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Applic.- 2 |  |
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. Other combinations were used to yield a better predictive power but they were not better than the combination used. The five-year quarterly data was used for each firm. In fact, the model needs more than five-year data. The quarterly data includes the fourth quarter of 1998 through the third quarter of 2003 with the total of 20 observations. Nevertheless, in order to regress the fourth quarter scale against four lag of itself, the data between the fourth quarter of 1997 and the third quarter of 1998 are needed. In fact, the model used six-year data. Adjusted R square value is 0,24 which means that the model has explained about 23,99% of the total sample variation in EBIT/TA value, after adjusting for sample size and number of independent variables in the model. (Mcclave et al. 2001: 556) The shocks correspond to forecast errors in the model. Forecast errors are deviations from their expected value. 136 firms with 20 observations offer 2720 forecast errors to study. The forecast errors of the firms are presented in Appendix C. The group of forecast errors is very important in this study. They are regrouped according to two characteristics. One is market capitalization, and the other is stock price volatility. Appendix D shows the market capitalization of the firms at the end of the third quarter of 2003 together with the stock price volatilities. The stock price volatility is calculated by the variance of the firms’ monthly stock price returns from the fourth quarter of 1998 to the third quarter of 2003. Two characteristics were chosen for having little or no correlation. That is, 136 firms’ market capitalization correlation with stock price volatility is 0,099 with 0,252 p value. There is an expectation about being little correlation between two characteristics because model would be biased if they were correlated high. The firms were grouped according to their market capitalization as a first step. The top one-third firms consist of “market-cap bucket 1”, the middle one-third firms consist of “market-cap bucket 2”, and the bottom-third firms consist of “market-cap bucket 3”. Then each market cap bucket is further grouped into three sub samples according to firms’ stock price volatility; that is, variance of their monthly stock price returns. Finally there were eight identical buckets having 15 firms and one final bucket of 16 firms. These forecast errors of the firms’ were placed into buckets, or bins, 2720 forecast errors are distributed into 9 bins according to how firms were grouped. Consequently, there are eight bins having 300 forecast errors and one bin having 320 forecast errors. The first bin, bin-1 shows the most risky firms with the highest market capitalization. The last bin, bin-9 shows the least risky firms with the lowest market capitalization. Appendix D shows firms’ bin classification. |
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This table shows the mean, standard deviations of forecast errors, average market capitalization in million dollars and average stock price volatilities of the bins. Mean and standard deviations of the bins’ were taken from the histograms. Average market capitalization and average stock price volatilities are the average of these figures of the bins. Stock price volatilities were calculated by taking the variance of the monthly stock price returns as well. |
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 Table 4: Summary statistics of bins |
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| 3.3.3 Distributions of Cash Flows:
C-FaR model expects that the forecast errors come from a relatively homogenous group of firms, which were matched on the two characteristics. When this assumption holds true, there is a powerful parametric way to find the C-FaR of any given firm. The 300 forecast errors for each firm can well describe their C-FaR distribution. That is, C-FaR needs to analyze the forecast errors distribution of each bin. The histogram of the each bin can be used for this purpose. Minitab Release 14 for Windows program was used to get the histograms of the forecast errors in each bin. The histograms of the forecast errors permits to evaluate any tail value for the empirical distribution. |
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3.3.2 F Test:
Adjusted R square is just a sample statistic in spite of its helpfulness. It is misleading to comment on the global usefulness of the model based only on adjusted R Square. Hypothesis involving all the b parameters should be tested with a better method. The hypotheses are as follows: Ho: b1= b2 = b3 = b4 =0 Ha: at least one of the coefficients is nonzero F statistics was used to test the hypotheses. F statistic is the ratio of the explained variability divided by the forecasting model degrees of freedom to the unexplained variability divided by the error degrees of freedom. The rejection region is: F > Fa where F is based on 4 numerators and 2695 denominator degrees of freedom. a was designated 0,05 for this study. Since it exceeds the observed significance level 9,1E-161 the data provide strong evidence at least one of the model coefficients is nonzero. As a result, the overall model used for cash flow estimation appears to be statistically useful for estimation. (McClave et al. 2001: 558) |
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| In order to get Figure 4-11 please e-mail me
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 Figure 3: Histogram of Bin-1 Figures 3-11 show the histograms of the bins. These figures are important because they offer crucial information. Bins are expected to show the empirical C-FaR distributions and figures ease to study these distributions. Each figure has also summary statistics of the bins. Mean and standard deviations are used to find the tail values of histograms with a given probability. In fact, tail values are x% C-FaR of the firms. Figures show the number of forecast errors as well. |
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