Empirical Results

4.3.1. Scaling by stock price

Purely in order to facilitate comparison with the study by DHS, I first report in Table 4.3 bias and accuracy statistics for value estimates using parameters obtained from price-scaled data. I recognise that scaling by price within an 'intercept-inclusive' value estimation procedure causes price to become an input to the value estimate. Such a procedure is not to be recommended as a means of estimating intrinsic value, and I include these results purely for the purpose of making the connection between this study and that by DHS. Table 4.3 reports bias and accuracy statistics for value estimates relative to price, for a constant assumed cost of equity of 12% (as used by DHS). Bias is

42 The significant difference revealed here between the expectations o f RI implied by analyst earnings forecasts and the RI realizations implied by the history o f earnings suggests that it is unwise to infer RI expectations from the history o f RI as recorded in archival databases. This problem could be due in part to bias in analyst earnings forecasts. Such bias is suggested by Table 4.2, which reports that the mean and median o f analyst-based RI forecasts for 1977-1995 (8.3% and 1.1%) exceed those ofR I realizations for 1977-1995 (2.2% and -0.7%). The existence o f such a bias is confirmed by a direct comparison o f analyst earnings forecasts with matching realized earnings for 1977-1995. Another potential contributory factor to the unreliability o f archival databases as sources o f expectations concerning RI is the possibility that the history o f RI, as reflected in those databases, is downward biased. Myers (1999a) argues that many reversals o f accounting conservatism come about within 'terminal income' that arises when companies are taken over, but that this 'terminal income', and its (normally positive) associated RI, is not reflected in the archival databases.

measured by reference to the median and mean of FE, and accuracy is measured by reference to the median and mean of AFE. I report results in respect of value estimates derived from (i) the intercept-exclusive approach (i.e., the Ohlson LID approach) employed by DHS and (ii) the 'intercept-inclusive' approach, using four assumed expected rates of growth in the scaling variable (0%, 2%, 4%, 6%).

For comparative purposes, I also report beneath my intercept-exclusive mean bias and mean accuracy statistics the corresponding figures reported by DHS. My statistics (- 0.214 and 0.454) are similar to those reported by DHS (-0.259 and 0.419). It is notable that the incorporation of intercept terms eliminates the substantial negative bias (median 32.2%, mean 21.4%) that is present in the intercept-exclusive value estimates. Focusing on the results where the median of FE is used to measure bias, a small positive bias of less than 10% is observed for assumed growth rates of 0% and 2%, whilst more substantial positive biases of 15.6% and 30.1% are observed for assumed growth rates of 4% and 6% respectively. The use of the mean of FE to measure bias gives rise to a similar pattern, although the magnitudes of the estimated positive bias are larger. I also note that inclusion of intercept parameters has substantially less impact on the accuracy statistics than on the bias statistics.

4.3.2. Scaling by book value

As noted earlier, an 'intercept-inclusive' valuation procedure based on price-scaled data involves circularity, as price becomes an input to the valuation model. Therefore my main results are based on book value-scaled data. Table 4.4 reports LID parameter

Chapter 4. R eliability o f the 'intercept-inclusive' linear information dynamics (LID) model: U.S. evidence

estimates derived from pooled (time series and cross-sectional) data for the periods 1977-1995. There are several points to note here. First, with the exception of the case in which cost of equity is assumed constant at 10%, the co0 parameter is negative, which suggests that, for these cases, the average value of the scaled RI used in deriving the co0 and cox parameter estimates are negative. Second, the col parameter estimates are all in the region of 0.60, which is similar to that reported by DHS (0.62) on the basis of price- scaled data.43 These estimates are rather higher than that reported by Myers (1999b) (0.234) on the basis of time series data. Third, estimates of y Q are all highly significant and positive, in the region of 0.025 (Panel C). The positive sign of y 0 implies that the average value of the scaled OI used in deriving the y 0 and y x parameter estimates, as reported in Table 4.2, is positive (i.e., that analyst-based forecasts of scaled RI tend to be higher than forecasts based on the parameters of the univariate model Eq. 4). Fourth, OI persistence parameters ( y x) are of a similar magnitude to RI persistence parameters (a>x), but are rather higher than the corresponding OI persistence parameter estimate of

0.32 reported by DHS on the basis of price-scaled data where the OI intercept parameter is ignored in the definition of OI. Note that for the application of the Ohlson LID approach, y x in Panel B, not y x in Panel C, is used.

Bias and accuracy statistics for value estimates constructed on the basis of data scaled by book value are reported in Table 4.5. As in Table 4.3, four assumed rates of expected

43 However, cox parameters are very sensitive to the trimming or winsorising criteria. See Section 4.3.3