguous and depends on parameter values, which makes calibrations at the individual CEO level the research strategy of choice. Our approach is also fairly general and does not require additional assumptions about functional forms other than concavity of the production function and convexity of the effort cost function of the CEO. However, two assumptions are necessary to ensure tractability. First, we do not endogenize the balance between stock and options and only discuss to what extent it is optimal to index the shares and options in observed contracts. The focus on observed contracts is necessary as the CRRA-lognormal setup would hardly feature options as part of the optimal contract (Dittmann and Maug 2007). Second, we do not allow for changes in the level of effort and hold it fixed at the level implied by the observed contract. We argue why we believe the effects we identify to be robust and why we believe the benefits from indexation to be always limited, if not outright negative, in nonstandard setups that overcome these limitations of our approach.

The intuitive appeal of indexation is closely related to Holmstrom’s (1979) seminal work on the informativeness principle. The informativeness principle implies that there exists an optimal contract that filters all exogenous risks. However, this optimal contract will generally be a highly nonlinear function, and Holmstrom himself observes that filtering risks does not take the simple form of subtracting an index from the output measure except for some special cases (Holmstrom 1982, 377). Nothing in our work contradicts the informativeness principle. Instead, we follow the compensation literature and analyze observed contracts that can be constructed from shares and stock options, which are empirically more relevant, but not necessarily optimal. Whether indexing these contracts improves efficiency is an open question that cannot be resolved by appealing to the informativeness principle. Our calibrations show that indexing options moves piecewise linear contracts further away from efficiency. Furthermore, other simple forms of indexation are more beneficial, even though they also fall short of filtering all exogenous risks. The informativeness principle can therefore provide only limited guidance for the optimal design of observed, piecewise-linear contracts.

The full paper is available for download here.