Benchmarking Historical Corporate Performance

Benchmarking Historical Corporate Performance James G. Scott ∗ This version: October 2010 Abstract This paper uses Bayesian tree models for statistical benchmarking in data sets with awkward marginals and complicated dependence structures. The method is applied to a very large database on corporate performance over the last four decades. The results of this study provide a formal basis for making cross-peer-group comparisons among companies in very different industries and operating environments. This is done by using models for Bayesian multiple hypothesis testing to determine which firms, if any, have systematically outperformed their peer groups over time. We conclude that systematic outperformance, while it seems to exist, is quite rare worldwide. 1 Introduction 1.1 Benchmarking with covariates This paper is concerned with the topic of statistical benchmarking—that is, as- sessing the relative performance of a subject compared to that of its peer group, in a situation where only an absolute measure of performance is available. Some examples of benchmarking include: Mutual-fund ratings, where the goal is to compare the returns of many funds against their respective benchmarks. Fund managers who broke even during the financial crisis of 2008, for example, may be superior to those posting double-digit gains during the dot-com bubble of the late 1990’s. University admissions, where many admissions committees wish to “adjust” for a student’s economic background and secondary school when comparing absolute measures such as standardized test scores. ∗Assistant Professor of Statistics at the McCombs School of Business, University of Texas at Austin. email: James.Scott@mccombs.utexas.edu. 1 arXiv:0911.1768v2 [stat.ME] 25 Oct 2010 Non-overlapping inter-rater comparisons in subjectively judged competi- tions like figure skating and high-school debate, where it is natural to control for the fact that different judges may rate participants on highly idiosyncratic scales. The notion of a peer group is somewhat loose, but can usually be represented through some combination of continuous and categorical measures. In such cases, it is natural to associate the peer score with the residual from a regression model. One’s peer group can then be interpreted as the group of other subjects having similar expected scores, and one’s “benchmarked score” as the bit left over after subtracting the expected score, or benchmark. If a linear model fits the data well, then the residuals from this model are enough to settle the issue. Complications arise, however, when the marginal distribution of performance is heavy-tailed, highly skewed, or both. These fac- tors can invalidate traditional parametric assumptions about the distribution of residuals. It may also simply be very difficult to recover the right “raw” marginal distribution through some probabilitistic model that depends upon the covariates. A further complicating factor is the presence of conditional heteroskedasticity— that is, when the volatility of performance differs by peer group, and not merely the expectation. Here, a benchmark should account for more than simply the absolute value of the residual; it should also adjust for the scale of the residual distribution, given the covariates. The intuition here is that performing “further out in the tails,” rather than simply differing from the benchmark by a large absolute margin, is the truly impressive—or ignominious—feat. 1.2 Data, goals, and method In this paper, the benchmarking problem is considered in the context of a large data set on historical corporate performance. Our goal is to use the proposed method to compare publicly traded companies against their peers using a stan- dard accounting measure known as Return on Assets (ROA), which measures the efficiency with which a company’s assets are used in generating earnings. (This is fundamentally different from a market-based measure like stock returns, and is much more stable across time.) All three complicating factors—skewness, heavy tails, and conditional heteroskedasticity—are present here. The data set, moreover, is quite large: we have 645,456 records from 53,038 companies in 93 dif- ferent countries, spanning the years 1966–2008. This poses serious computational challenges, but also an opportunity for nuanced modeling. It is necessary to benchmark raw performance numbers because certain fea- tures of a company—its industry, its size, its leverage, its country of operation, its market share—make it intrinsically easier or harder to score well on our ROA measure. These same facts may also entail different levels of volatility in perfor- mance. Such differences, moreover, may be completely unrelated to the differ- 2 ences in managerial talent or performance that we are hoping to measure. The pharmaceutical industry, for example, is characterized by very high barriers to entry and patent-protected monopolies on specific drugs, allowing these firms to enjoy unusually high returns.

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