Evaluating cross-sectional forecasting models for implied cost of capital

We observe that parsimonious models in general outperform complex models. For example, we test the forecast model of Abarbanell and Bushee (1997), which is based on the forecast approach by analysts, a model that forecasts future sales growth and profit margins, and a model that combines RI and HVZ. None of these more complex models outperforms the EP or the RI models.

We estimate the HVZ model at the dollar level as it is specified in their paper. We also perform robustness test by estimating their model at the per-share level. The inference still holds.

The model including B_t−1 produces similar results.

This represents a departure from HVZ as they estimate earnings before extraordinary items, without excluding special items. We exclude special items because they are less predictable by nature. We perform a robustness test using earnings before extraordinary items. The forecast errors are bigger for all models. However, the inferences do not change as the rank ordering of the models in terms of forecast accuracy and ERCs is unaltered.

We also perform robustness test by estimating the cumulative ERC the same way as the “Annual ERC” in HVZ. Specifically, we estimate ERCs by regressing the buy-and-hold returns over the next 1, 2, and 3 years on the unexpected earnings over the same horizon. The tenor of the results does not change.

We further partition our sample into four time periods (1969–1978, 1979–1988, 1989–1998, and 1999–2008). We do not observe any systematic changes in forecast accuracy of the HVZ, EP and RI models. However, the forecast accuracy of the RW model deteriorates over time. This is not surprising as the naïve model is not well suited for more complex operations.

This represents a departure from HVZ, who form calendar time portfolios starting on July 1. The advantage of our approach is that the financial statement information is equally timely for all observations. The disadvantage is the fact that the compounding period may not be identical for all firms in our sample. As a robustness test, we carry out all tests in a subset of firms with December fiscal year-ends (over 60 % of the sample) and find virtually identical results.

Easton and Monahan (2005) recommend running regressions with the ICC measure and proxies for cash flow news and discount rate news. However, these proxies require forecast revisions, which are not feasible to estimate for cross-sectional models. Hence, we only run univariate regressions.

A concern might be that the lower coefficients on the HVZ model in the return regressions might arise mechanically due to the greater magnitude and greater spread of the ICC estimates generated from the HVZ model. To account for this, we perform the following sensitivity test. We standardize all the ICC measures each year by subtracting the minimum and then dividing by the range (maximum–minimum) for ICC using that method in that year. In other words, we set each ICC = (ICC − min)/(max − min). We then re-estimate the regressions using the standardized ICC measures. We continue to find the weakest relation between ICC from the HVZ model and future returns. For instance, for 1-year-ahead returns, the average coefficients on ICC_HVZ, ICC_EP, and ICC_RI from the Fama–MacBeth regressions are 0.230, 0.331, and 0.411, respectively. For 2-year-ahead returns, the average coefficients on ICC_HVZ, ICC_EP, and ICC_RI are 0.190, 0.360, and 0.342, respectively. For 3-year-ahead returns, the average coefficients on ICC_HVZ, ICC_EP, and ICC_RI are 0.120, 0.309, and 0.298, respectively.

Easton and Monahan (2010) argue that the latter approach is logically inconsistent as ICC metrics are estimated precisely because of the flaws in conventional measures of risk that often rely on ex post returns. We present these results to ensure a comparison between our results and those presented in HVZ.