Forecasts Based on Extrapolative Statistical Models Our discussion focused only on analyst forecast errors, not on how ana-

Forecasts Based on Extrapolative Statistical Models Our discussion focused only on analyst forecast errors, not on how ana-

lysts develop their forecasts. Some analysts use the techniques of funda- mental analysis. Cragg and Malkiel in their assessment of analysts forecasts in late 1968 found that most analysts projected future earnings based on a linear extrapolation of recent trends in earnings. 18

Today, some analysts use statistical models to extrapolate future earnings. The models range from very simple regression models in which time is the explanatory variable and earnings per share is the dependent variable to much more sophisticated time series statistical models. For example, in the simple model, the equation that is estimated to forecast EPS for time period t is:

EPS for time period t = a + b Time

where a and b are the parameters estimated using regression analysis. The above model assumes a linear relationship between EPS and time. Nonlinear relationships can also be estimated.

An example of a time-series of EPS for a company is shown in Exhibit 23.5, with EPS for the Crane Co. shown in Panel A for the 1983–1997 period. A time-series linear trend is estimated and shown in Panel B. This linear time-trend captures the general trend of Crane’s EPS, but appears to be ill-fitting starting in 1990. A better fitting time- trend is found using a nonlinear relationship (specifically a polynomial time trend), as shown in Panel C.

Other statistical models use previous period’s EPS as the explana- tory variable in the model. For example, the forecasting model can be formulated as:

EPS for time period t=a+b × (EPS for time period t-1) Relationships in which EPS in a future period is assumed to depend on

EPS in one or more previous periods are called autoregressive models. Often the data used in forecasting EPS are time and historical EPS of the company, but it is critical that EPS be adjusted to reflect changes in accounting requirements. For example, an analyst who used a statisti- cal model would want to adjust previously reported EPS based on pri- mary, diluted, or fully diluted EPS for the new reporting requirements.

18 J. G. Cragg and Burton Malkiel, “The Consensus and Accuracy of Some Predic- tions of the Growth of Corporate Earnings,” Journal of Finance (March 1969), pp.

FINANCIAL STATEMENT ANALYSIS

EXHIBIT 23.5 Earnings per Share for Crane Co., 1983–1997

Panel A: Actual Earnings per Share

Panel B: Linear Trend Fit to the Earnings per Share

Earnings Analysis

EXHIBIT 23.5

(Continued) Panel C: A Nonlinear Trend Fit to the Earnings per Share

Source: Earnings per share figures are from the Value Line Investment Survey, var- ious issues

Forecasting based on trends of EPS can be hazardous and does depend on the particular model used to capture the trend in EPS. Con- sider the Crane Co. example in Exhibit 23.5. If a forecast for 1998 EPS is made from the linear trend, EPS are forecasted to be around $1.20. If, on the other hand, the nonlinear trend is selected, the EPS forecast would be much higher, over $1.60 per share.

The question is, how good are EPS forecasts based on extrapolative statistical models compared to analysts’ forecasts based on fundamental analysis? There is an extensive literature that supports the view that analyst forecasts do not outperform forecasts based on naive extrapola- tive statistical models. But there are some studies that do suggest superi- ority because of the advantages that analysts have in utilizing more

current information. 19 The preponderance of the evidence, however, cer- tainly supports what two researchers found back in 1972 which still

19 For an overview of this literature, see T. Daniel Coggin, “The Analysts and the In- vestment Process: An Overview,” in Frank J. Fabozzi (ed.), Managing Institutional

Assets (New York, NY: Harper & Row, 1990).

FINANCIAL STATEMENT ANALYSIS

holds, “... mechanical techniques have been shown to do about as good

a job of forecasting earnings as do security analysts.” 20 Why might extrapolative statistical models do better in forecasting earnings than fundamental analysis? Daniel Coggin suggests based on stud- ies in the area of clinical psychology why forecasts from statistical models

might be superior to that of trained experts. 21 Specifically, he cites studies that show that for classifying subjects, statistical models outperformed psy- chologists. The reason proferred is that statistical models are not biased by human judgment and other imperfections in processing information. Another reason is that researchers find that in forecasting earnings, analysts do not employ time series properties of earnings correctly. 22

Most of the studies have used simple or naive extrapolative statistical models. Statisticians have developed more complex models for forecast- ing time series data. Do such complex models do a better job of forecast- ing earnings than simple or naive models? The evidence does not suggest that complex statistical models lead to significantly better forecasts. 23