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Resurrecting the Capital Asset Pricing Model Resurrecting the Capital Asset Pricing Model Hammad Siddiqi University of Queensland [email protected] This Version: October 2016 Abstract The capital asset pricing model is generally considered incapable of explaining the stock market behavior. I show that this conclusion is premature, and incorporating a pragmatic approach to approximating optimal Bayesian inference in the model resurrects CAPM. The adjusted CAPM internalizes the well-known size, value, and momentum effects, high-alpha-of-low-beta-stocks, accruals, low volatility anomaly, stock-split anomaly, and reverse stock-split anomaly. The market equity premium is also larger with anchoring. Immediate applications of the adjusted CAPM include improved cost of equity calculation, and improved evaluation of managed portfolio performance. Keywords: Size Premium, Value Premium, Stock Splits, Equity Premium Puzzle, Anchoring and Adjustment Heuristic, CAPM, Asset Pricing, Accrual Anomaly, Low Volatility Anomaly, Low-beta-high- alpha, Momentum Effect JEL Classification: G12, G11, G02 1 Resurrecting the Capital Asset Pricing Model It is fair to trace the birth of asset pricing theory to the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965). Over five decades later, CAPM is still the most widely used model in practice. However, academic finance has largely moved away from CAPM due to the discovery of a large number of phenomena that are generally considered to be inconsistent with the model.1 Such empirical difficulties have led Fama and French (1992) (and others) to claim that the CAPM is dead. In this article, I show that it is theoretically possible to internalize almost all of the prominent anomalies if a pragmatic approach to approximating optimal Bayesian inference is incorporated in the model. Hence, the conclusion that the CAPM is dead is premature. The key principle on which financial decisions turn is the relationship between risk and return. How are beliefs about risks formed? In general, a large number of factors contribute to risk in any given situation. Consider any given firm. A large number of factors (such as industry structure, regulations, labor relations, technology, input supply constraints, business strategy, and investment policy) matter for the volatility of its stock. There are nearly 5000 firms listed in the New York stock exchange alone, so optimal Bayesian inference requiring an accurate assessment of all the relevant factors for every firm is intractable. The problem becomes more manageable with the realization that many factors are sector-specific, that is, are common to every firm in the same sector. So, instead of re-inventing the wheel for every firm, a pragmatic approach is to leverage such commonalities by using the sector-specific factors to furnish an informative starting point and then attempting to make appropriate adjustments pertaining to individual firms in the same sector. This is the approach taken by brokerage houses, commercial banks, and investment banks, as they typically employ sector specialists who focus on a group of firms in the same sector. To take a concrete example, suppose adverse weather conditions are affecting the supply of coffee beans. Clearly, this is a factor that matters for all coffee producers. A pragmatic approach is to analyze the impact of adverse weather conditions on the sector leader (about which information is readily available) and use it as an informative starting point for other firms. 1 Two prominent CAPM anomalies are size and value effects. Size effect is documented in Banz (1981), Reinganum (1983), Brown et al (1983), and more recently in Hou, Xue, and Zhang (2014), and Fama and French (2015) among many others. Value premium is documented in Fama and French (1998) among many others. 2 This informative starting points needs to be adjusted as other firms may have hedged differently in the futures market, may hold different levels of inventory, and have varying relations with suppliers among other factors. This pragmatic approach has the added advantage of making it likely that an analyst would at least be qualitatively correct in ranking the firms even if he gets the magnitudes wrong. Unsurprisingly, Da and Schaumburg (2011) find that equity analysts are consistently able to rank stocks correctly making them qualitatively or rank-order correct even though they are often quantitatively incorrect. In this article, I study the implications of incorporating this pragmatic approach into CAPM. The surprising finding is that it gives rise to a unified theoretical explanation for almost all of the prominent anomalies concerning CAPM. Without asserting that anomalies are completely resolved, which requires a comprehensive empirical examination of a large number of phenomena, and so is beyond the scope of any single article, this article shows that the reliance on the pragmatic approach must be considered as an alternative explanation before rejecting CAPM. In this respect, the article paves the way for such empirical testing by explicitly deriving CAPM formula, adjusted for reliance on the pragmatic approach, form first principles. In practice, CAPM is also widely used in calculating the cost of equity and in evaluating the performance of managed portfolios. This practice is considered problematic due to various anomalies facing CAPM (Fama and French 2004). As integrating the pragmatic approach with CAPM internalizes the anomalies, immediate applications of the adjusted CAPM are improved estimation of cost of equity and improved evaluation of portfolio performance. This article is organized as follows. Section 1 discusses the importance of informative starting points in decision-making. Section 2 and 3 derive CAPM adjusted for reliance on informative starting points. Section 4 shows how various prominent anomalies are internalized. Section 5 discusses the improved calculation of cost and equity and improved evaluation of managed portfolios with the adjusted CAPM. Section 6 concludes. 1. Reliance on Informative Starting Points Bayesian inference provides a unified framework for making decisions as new information arrives. However, outside of the simplest of situations, exact Bayesian inference is intractable, and must be approximated. Relying on informative starting points that are somewhat incorrect 3 and attempting to adjust them appropriately is a pragmatic solution, which is considered an optimal response of a Bayesian decision-maker facing finite computational resources (Lieder, Griffiths, & Goodman 2013). Evidence of the anchoring-and-adjustment process has been found in brain imaging studies demonstrating that we are hard-wired to rely on informative starting points and then attempting to adjust them (Quo, Zhao, and Luo 2008). It is intractable for anyone to accurately measure all of the risk factors, which is what needs to be done, in order to make the optimal decision. A pragmatic approach is considering the factors that one can assess, and using them to furnish an informative starting point (anchor), and then attempting to adjust the starting point appropriately. Such anchoring-and-adjustment is a robust human decision-making heuristic. Describing the anchoring heuristic, Epley and Gilovich write (2001), “People may spontaneously anchor on information that readily comes to mind and adjust their response in a direction that seems appropriate, using what Tversky and Kahneman (1974) called the anchoring and adjustment heuristic. Although this heuristic is often helpful, the adjustments tend to be insufficient, leaving people’s final estimates biased towards the initial anchor value.” (Epley and Gilovich (2001) page. 1). It is easy to provide several examples of such reliance on informative starring points. When respondents were asked which year George Washington became the first US President, most would start from the year the US became a country (in 1776). They would reason that it might have taken a few years after that to elect the first president so they add a few years to 1776 to work it out, coming to an answer of 1778 or 1779. George Washington actually became president in 1789, implying that, starting from 1776, adjustments are typically insufficient. Another example is the freezing temperature of vodka. People typically know that vodka freezes at a temperature below the freezing point of water (0 Celsius). So, when asked about the freezing point of vodka, they tend to start from the freezing point of water and then adjust downwards to form an estimate. However, their adjustments do not go far enough, and fall short of the right answer (which is -24 Celsius). The adjustments tend to stop once a plausible value is reached leaving the final answer biased towards the starting value (Epley and Gilovich 2006). Hirshleifer (2001) considers anchoring-and-adjustment to be an “important part of psychology based dynamic asset pricing theory in its infancy” (p. 1535). Shiller (1999) argues that anchoring appears to be an important concept for financial markets. This argument has been supported quite strongly by recent empirical research on financial markets. Anchoring-and-adjustment has been found to matter for credit spreads that banks charge to firms (Douglas et al 2015), it matters in determining the price of target firms in mergers and acquisitions (Baker et al 2012), and it also 4 affects the earnings forecasts made by analysts in the stock markets (Cen et al 2013). Furthermore, Siddiqi (2015) shows that anchoring-and-adjustment provides a unified explanation for a number
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