Equity Value as a Function of (eps1, eps2, dps1, bvps, beta): Concepts and Realities. Discussion of Ohlson and Johannesson
讨论Ohlson和Johannesson提出的基于异常盈利增长的新估值模型（OJ-m），该模型优于剩余收益模型，强调每股收益在解释股价中的重要作用，并指出账面价值影响很小。
Equity valuation plays a central role in accounting and finance research as well as in business and capital markets. Valuation helps to understand what is the firm value and how it is driven by firm fundamentals. It helps to determine expected future returns and cost of capital implied by stock prices. It helps to make investment decisions and improve the efficiency of capital allocation by identifying mispricing. Ohlson and Johannesson (2016) focus on the first issue of how valuation models and model inputs help explain stock prices. In particular, they propose and test valuation based on abnormal earnings growth (AEG). The paper also critiques residual income valuation (RIV). The issue is important since the two valuation approaches play a central role in research and textbooks. In examining AEG-based valuation, prior research has focused on the OJ model (Ohlson and Juettner-Nauroth, 2005) as a practical implementation of the more general AEG framework. Research finds that the OJ model has several theoretical advantages over RIV (Ohlson and Juettner-Nauroth, 2005; Ohlson and Gao, 2006) but underperforms RIV in terms of valuation accuracy (Penman, 2005, Jorgensen et al., 2011). It appears that one of the main reasons for the OJ model's underperformance is the assumption that forecasted abnormal earnings will continue to grow after the forecast horizon (at the long-term growth rate in GNP). The result of this assumption is that any noise, bias, or transitory component in the AEG will have a large impact on value estimates. Another source of greater valuation errors of the OJ model can be traced to its double-capitalization feature. The practical outcome of the double capitalization is that any noise in the CAPM of Fama-French cost of equity estimates—which are notoriously noisy—will have an exponentially larger impact on value estimates in the OJ model than under the simple capitalization in RIV or the FCF model. The main contribution of the paper is that it develops and tests a new model (henceforth referred to as the OJ-m model) to examine the validity of AEG concepts. The OJ-m model is closely related to the OJ model but differs in several aspects that address the above-mentioned practical issues of the OJ model. Instead of growing, AEG fades to zero at a relatively high rate. Instead of anchoring on capitalized forward earnings, the model anchors on forward earnings times the typical forward price-to-earnings (P/E) ratio. And instead of directly applying noisy estimates of the cost of equity, the model estimates valuation weights using stock price data. In a sense, the OJ-m model combines features of a purely theoretical model like OJ and the use of market multiples such as the forward P/E multiple. An important advantage of the OJ-m model is that, by avoiding the implementation issues of the OJ model, it allows the researcher to focus on testing the role of abnormal earnings growth in determining stock prices. The empirical analysis of the paper revolves around a comparison of the OJ-m model and RIV. Ohlson and Johannesson show that the OJ-m model outperforms RIV by producing value estimates that are closer to observed prices. The paper also shows that even though book value seemingly plays a key role in RIV by serving as a valuation anchor and determining residual earnings, in reality the effect of book value on RIV value estimates as well as actual prices is very small. While this finding does not invalidate RIV from an empirical point of view, it calls into question the conceptual role of book value in RIV. Furthermore, the paper shows that in contrast to book value, eps1 and eps2 are important in explaining stock prices. The findings are in line with the fact that financial analysts and the media refer to earnings and earnings growth multiples much more often than price-to-book (P/B) multiples. The paper also shows that the effect of expected dividends and the CAPM beta on stock prices is generally consistent with the valuation theory. The role of eps1 is what most significantly differentiates the OJ-m model from RIV. While RIV value estimates put only very small weight on eps1, the OJ-m model predicts that eps1 plays a significant role in explaining stock prices. The results of the analysis of actual stock prices are consistent with the latter. In fact, the coefficients on eps1 and eps2 are remarkably consistent with the predictions of the OJ-m model and inconsistent with those of RIV. This finding is the single strongest support in favour of the OJ-m model. RIV: Expression (1) for RIV leads to the following observations. First, as Ohlson and Johannesson point out, although book value is commonly viewed as the RIV's valuation anchor, the weight on bvps is actually small and negative since typical gRIV ranges from 0–3%. In fact, even if RIV is a perfect representation of reality but the average growth in residual earnings is zero, the average weight on book value is exactly zero. Based on the study's results for 2013, the implied gRE = (−coefficient on bvps0)/(coefficient on eps2) = 0.10/33.7 = 0.3%, which certainly falls into the range of reasonable values of gRE (small gRE also makes sense given the optimistic bias in eps2 and the sample of relatively mature firms). The point that book value is not important in explaining stock prices does not invalidate RIV but is certainly not commonly appreciated in the literature. 1Second, if one takes the coefficient on eps2 as a benchmark, the predicted coefficient on dps1 is very similar in RIV, the OJ model, and the OJ-m model since 1/m ~ r. Third, as a reasonable special case in which gRIV is zero and the relatively small term r*dps1 is ignored, one obtains the simple benchmark VRIV = eps2/((1 + r)r), which Ohlson and Johannesson show performs very well and similarly to the RIV model. The good performance of this reasonable special case does not invalidate RIV, just as a good performance of the PEG model would not invalidate the OJ model. Where RIV fails is in its prediction that eps1 and hence short-term growth, STG, are largely irrelevant. The coefficient on eps1 equals the coefficient on bvps0 and is economically small compared to the coefficient on eps2. 2The empirical findings in the paper strongly reject this prediction: the magnitude of the weight on eps1 is actually comparable to the weight on eps2 and much greater than that on bvps0. OJ: In contrast to RIV, the OJ model puts zero weight on book value and much larger weight on eps1 and hence earning growth. In fact, expected earnings growth, eps2–eps1, is the main driver of value since gOJ*eps1 and r*dps1 are relatively small for a typical dividend level and a commonly assumed growth parameter gOJ of 3–5%. Earnings growth is double capitalized, that is, multiplied by 1/(r(r – gOJ)), to obtain firm value. Since earnings growth is essentially a flow-in-flow variable, the first capitalization converts it to a flow variable and the second capitalization converts it to a stock variable–firm value. The heavy dependence on expected earnings growth and double capitalization makes theoretical sense but poses an empirical challenge. First, while forecasted earnings levels are typically uncertain, noisy, and biased, forecasted earnings growth is even more uncertain, noisy, and biased. As Ohlson and Johannesson note, there is a large optimistic bias in the analyst forecast of earnings growth. Second, the double capitalization makes the impact of any noise and bias exponentially larger. For a typical cost of equity of 9% and gOJ of 3%, 1/(r(r – gOJ)) is about 185. Furthermore, the well-known noise in the CAPM cost of equity is also magnified by the double capitalization. Because of these empirical challenges, the direct applications of the OJ model have enjoyed only modest success. OJ-m: The OJ-m model differs from the standard OJ model in three respects. First, in contrast to a small positive growth in AEG, the OJ-m model postulates that abnormal earnings growth will decline at a certain fade rate or contraction parameter, gOJ-m (=1 – G in Ohlson and Johannesson's notation), which is estimated to be about −20%. Second, the OJ-m model introduces a new parameter, m, which replaces the capitalization parameter, 1/r, and is interpreted as a typical forward P/E ratio. The new parameter adds an additional degree of freedom that allows a greater flexibility in how earnings and earnings growth map into stock prices. Third, in contrast to RIV and the OJ model, the model parameters of the OJ-m model are not directly derived from first principles but obtained by fitting the model to stock price data. These changes successfully resolve the empirical issues of the OJ model. First, the fade rate mitigates the effect of noise and optimistic bias in forecasted earnings growth. Replacing the growth rate with a fade rate has an interesting implication for the asymptotic growth in earnings. In the OJ model, a sufficiently high dividend payout guarantees that earnings growth, epst+1/epst, converges to gOJ, which does not depend on risk or payout ratio (Ohlson and Juettner-Nauroth, 2005). In the OJ-m model, earnings growth converges to r – (1/m)*(Payout Ratio), which, in an intuitive way, increases with risk and decreases with the dividend payout ratio. Second, assuming a typical cost of equity of 9%, gOJ of −20%, and m of 14, the effective capitalization factor 1/(1/m)(r-gOJ-m) is about 48, which is a substantial reduction from 185 for the OJ model. The smaller capitalization factor leads to a lower sensitivity of firm value to the noise and bias in the valuation inputs. Finally, using fitted parameters instead of the direct application of the CAPM cost of equity substantially reduces the sensitivity of value to the noise in the CAPM beta. In contrast to RIV, the OJ-m model predicts a significant role of eps1 and hence earnings growth. Specifically, the OJ-m model predicts that the magnitude of the weight on eps1 is somewhat smaller but comparable to that of eps2 (−coefficient on eps1/coefficient on eps2 ~ 0.8). The empirical findings are very much consistent with this prediction. In other respects, the empirical differences between RIV and the OJ-m model are less striking. The goodness-of-fit metrics are somewhat better for the OJ-m model than for RIV. The weight on dps1 is consistent with both models. The weight on bvps0 is consistent with the RIV's prediction but is economically small. To be fair to RIV, it should be noted that the model has an impressive list of accomplishments, most of which cannot be not erased by a single paper. Many studies use RIV to explain future stock returns. Research finds that value-to-price ratios based on RIV reliably predict the cross-section of stock returns as well as returns at the market level (Frankel and Lee, 1998; Lee et al., 1999). RIV's ability to predict returns has been documented for a broad population of firms in different countries and time periods; it has also been documented using different measures of expected earnings—analyst forecasts, statistical forecasts, and past earnings as a proxy for expected earnings. RIV has been used in many different forms in the accounting and finance literature. A number of finance studies use RIV concepts to decompose book-to-market (B/M) ratios and explain the cross-section of stock returns. Some of these studies refer to earnings as cash flows and use past or future earnings instead of analyst forecasts. Two key ingredients of the RIV model—the B/M ratio and ROE—are useful in predicting the cross-section of stock returns and their time variation (Lyle and Wang, 2015). RIV has also been successfully used to measure implied cost of equity for US and international firms and to test asset pricing models (Gebhardt et al., 2001; Lee et al., 2009). Regarding the valuation used in practice, there seems to be a gap between what is used and what works. Most analyst reports mention earnings multiples and analysts' target prices, and stock recommendations are typically based on valuation heuristics such as P/E and PEG ratios rather than RIV (Bradshaw, 2002; Asquith et al., 2005). If the analysts' goal is to boost investor confidence by showing that firm stocks are fairly priced, then the finding in the paper validates analysts’ focus on earnings and earnings growth multiples. If, however, the purpose of analysts’ target prices and buy/sell recommendations is to provide insight about future investment performance, then the key question is whether the valuation approach predicts future stock returns. Here, research finds that the return predictability of analysts’ target prices and stock recommendations is significantly higher when analysts appear to be using RIV and lower when using earnings and earnings growth multiples (Bradshaw, 2004; Gleason et al., 2013). Although the OJ-m model shows impressive results in explaining stock prices, some questions remain open. As the authors note, the analysis is a case study of mature firms in two recent years. Sample firms have positive eps1 and short-term growth. The extent to which the model is successful when applied to a broader population of firms across different market conditions remains to be examined. Also, one of the most common applications of valuation in research and practice is to explain and predict stock returns. In this regard, for the OJ-m model to supplant RIV, it needs to predict stock returns better than RIV. Relatedly, it is useful to examine the role of the OJ-m model's key ingredients—expected earnings and earnings growth—in predicting future returns. Finally, the current implementation of the OJ-m model is based on market multiples rather than directly using forecasts and discount rate as inputs in the valuation formula, as is typically done in the classroom and in research. To apply the OJ-m model in this direct way, one needs to decide what the model parameters should generally be and why. Should gOJ-m of −20% and m of 15 be used for all firms and years? Can one derive the value of these parameters based on fundamentals, for example, the historical dynamics of expected earnings growth? What is the role of the LTG forecast, which is commonly used in valuation research and practice?