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• W2506866506 abstract "There is a large body of empirical research in accounting and finance documenting that many accounting-based variables predict future stock returns. Perhaps the most well known of these variables is the book-to-market ratio (B/M). B/M has been a key variable in empirical asset pricing since the early 1990s when Eugene Fama and Kenneth French published their now famous (1992) paper, which documented a robust association between future average stock returns, size, and B/M. Factor-based asset pricing models, including the well-known Fama-French three factor model (Fama and French, 1993) have been built around these findings and it is now considered a given that B/M carries information about ‘priced risk’, but as an academic community we are still not sure why. 1Penman's (2016) thought piece titled ‘Valuation: Accounting for Risk and the Expected Return’ (henceforth VARE), which I discuss in the text to follow, is important because it offers potential insights that can help us understand why B/M and other accounting variables may impact stock returns. It does so by considering the way accounting systems measure assets and income and how these systems deal with risk. VARE outlines several important issues in accounting and asset pricing research including implied cost of capital (ICC) estimates, the Vuolteenaho (2002) log-linearization, the connection of expected returns/discount rates to accounting data, and ‘accounting anomalies’. My discussion will touch on many of these points, but I will spend most of my time discussing what VARE calls ‘Accounting for Risk’, and the role of log-linear models in valuation. At the suggestion of Abacus I have brought some of my own research into the discussion. However, I also try to offer suggestions about how the ideas in VARE could be used in future valuation research and try to trace empirical predictions that come from the thought piece. The Feltham and Ohlson (1999) result is important because it offers a way of formally linking accounting numbers to consumption-based asset pricing. Lyle et al. (2013) use this identity to extend Ohlson (1995) and solve for expected stock returns when risk in the economy is time varying. They show that expected equity returns can be expressed as a linear combination of firm characteristics, including: size, B/M, earnings-to-price (E/P), and expected E/P. Their findings show that these accounting-based ratios rationally reveal expected returns within a classic asset pricing setting and suggest that accounting numbers, when combined with market values, reveal priced risk. These results offer some insight into why prior empirical studies have found an empirical relation between accounting-based characteristics and future stock returns. However, the Lyle et al. (2013) results are somewhat unsatisfying because they take accounting numbers as given and do not consider how these numbers are generated from the accounting system that measures them, and hence, their results cannot tell us why the above-mentioned characteristics forecast stock returns. While there is no doubt that residual income models (RIV) and the work of Feltham and Ohlson (1995, 1999), Nekrasov and Shroff (2009), Ohlson (1995), and others have been important in our understanding of the role that accounting numbers play in asset pricing, in the end, they are algebraically replacing dividends in the dividend discount model via the clean surplus accounting identity. VARE points out that these models, which are very much the ‘state-of-the-art’ in valuation, do not consider how accounting systems actually measure income or book values and, indeed, models can be solved that are based on purely random numbers. This lack of a formal connection between accounting systems and valuation models is the central point in VARE because in order for us to understand why accounting numbers forecast returns, one needs to consider the nature of the accounting system that generates those numbers. Moreover, a common and related criticism of RIV is that they do not formally model information, or how investors update their beliefs based on accounting information. The world is fully informed in the above-mentioned papers. This disconnects from much of the information, economics-based research conducted in accounting. As I outline in the next section, the arguments presented in VARE bring traditional accounting-based valuation models closer to approaches commonly employed in information economics. I believe that the most important contribution of VARE revolves around the idea that the accounting measurement system can be thought of as a way of measuring risk. Consider the following: Suppose that a firm is expected to generate a stream of future risky cash flows, C1, C2, … CT. Because these cash flows have not been realized, they are uncertain and the accounting system does not record their values until this uncertainty has been resolved. VARE calls this ‘the realization principal’. As each cash flow is realized, its risk has been resolved and, hence, investors face less uncertainty upon this realization. The cash flows are then either paid out to shareholders or stored in book value. This plays an important role for investors because, if the values recorded in book have largely been resolved of risk, this provides investors with a useful piece of information, the lower bound of the ‘true’ value of the firm. This gives us something similar to the classic RIV. The difference is how one arrives at this equation. Unlike the algebraic clean surplus substitution used to derive the RIV, equation 4 shows that the relation between price and book can arise because of the way investors use the accounting system to determine a lower bound on value. This is because of the way accounting treats risk. We need not invoke clean surplus or specify dividend policy to arrive at this relation; the realization principal essentially ensures a valuation structure similar to equation 4. Here Ft = {xk}k ∈ {0,1,…,t} represents the entire history of firm earnings from which investors set their expectations. Assuming that investors are Bayesian and that by observing a realization in earnings, xt, the variance of their beliefs around future earnings, xt+τ, is reduced. Then, depending on the convexity in f, prices, stock return volatility, and expected stock returns can change in a multitude of ways. For example, if f(xt+τ) has option-like characteristics, the earnings realization that lowers the variance of investors’ beliefs around xt+τ , all else being equal, can actually lower stock prices and increase expected stock returns. (While I do not formally model this scenario in this discussion, a simple example of this is if f(xt+τ) represents a real option to expand the operations of the firm. In such a case, the fair price of the firm would be the assets in place plus the option to expand.) Having established a price equation, we can now examine how accounting information can affect stock returns. If investors are Bayesian and their expectations are updated based on optimal filtering, then their beliefs are a (information precision) weighted average of their prior beliefs and information contained in the realizations of earnings (see, e.g., Liptser and Shiryaev, 1977). A large positive realization (relative to prior beliefs) in earnings increases E[xt|Ft−1] and also impacts the variance around those beliefs. Thus for a fixed Bt−1 and Pt−1, a large ‘earnings surprise’ can have two effects on expected stock returns: 1) The surprise (high current earnings) will rationally be associated with higher future stock returns through E[xt|Ft−1] because this increases investors' beliefs about future income and hence the E/P ratio can rationally be associated with future stock returns; and 2) If this surprise decreases (priced) variance of investors beliefs around xt+τ, this will lead to lower future stock returns because investors believe that the xt+τ is less risky conditional upon observing realized earnings. This simple setting connects well with what VARE argues as a rationalization of the accruals anomaly. High current accruals mean that cash that will be earned in the future (but is not yet realized) contains little risk and hence is not discounted by the market, which leads to lower average future stock returns. Equation 7 tells a similar story. High current accruals lower investors’ expectations of future income, E[xt|Ft−1], because future income has been booked, and hence by equation 7 they expect lower future stock returns. Moreover, if high accruals indicate low risk to future income, then the variance around xt+τ can also be lower, which will reduce the priced risk in E[f(xt+τ)|Ft−1] and hence lower expected stock returns. Because of the close relation between accruals, investment, and growth in net operating assets, the arguments for accruals also hold for the other listed anomalies as well. Clearly equation 7 is overly simple and cannot explain many of the relations we observe in empirical data, but it appears to connect reasonably well with VARE's more traditional approach in trying to rationalize accounting-based anomalies and suggests that there is hope. An important next step in valuation research would be to formalize a model that can be used to test these arguments, which requires formally modelling how the accounting system measures income. A lot of potentially important research can be done in this area, including trying to formalize some of the ideas about how accounting numbers relate to ‘anomalies’ and if these anomalous findings can be rationalized under plausible assumptions. VARE highlights the importance of Miller and Modigliani (MM) (1961) in classic valuation theory and also makes the important point that log-linear models likely violate MM. In this section I discuss log-linear models and some of their potential shortcomings, which are highlighted in VARE. The prior sections outlined linear models, which have many appealing features, but they quickly become intractable when time-varying discount rates are introduced. In their now classic paper, Campbell and Shiller (1988) pioneered a method, a log-linearization, that allowed the price-to-dividend ratio to be expressed in terms of time-varying dividend growth rates and discount rates. The method has been used extensively ever since and is appealing for many reasons. Campbell and Shiller (1988) show that the log-linearization, an approximation, was quite accurate in practice and that working in logs, as opposed to levels, tends to fit empirical data well. However, the Campbell and Shiller (1988) log-linearization requires dividends to be paid, and so could not readily be applied to the cross-section of stocks, many of which do not pay dividends. Several recent studies have found that the empirical performance of log-linear models (measured as the ability to predict future stock returns) has been rather impressive when compared to traditional approaches based on factor models (such as Kelly and Pruitt (2013)) or ICC estimates. The lack of association between future stock returns and factor models as well as ICCs can be considered a failure in validation. Moreover, as VARE points out, even though ICCs are largely based on accounting inputs that do forecast stock returns (book values and earnings), ICCs do not. One potential explanation for this could be the problematic assumption in ICC models, that discount rates are constant through time—an assumption problematic enough that overcoming it was one of the main reasons for Campbell and Shiller's (1988) log-linearizations in the first place. Models that are similar in many regards to ICCs, but relax the constant discount rate assumption, have been shown to have strong out-of-sample associations with future returns. For example, Kelly and Pruitt (2013) use equation 8 as a starting point to derive a model and estimate time-varying expected returns for the market portfolio. Lyle and Wang (2015) use equation 8 to solve a model based on bp and roe and extract time-varying expected returns in the cross-section of equities in US markets and find that their estimates forecast out-of-sample future stock returns up to three years into the future. In a follow-up study, Chattopadhyay et al. (2015) find that a similar model, but with fewer assumptions, forecasts out-of-sample stock returns in 26 out of 29 international markets, whereas factor-based models forecast returns in one out of 29. That country is Pakistan. All of these points are important. However, Lyle and Wang (2015) point out, in footnote 5, that the convergence in bp is not necessarily required, and this is the case only if the expansion point in Vuolteenaho (2002) is the unconditional mean of either the dividend-to-price ratio or the dividend-to-market ratio. If the expansion point is some convex combination of the two ratios, then the approach does not require bp to converge. The convergence of roe to r is also not required in the Vuolteenaho (2002) approach. The only requirement of roe and r is that |roe − r| do not grow faster than k1 discounts them. But given that both roe and r tend to be stationary processes, this is not an unreasonable constraint. One point that was not mentioned in VARE, but I feel is worth discussing, is that, even though the Vuolteenaho (2002) approach does not require convergence in bp or roe to r, it does require firms to pay dividends. I concede that this probably makes little difference empirically, but, for many firms, the approach does not work the way it is laid out—many firms do not pay dividends and, as such, equation 8 does not hold. Chattopadhyay et al. (2015) identify this shortcoming of the Vuolteenaho (2002) approach and show that one can generate a similar equation to equation 8 without the requirement of payment of dividends. The only condition is that the bp must have a finite and time-invariant unconditional mean. An important implication, which Chattopadhyay et al. (2015) point out, is that, if bp satisfies this condition, then growth in book and the growth in market must converge. They test these assumptions in many countries around the world and find compelling evidence in favour of them. Moreover, for the purpose of this discussion piece, I tested these assumptions using data taken from CRSP and Compustat for the company Coca-Cola, which is the company mentioned in the last sentence of VARE. Using annual accounting and stock return data from 1962 to 2012, I conducted two tests: 1) an Augmented Dickey-Fuller test on the B/M; and 2) that the difference between growth in market and growth in book is on average zero. The null of non-stationarity of bp was rejected, and the average difference between annual growth in book and annual growth in market was −0.00265 with a t-stat of −0.01. VARE stresses the importance of MM, and indicates a concern that working in logs may violate MM conditions. I agree that this was probably the case for most log-linear models, however, it is unclear to me that a model must satisfy the MM conditions because the conditions are based on assumptions that may not be realistic and may, in fact, be less realistic than the assumptions underlying log-linear models. My point here is not to disagree with VARE's issues with log-linear models; I agree that log-linear models are far from perfect and leave a lot to be desired. But in my opinion, they do offer some promise and are practically useful because of their tractability and, given this tractability, they may serve as a useful tool in solving models that exhibit some of the traits outlined in VARE. However, to date, they too suffer from the same issues that the traditional RIV do: they are devoid with respect to how accounting numbers are measured, and how accounting deals with risk. VARE discusses many issues in accounting-based valuation, and particularly how accounting systems handle risk. I see a very interesting area of research that follows immediately from the thought piece. VARE conjectures that realizations in earnings reduce risk, but this is potentially a testable conjecture. Nobel prize-winning research has been conducted in the area of variance/volatility estimation and there is a wide range of variance models which are commonly used in both academia and in practice. If VARE's conjecture that earnings realizations reduce risk holds, it stands to reason that earnings, and not just the historical variance of earnings, are related to the variance of stock returns. Moreover, if the accounting system, particularly book values, record assets for which uncertainty is low, one would also expect a relation between B/M and stock returns volatility. Specifically, the arguments in VARE suggest that firms with high bps and firms with high E/P ratios, all else being equal, should also have lower stock return volatility. I believe an investigation of this is important because, as mentioned in the introduction, numerous articles document a positive association between the B/M and various measures of firm profitability, including E/P (Basu, 1977). But if VARE's conjectures are correct, then this implies that low-risk (low-volatility) firms have higher future stock returns. Using stock return volatility in conjugation with stock returns and accounting-based models may help to reconcile, at least at first glance, what would appear to be a contradiction and may shed new light on the puzzling findings in finance that document lower stock returns for firms with higher stock return volatility (e.g., Ang et al., 2006, 2009)." @default.
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• W2506866506 title "Valuation: Accounting for Risk and the Expected Return. Discussion of Penman" @default.
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