value estimates is very sensitive both to the assumed cost of equity and to the assumed rate of growth in the scaling variable. This is not surprising since the approach involves capitalising the mean RI term as a growing perpetuity (see Chapter 3 for details).
Although Table 4.5 shows that inclusion of intercept terms can significantly improve bias in LID-based value estimates, it provides little evidence of improvement in the accuracy of such estimates. Particularly, inaccurate value estimates are observed for the 'intercept-inclusive' model for the lowest assumed cost of equity (10%) and the highest assumed rate of growth (6%). Where the cost of equity is higher (14% and year- specific), the level of accuracy of the 'intercept-inclusive' model is very similar to that of the intercept-exclusive model. One explanation concerning the reasons for the lack of improvement in overall valuation accuracy could be the increased dispersion in valuation errors arising from capitalisation of mean effects as perpetuities. For example, for the year-specific cost of equity, the dispersion in the valuation errors for the intercept-exclusive model is 0.79, while for the 'intercept-inclusive' model it is 0.91 for BG = 1.0, 0.93 for BG = 1.02, 0.96 for BG = 1.04 and 1.01 for BG = 1.06. A similar pattern is observed for other assumed costs of equity. Particularly high dispersion in valuation errors is observed where the cost of equity is assumed to be 10% and BG is assumed to be 1.04 or 1.06.
However, the lack of improvement in overall valuation accuracy mainly arises from the poor applicability of the 'intercept-inclusive' LID approach for low stock price firms. In other words, although recognition of intercepts improves accuracy in one respect by shifting large negative valuation errors closer to zero for moderate and high stock price
firms, it reduces accuracy in another respect because it also shifts valuation errors that are close to zero to be large positive valuation errors for low stock price firms. Interestingly, upward shifting occurs very consistently regardless of firm-years, and the distribution of valuation errors is highly related to stock price. Figure 4.1 illustrates this relationship graphically. Based on a book value growth rate of 4% and year-specific discount rates, I rank signed and absolute valuation errors by stock price and make 100 portfolios. Then, I depict the mean valuation errors (Panel A) and the mean absolute valuation errors (Panel B) of each portfolio. There are several noteworthy results in Figure 4.1. First, the bias pattern of the models based on the Ohlson LED and the 'intercept-inclusive' LID approaches is peculiar compared to the model based on the 1- year forecast horizon EBO approach. Valuation errors based on the former two models are negatively correlated with stock prices, whilst those based on the EBO model are unlikely to be correlated with stock prices. Second, the pattern of biases arising from the 'intercept-inclusive' LID approach is very similar to that arising from the Ohlson LED approach, but its biases are consistently shifted upward regardless of stock prices. Note that in the area of low stock price, the 'intercept-inclusive' LID approach gives rise to large positive bias, and is dominated by the Ohlson LID approach. Third, because of the poor applicability of the 'intercept-inclusive' approach for low stock price firms, its overall accuracy does not improve significantly compared to that based on the Ohlson LID approach. Panel B confirms this phenomenon. In the area of low stock price, the Ohlson LID approach dominates the 'intercept-inclusive' LID approach in terms of accuracy. Finally, a potentially important research issue arises from these results. Figure 4.1 just shows the different applicability of each valuation model along the dimension of stock price. One could also use other firm-specific characteristics (e.g., M/B ratio, firm
Chapter 4. Reliability o f the 'intercept-inclusive' linear information dynamics (LID) model: U.S. evidence
size) in order to examine which firm-specific characteristics are determinants of a model's applicability.
In order to examine the reason why the 'intercept-inclusive' LID approach does not improve the overall accuracy considerably, I do a complementary test. This is to examine the effect of conservative accounting on value estimates. I do this by partitioning the pooled sample into 5 groups according to the market-to-book (M/B) ratio, which is often used as a proxy indicating the degree of conservatism. Then, I re- estimate LID parameters for each portfolio and feed them into pricing formula in order to get value estimates.44 Table 4.6 shows bias and accuracy statistics when LID parameters are estimated separately for 5 groups partitioned by the M/B ratio. We see here that considering conservatism when constructing value estimates seems to improve the accuracy. Figure 4.2, Panel B also shows that in many areas of stock price, value estimates based on separate parameter estimation are more accurate than those based on pooled parameter estimation. These results encourage the possibility for further improvement of the overall accuracy of the 'intercept-inclusive' LID-based value estimates. That is, the elaborate application of the 'intercept-inclusive' LID approach could improve the accuracy more. I leave this to further research.
44 In order to re-estimate LID parameters, I actually classify firms rather than firm-years into 5 groups. For this, I rank all firms by the mean value of M/B.
4.3.3. Effects o f winsorising and trimming
For the main results reported above, I trim the most extreme 1% cases of regression variables when LID parameters are estimated, and retain all such outliers for the purpose of constructing value estimates. In this sub-section, I investigate the effects of winsorising and trimming on LID parameters and value estimates by adopting some other approaches to dealing with extreme observations.45 First, I delete outliers for the purpose of LID parameter estimation as for the main results (i.e., trimming the most extreme 1% regression variables), but construct bias and accuracy statistics after deleting the 1 % most extreme values of FE and AFE, respectively. The purpose of this complementary test is to examine how much the overall bias and accuracy are affected by deleting extreme outputs (i.e., FE and AFE). Table 4.7 shows that the improvement in the overall accuracy arising by deleting extreme outputs is not much. Especially, the relative reliability (bias and accuracy) of the three models is qualitatively similar to the main results. One more interesting point is that the most extreme biases arising from the application of the Ohlson and the 'intercept-inclusive' LID models are positive. Of bias values deleted according to the 1% most extreme criteria, positive values are over 95% for both models, while they are about 35% for the 1-year forecast horizon EBO model.
Second, I use various trimming and winsorising criteria when estimating LID parameters, but use untrimmed (when trimming criteria are used) and winsorised (when winsorising criteria are used) data when constructing value estimates. Criteria used to
45 For this supplementary test, only year-specific cost o f equity capital is used. Data are scaled by book value as for the main results.
Chapter 4. Reliability o f the 'intercept-inclusive' linear information dynamics (LID) model: U.S. evidence
deal with extreme outliers are as follows: no trimming/winsorising, trimming 1%, trimming 2%, trimming 5%, winsorising 1%, winsorising 2%, and winsorising 5%. When trimming criteria are used, I truncate the most extreme cases of regression variables (i.e., scaled per-share data) at the stage of LID parameter estimation. On the other hand, the winsorisation is done at the outset by reference to scaled variables in their most primitive available form, and the winsorised values are then carried through the various stages of the analysis.
Table 4.8 shows RI and OI parameters estimated using various trimming and winsorising criteria. There are some points to note. First, the selection of trimming or winsorising criteria makes RI and OI persistence parameters quite different. Second, even in the same trimming or winsorising criteria, the percentage of outliers deleted or winsorised makes RI and OI persistence parameters sensitive. Third, even though the magnitude of RI and OI parameters are sensitive to the trimming and winsorising criteria, the statistical inferences from those parameters are the same: (i) RI intercept is negative (except for no trimming / winsorising criteria) and statistically significant, and OI intercept is positive and statistically significant, (ii) RI and OI persistence coefficient is greater than zero and less than one, and statistically significant.
From feeding these different parameters to pricing models, I now examine how much these different parameters affect the overall bias and accuracy. Table 4.9 summarizes median and mean statistics for both bias and accuracy. First, bias and accuracy statistics arising from the Ohlson LID approach are not sensitive to different LID parameters estimated using different trimming and winsorising criteria, and show large negative
bias and low accuracy consistently. This indicates that RI and OI persistence parameters per se together with current RI and OI seem to fail to capture 'unrecorded goodwill'.
Second, bias and accuracy statistics arising from the 'intercept-inclusive' LED approach are relatively sensitive. However, the relative reliability of competing value estimates produced by adopting different trimming and winsorising criteria does not differ substantially from the main results (i.e., results with criteria of trimming 1%). This supplementary test confirms the contribution of the 'intercept-inclusive' LID approach to equity valuation, especially in the context of significant elimination of large negative bias produced by applying the Ohlson LID approach. However, as discussed earlier, further research is needed for the improvement of the overall accuracy.
4.4. Conclusions
The Dechow, Hutton & Sloan (1999) (DHS) approach to the empirical application of the LID approach to residual income-based valuation is a novel one. It allows an empirical application of Ohlson's (1995) model of the joint role of accounting information and 'other information' in the determination of share prices. Motivated by the magnitude of the bias reported by DHS, I focus on one potential source of this bias. I explore the possibility that the large downward bias reported by DHS may be due in part to their non-recognition, following Ohlson (1995), of information about the mean value of expected future residual incomes contained in the intercept terms of the residual income generating process. In order to investigate this issue, I augment the DHS procedure such as to recognise all intercept terms from the residual income generating process.
Chapter 4. R eliability o f the 'intercept-inclusive' linear information dynamics (LID) model: U.S. evidence
Analysis based on the augmented procedure suggests that the valuation effects represented by such intercept terms could easily be of an order of magnitude comparable to, or larger than, that of the bias reported by DHS. This is confirmed by empirical analysis using a U.S. data set similar to that employed by DHS. I note, however, that biases in value estimates from such an 'intercept-inclusive' procedure are very sensitive to assumptions about the cost of equity and about growth. I also note that the 'intercept-inclusive' approach does not outperform the intercept-exclusive approach in terms of accuracy of value estimates.
There are, of course, many ways in which the approach could be further augmented in order to improve the understanding of the joint role of accounting information and 'other information' in the determination of share prices. Such augmentations could incorporate such factors as time- and firm-specific estimation of the cost of equity, of expected growth and of LID parameters. These are potentially interesting avenues for further research.
Figure 4.1: Distribution o f valuation errors arising from 3 different models Panel A: Signed valuation errors (FEt = (Vt - Ptc’3) / Pt0,3)
0.6 in g 0.4 in c o ra ra > •a a> c 0. 2 'Intercept-inclusive' LID Ohlson LID - 0 . 2 - 0 . 4
1-year horizon EBO with zero RI growth
- 0.6
Stock Price
Panel B: Absolute valuation errors (AFE. = V - PY t 1 tc,3 /pC )
'Intercept-inclusive' LID t=
U J
c
o 1-year horizon EBO with zero RI growth