3.2.3. Special cases
Table 3.1, Panel A summarizes the Ohlson LID model and its special cases. LED9 is the general Ohlson LID model given by Eq. 12. The models shown in Panel A are the same as the models used in DHS except for the separation of (cox = 0, y x = y x) and (a>x =
Y\ = 0) cases. As DHS stated, the valuation model based on (cox = 0, y x = y x) is theoretically identical to the model assuming (cox = cbx, y x = 0). However, analyst- based RI forecasts are biased practically so that y x when cox = 0 is different from cbx when y x = 0. Note that for the estimation of y x in LID7, OI is defined as analyst-based RI forecast. That is, f x is the estimated slope coefficient from f ta+x = y0 + y ja g ( fta+x) , because vt = f ta+x in this case.
Note also that LID1 is the book value model in which current book value is sufficient for all expected future payoffs, and LID2 is the earnings model in which capitalized current earnings (adjusted for dividends) is sufficient for all expected future payoffs. LID6, which is reported by DHS as a more reliable model than the Ohlson LID model, is the same as the EBO model that assumes 1-year forecast horizon and zero RI growth.
Table 3.1, Panel B summarizes the empirically testable special cases of Eq. 19 used in this thesis. The special cases of the 'intercept-inclusive LID model are defined according to the assumption of OI and/or the restriction of RI and OI persistence parameters (i e., cox and yx). In addition to some combinations of assumptions about
0) and (col — 0, ft — 1) in Panel B. This is because these cases give rise to random walk models with drift so that RI streams are non-stationary. That is, these cases violate the assumption of mean reverting process.
In Table 3.1, Panel B, LID10, LID11 and LID12 are models when OI is ignored in the linear information dynamics, while LID 13 to LID 16 are models when OI is dealt with. LED 16 represents a general 'intercept-inclusive' LID model given by Eq. 19, and LID 10 to LED15 are special cases of LID16. Here, note that d)'Q, y'0 and ft in LED10, LED13, LID 14 and LED 15 except a)'0 in LED 15 are different from the parameters estimated using the above procedures given by Eq. 16, Eq. 17 and Eq. 18. This is because the restriction of cox = 0 and/or ft = 0 is conditional for the estimation of those parameters so that the parameters estimated using the above procedures given by Eq. 16, Eq. 17 and Eq. 18 cannot be employed directly to the corresponding pricing model.
Specifically, in LID 10, LED 13 and LID 14, <£' for year t is the mean of book value- scaled RI using data up to year t (i.e., (*,%,- j ) , because the assumption of cox = 0
makes cb'Q absorb the whole mean value of scaled RI. Similarly, the assumption of
= 0 in LID 13 and LED 15 makes y'Q absorb the whole mean value of scaled OI so that y ' for year t is the mean of book value-scaled OI using data up to year t. Thus, y 0 for
year t in LID 13 is /*.-.) and for year ' in LID15 is
/ 6m )_ s ’J b ,/*_,) - & u (.< /*_,)• Finally> in LID14’ 316 the estimated
Chapter 3. D evelopm ent o f the 'intercept-inclusive' linear information dynamics (LID) m odel an d research design
less cbJ times book value (i.e., v, = f ta+x - S'0 tbt ).
3.2.4. Some EBO models
In addition to the LID models, some EBO models are considered in this study. Although Frankel and Lee (1998) and Lee et al. (1999) show the evidence that the choice of alternative forecast horizon has little effect on the results, I use three EBO models based on different forecast horizon (T) using I/B/E/S analysts' consensus forecasts for one- year ( f M ) to three-year ( f t+3) ahead earnings.31 Here, after the explicit forecasting period, terminal value is assumed to be the present value of year-71 residual income in perpetuity. Then, I also consider three more EBO models that allow for growth in the post-horizon period. Note that EBOl is the same as LID6.
The requirement of estimating terminal values usually applied in the EBO approach is not only from earnings power (i.e., growth in the post-horizon period) but also from measurement error consistently occurred in the measurement of earnings and book values o f equity (Penman, 1997). In other words, a terminal value is needed to correct both errors occurring i) by truncating the horizon and ii) when forecasting attributes up to the horizon. The error arising by truncating the horizon is of course because forecasts of attributes beyond the horizon are omitted in the truncation. On the other hand, the error in the forecasts to the horizon is due to the accounting rules that allow for the
31 Actually, f x, f t+2, and f t+3are earnings forecasts for current fiscal year, next fiscal year and next but one fiscal year, respectively.
differences on recognition and measurement of forecasts. Such consistent measurement error prevents future RI streams from converging to zero and is usually the result of conservative accounting consistently applied (Sougiannis and Yaekura, 2000). Thus, it is essential to specify terminal value that correctly captures the effect of a firm's specific economic fundamentals including the degree of conservatism. Myers (1999a) argues that many reversals of accounting conservatism come about within 'terminal income' that arises when companies are taken over, and ignoring this 'terminal income' when estimating terminal value could be a source of unreliable intrinsic value estimates based on the EBO approach. I leave the issue of terminal value specification in future research, and just consider 6 EBO models generally adopted in the earlier studies.
EBO models assuming no growth in the post-horizon period: f M - rb, i V , = b , + t+l /+1 v = b , + — — rL - + L il— rL ' ' R rR r , , /r+1 r b t . f ’+2 r b M . f t * 3 r b M V' = b' + - ^ + R l - + rR> EBO models assuming growth in the post-horizon period:
f M ~ rb, V , = b , + (■r - g r) T/ , ~ rb> , f<+2-rb<« r, = b, + — ^ R (r - g r)R / , +i ~ rb, f M - rbHl V ‘ = b ' + R ^ + (EBO 1) (EBO 2) (EBO 3) R 2 { r - g r)R- (EBO 4) (EBO 5) (EBO 6)
Chapter 3. D evelopm ent o f the 'intercept-inclusive' linear information dynamics (LID) m odel an d research design
where f t+. is z-year ahead analysts' consensus earnings forecast, bt+. is /-year ahead estimated book value, and gr is the estimated growth rate of RI in the post-horizon period. EBO 1 (EBO 4), EBO 2 (EBO 5) and EBO 3 (EBO 6) are respectively 1-year, 2- year and 3-year horizon model.
3.2.5. Pricing test o f competing valuation models
After measuring persistence parameters, the competing valuation models will be compared in order to show which provides the value estimates that accord most closely with current stock prices. At this stage, value estimates from Ohlson-type LID models, 'intercept-inclusive'-type LID models and EBO models will be computed and compared. It is o f interest to examine whether and where the 'intercept-inclusive' LID model brings significant benefit over its special cases and other models. In contrast, if there is clear evidence that the simpler EBO model produces more reliable value estimates in all cases, linear information dynamics still need to be modified.
In order to run 'horse races' between different valuation models, I contrast the reliability of value estimates from the alternative models in terms of three performance dimensions. They are the bias metric, the accuracy metric and the explainability metric. The bias (the accuracy) is defined as the signed (absolute) difference between the value estimate and the current stock price, scaled by the current stock price, while the explainability is defined as the ability of value estimates to explain cross-sectional variation in current stock prices. Therefore, under the bias, the accuracy and the explainability metrics, value estimates with, respectively, the closest signed forecast
errors to zero, the smallest absolute forecast errors and the highest OLS R2 are the most reliable. The accuracy and bias of an estimated value can be of great concern to an investor who wants to determine whether to buy, hold, or sell a firm's stock, to an analyst who wants to provide, along with his/her earnings forecasts, a stock recommendation, to an investment banker who wants to determine the offer price of an IPO, or to a researcher who wants to use such a price in examining a specific research question (Sougiannis and Yaekura, 2000)
Given the fundamental firm value, the signed forecast error and the absolute forecast error, scaled by stock prices, can be calculated as in Eq. 20 and Eq. 21. Furthermore, the
9 • • •
regression of stock price on value estimate is used to get R as the explainability metric
where FEsp is the forecast error of stock prices, AFEsp is the absolute forecast error of stock prices, Ptc,n is the observed stock price at n months after the end o f the fiscal year t, and Vt is the fundamental value estimated by the Rl-based valuation model for year t. Note that in order to make comparable the value estimate and the stock price, I use stock price at a few months (usually 3 months) after the fiscal year end rather than stock price at the fiscal year end.
(Eq. 22).
(Eq. 20) (Eq. 21) (Eq. 22)
Chapter 3. Developm ent o f the 'intercept-inclusive' linear information dynamics (LID) m odel an d research design
Table 3.1: The competing valuation models
Panel A: The Ohlson model and its variants When 'other information' is ignored
LID1: 0)x = 0 £ , f c ] = o V = b , LID2: cox = 1 Vt = b , + - x ° = — x, -rf, r r LID3: cox - cbx E t [x;‘+X] = d j xx “ Vt = b t + 0)1 x at ( R - & x) LID4: 3 ii E t \ ? ? + x ] = a { x t V < = b t + x “
When 'other information' is incorporated
LID5: E , h , ] = / , : , o ' II o" II « + + -c r ii LID6: (cox= 1 , 7, = 0) or ( <Wj = 0 , y x= 1) y , = - f Mr LID7: (o)i = 0 , y x= y x) ’ , - 6 , ' LID 8: (0) x = cbx , y x =0) v‘ = b' + (R - s / ' :' LID9: (g>,= &x , y x= y x) rr » . ~ ® \ Y \ a . R f a r , — Ot + * ^ ^ * \ At 1 ~ \ s r> * \ Jt +l ( R-cQx) ( R - y x) ( R- a>x) ( R - y x)
Table 3.1 (continued)
Panel B: The 'intercept-inclusive' LID model and its variants - scaled by book value When 'other information' is ignored
LID 10: cox = 0