 When does beta shrinkage help, and why does the leverage adjustment fail? Out-of-sample evidence from Indian equitiesOnkar Chakrawar MPRA Paper from University Library of Munich, Germany Abstract: Beta is the single firm-specific input to the Capital Asset Pricing Model, and Indian valuation practice offers analysts three broad ways to estimate it: the raw regression beta, a shrinkage adjustment such as Blume’s or Vasicek’s, and the bottom-up beta assembled from industry peers by unlevering and relevering. No published study establishes which of these actually forecasts a firm’s future systematic risk in the Indian market. This paper runs that test. Using 4,781 firm-origin observations across 398 Nifty 500 constituents and 15 annual forecast origins from 2010 to 2024. Each estimator is built using only the information that was available at the time the estimate was made and is then evaluated against the actual beta observed over the following two years. Three main findings emerged. First, all genuine beta estimators perform significantly better than simply assuming β = 1 (t = 7.64). However, the differences in performance among the various estimators are relatively small and, at the overall market level, are not statistically significant. The Blume adjustment performs the best, as it has the lowest estimation error and shows much better calibration. Its Mincer–Zarnowitz slope is 1.105, compared with only 0.737 for the raw regression. Second, shrinkage does not improve beta estimates in every situation; its effectiveness depends on the level of estimation error. The benefit from shrinkage increases as the estimation error becomes larger. It provides the greatest improvement for illiquid firms and sectors where betas tend to change or quickly revert toward their average levels. However, among the most liquid one-third of the market, the raw OLS method performs better than shrinkage. Third, and most importantly for practical use, the bottom-up beta has no out-of-sample content whatsoever (no ability to predict future beta). Its Mincer–Zarnowitz slope is −0.009, and its R² is 0.0004. In comparison, the raw regression beta that it replaces has a +0.44 correlation with the beta realized later. The main reason for this failure is the relevering step, which increases the peer-group estimation error by multiplying it by (1 + (1−T)·D/E). The study also shows that this problem cannot be solved simply by choosing better peer companies. This last finding is not new- Fuller and Kerr (1981) and Butler, Mohr and Simonds (1991) reached the same conclusion on US data, and Alanis et al. (2025) have confirmed it recently. However, this finding has been largely ignored in valuation practice. The leverage adjustment, which was shown to be unnecessary in 1991, is now commonly taught and used as a standard part of valuation. This paper provides the first Indian evidence, the first test based on how accurately beta can be forecast, rather than on predicting returns, and a measured explanation of why the adjustment fails. It also finds that thin-trading corrections are no longer useful. Dimson and Scholes–Williams adjustments improved beta estimates in India before 2016, but they made the estimates worse after 2016, as non-trading on the NSE fell by roughly three-quarters. Keywords: beta estimation; CAPM; shrinkage; bottom-up beta; Indian equities; out-of-sample forecasting (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:130509 Access Statistics for this paper More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC. |
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