NUMEROUS VARIABLES can be posited as explanations observed CEO compensation levels. In past articles, we explored variables such as shifting participation constraints (or reservation wages), board-CEO relationships, and absolute and relative performance. This article complements our earlier approaches by employing statistical techniques to understand the variables affecting CEO compensation. The questions that we have attempted to answer include: How strong is the statistical relationship between performance and pay? Does the peer group’s compensation have a disproportionate statistical influence on a CEO’s level of pay? Or, is it the size of a company the CEO manages that is most relevant to explaining the compensation a CEO is entitled to?

Background and importance
As companies and jurisdictions in North America and elsewhere come to grips with how to remain competitive and grow in the changing world economic order, it has become critical for leaders to once again examine the broader good of shareholders, employees, management and other stakeholders, in order to successfully recalibrate the society’s underlying business structures. In the spirit of this endeavour, this study offers an intriguing look into a larger dimension of corporate performance during times economic expansion (macro and micro), and how particular companies and their leadership have faired over the same period. The overarching goal is to offer a Board of Directors the data, tools, and rigorous analysis required to correct sub-optimal decisions and structures of the past and incorporate new models for compensation, performance evaluation, equity and capital structure, and selection of management.

Data and methodology
A group of 43 CEOs across 27 companies and four industries were selected for the purposes of this analysis. The selection was originally comprised of 32 large public companies – as measured by trailing twelve-month revenues – across automobiles, household products, metals and mining, and telecommunication services. In order to control for regional variations, selection was restricted to North American companies for all industries except automobiles. In the latter case, we felt that regional variations were not as much of an issue, owing to the high degree of globalization within the auto sector. Given the lack of data available on CEO compensation, this selection was reduced to 27 companies (Exhibit 1).

After the selection process, total returns to share holders (TRS) were calculated for each company for a twenty (20) year period from 1998 to 2007. The TRS for an industry was calculated as an arithmetic average of the TRSs of its constituent companies. Thereafter, to the extent possible, CEOs for each company were determined for the same 1998–2007 period, and their total compensation figures (i.e. all cash and non-cash compensation) were gathered. The year the CEO began or ended his or her tenure was excluded from the analysis for two reasons: first, the CEO would have joined or left the company midway through the year, making it difficult to reconcile compensation with the annual TRS calculated for the company; second, compensation figures in these years tended to be uncharacteristically high, and represented a special circumstance not associated with the normal annual cycle of the company. Nonetheless, we recognized these excluded data as interesting in their own right, and as possible candidates for a future analysis.

The final variable we gathered was a proxy for company size, namely, the annual revenues. To simplify the data gathering process, annual revenues were collected during the midpoint of the CEO’s tenure. For instance, if a particular CEO’s information ranged the period 2000–2005, the annual revenues for 2003 were used to represent the company size. The relevant variables are listed and described in Exhibit 2.

Now that all the variables were in place, a number of regression models were tested to relate average annual total compensation (i.e. the dependent variable) with absolute performance, relative performance, peer group compensation, and company size (as measured by annual revenues).

Correlations
Investigating the correlation between average compensation and the various explanatory variable candidates showed interesting trends (Exhibit 5 and Exhibit 6). First, the correlations suggested that a model incorporating logarithms would demonstrate superior explanatory power to one dependant on absolute measures (e.g. the relationship between log(size) and log(average compensation) was much stronger than that of size with average compensation). As the reader may recall, the log form of specification addresses the question of elasticity, e.g. the extent to which compensation changes for a one percent change in annual revenue. Second, the correlations suggested that annual revenues and peer compensation (in their log forms) would likely hold the most explanatory power. Third, and somewhat strangely, performance appeared to have a negative relationship with compensation. Our hypothesis was that this negative relationship was not likely to be statistically significant. That is, once size and/or peer compensation had been accounted for, performance would likely have no statistical relationship with compensation. Finally, absolute and relative performance had a very strong mutual correlation, suggesting that both variables would not be needed in a regression model (Exhibit 6).

Results
The observations we made during the last section were borne out in the multivariate regression analysis. Namely, we found that the only statistically significant explanatory variable was size. Performance and peer compensation were not significant as explanatory variables. A summary of the various models that we iterated through is given in Exhibit 7. Size, as measured by annual revenues, accounted for 29% of the variation in average compensation. Its coefficient of 0.33 could be interpreted as: on average, a 1% increase in size is associated with a 33% increase in compensation.

Discussion and recommendations
Our statistical analysis yielded the surprising result that pay for performance is not supported by the data, or more specifically, by regression analysis. In other words, CEO compensation (according to our data and analysis) is not based on performance of the corporation, absolute or relative. This seems to be at plain odds with Board experience in shaping CEO compensation based on incentive contracts. We can anticipate some objections to our methodology and the results found. We will consider and address some of these here.

First, the selection of companies (and the CEOs) was not performed in a statistically random manner, but was a conscious choice of the highest revenue-generating firms in four select industries. The reasoning for these industry choices was their relevance within current events and the availability of CEO compensation data. Statistically speaking, better industry representation would make the results more accurate, but not alter the essential insights.

Second, using a geometric average (CAGR) to measure performance is contrary to arithmetic average schemes usually used in incentive contracts. This objection can be addressed in two ways: first, even though the two averages are different, the more accurate representation of a CEO’s performance is CAGR, thus its use is justified; second, the two averages aren’t as different as one may perceive, especially over relatively short time horizons (the geometric average or CAGR is always less than or equal to the arithmetic average).

Third, the results found are contrary to the intended outcome of the process that Boards undertake in setting compensation. Specifically, while Boards seek to develop and optimize compensation contracts based on performance, our analysis has shown that they in fact fail to achieve this. Additionally, Boards also calibrate compensation based on peer averages, while the regression analysis shows that peer compensation is not statistically significant.

The third criticism is, in our opinion, the most intriguing. How can it be that the results outright contradict the Compensation Committee’s intent? Pay for performance is typically determined on an annual basis in contracts, not over an extended period of time. This practice may have the effect of undermining the entire pay for performance principle. For instance, if a company’s returns are -20% one year and 20% the next, the net gain is close to zero, despite which the CEO gets a large bonus the second year for the 20% gain. Similarly, the practice of re-pricing and back-dating stock options undermines the pay for performance principle. If one is to take a slightly cynical view of Board-CEO relationships, one could argue in line with scholars who suggest that the Board-CEO nexus tries to maximize compensation in any way that is tolerated by shareholders. To the extent that variable compensation in stock and stock options is perceived as being aligned with shareholder interests, significant overpayment of this kind of compensation may be occurring. An empirical study showing that stock option compensation had proliferated to sectors outside of IT by the end of the dot-com era would substantiate this argument, and would be in line with the finding that compensation took off after 2003.

Interestingly, company size was found to be statistically significant, and helped explain about 30% of the variation in compensation. As a rule of thumb, size is a measure of complexity. The bigger a company, the more actors and strategic interactions it has. Thus, it makes intuitive sense that the market pays more to leaders that can manage more complexity. One reason that peer compensation may not have proven to be statistically significant is that the peer group we chose for the analysis wasn’t appropriately stratified based on size. This line of reasoning would suggest that peer compensation, as an explanatory variable, largely overlaps with size of company. Peer compensation may even be subsumed or included within size if Compensation Committees are found to routinely incorporate peers that are from outside the industry. Thus, a compelling case could be made for the importance of size.

What are Board members to make of these findings? First, the pay for performance principle should not be undermined as a result of near-term bonus or stock option schemes. Second, Directors should realize that if everyone is overpaying CEOs (as a result of the post-2003 stock option proliferation hypothesis), the rational choice of going with the majority should be systematically combated. Boards should work together as part of broader governance efforts to take corrective action to adjust compensation principles collectively. At a minimum, they should ensure that Board-CEO independence is established in a bullet-proof way as far as compensation decisions are concerned. Third, Board members should not underestimate the power of reviewing and renewing their understanding of incentive contracts. As our analysis demonstrates, CEO compensation is highly divergent from company growth, performance, and the intent of the structures imposed by Boards. Boards would do well to undertake an exhaustive audit of the compensation structures in place within their own organizations, incorporate analyses of the performance of their officers, compare this with company as well as officer peer groups, and see what the results are. Further, a detailed analysis should be undertaken breaking down the various components of their executive compensation, to see if they are truly aligned with the goals of the corporation vis-à-vis the shareholders and value to them.
 

Yousuf Haque is an associate and Sridhar Parthasarathy is a principal in Surje’s Toronto office.
 

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