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Source: http://www.doksinet Global Asset Allocation and Stock Selection Assignment 1 Predictors for the DJIA: Going up the income statement BSD Roberto Alatorre Prakash Arya Brian Chin Philipp Schmahl John Withrow Source: http://www.doksinet Introduction and Project Hypothesis Certain studies indicate that dividend yield is a reasonable predictor of future stock behavior. Dividend yield, it is argued, predicts the health of a company because stock prices ultimately reflect cash flows accruing to the shareholder in the form of dividends. However, critics of the dividend yield argue that it is not necessarily a good predictor. Dividends are often subject to considerable discretion. There are many cases where a company may not have enough cash but it is still a solid investment with considerable upside. Additionally, critics point out that increasingly, many companies simply do not issue dividends. If there are fewer and fewer companies issuing dividends, then the validity of the

dividend yield as a predictor is also increasingly irrelevant as well as questionable. Many sell-side analysts and investors therefore focus on financial indicators that appear to better reflect the operating health of companies. One commonly used indicator is earnings before interest, taxes, depreciation and amortization (EBITDA). This measurement, it is argued, removes items that both significantly impact earnings and are subject to management discretion. Therefore, EBITDA is more difficult to manipulate and hence, is a more meaningful measurement. In addition, EBITDA can be readily calculated from any set of financial statements, making it a more relevant measurement than dividends. We asked ourselves: does the evidence support this logic? Is it possible that by “going up” the income statement and removing extraneous material that we can arrive at a better predictive indicator of a company? For sell-side analysts, investors and academics like, we believe this question merits

investigation. The goal of this paper is to test the hypothesis that it is possible to improve on the dividend yield indicator by using a more “meaningful” indicator like EBITDA yield. To test this hypothesis, we selected three measurements to compare: the dividend yield, earnings per share yield, and EBITDA yield. If the hypothesis is correct, then EBITDA yield would best predict future returns, followed by the earnings yield and dividend yield. Methodology Index Since the dividend yield of the Standard & Poor’s 500 index (S&P500) was cited in studies, we decided to calculate our three measurements as ratios of a broad index as well. Given the time constraints of our project, we elected to use the Dow Jones Industrial Average (DJIA). More specifically, we would calculate the EBITDA yield, earnings yield and dividends yield of the DJIA and compare them to future returns of the DJIA itself. 1 Source: http://www.doksinet We believe the DJIA substantially replicates the

properties of the S&P500 (and the larger market, for that matter) for the purposes of this paper. We note that although the stocks in the DJIA differ from the broader market in many ways, the central tenets of this paper should still be relevant. Time Frame Prior dividend yield studies focused on index performance over a 3-5 year span. We judgmentally selected a 3 year lagged return for our project. We also selected the twenty year period from 1979 to 1999 as our timeframe. We also selected a quarterly frequency, thus providing 80 data points. Specific Tests We decided to measure the effectiveness of our three measurements in three ways: First, we would scatterplot the returns of the DJIA with the three measurements, lagged by three years. This would test for relevancy since a criticism of prior dividend yield studies is that the dividend yield model suggests irrelevant current S&P500 returns that are far outside the in-sample data range. Second, we would perform an

auto-regressive conditional heteroskedacity (ARCH1) model with each of the three yields. We would include in each of the three models larger macroeconomic variables that are commonly used in regressive models: credit spreads, interest rate spreads and overall interest rate levels. From these regressive models we would compare the R2 of our three yields. Third, we would create forecasts from our three ARCH1 models and compare them to out-of-sample data for validation purposes. We believed that based on these tests, we could reasonably ascertain which of our three yields was the best indicator and therefore prove or refute our hypothesis. Data Collection Database Source We used the COMPUSTAT database at the Wharton School of the University of Pennsylvania. From this database we obtained the following data: • • • • Company name, ticker symbol, date of 10Q and CUSIP number Dividends per share Earnings and earnings per share (primary EPS prior to SFAS 128 in 1997, basic EPS after

1997) Depreciation & amortization (larger of that reported on the income statement or statement of cash flows since these amounts are often not listed separately on the income statement but the statement of cash flows is not available prior to SFAS 95 in 1988) 2 Source: http://www.doksinet • • • Interest expense Income tax expense Common shares outstanding From these items we calculated dividends per share, earnings per share and EBITDA per share for each company. We then calculated dividends yield, earnings per share yield, and EBITDA yield for each company by dividing the per share amounts by each company’s concurrent stock price. Creation of DJIA Yields At this point, we noted that properly combining per share amounts into DJIA yields was extremely important. This was because the DJIA was a price-weighted index, which meant that our data had to be consolidated accordingly. We therefore researched the DJIA’s history and methodology to best replicate what, exactly,

the index actually measured. Charles Dow originally calculated the DJIA as a straight average of 30 stock prices. As such, a larger company was not necessarily given more weight in the DJIA than a smaller company; the sizes of the stock prices themselves determined the weights of the companies in the index. Therefore, per share data was the basic unit of measurement in the index. As stocks split, Dow Jones changed the divisor to maintain a pro forma, price-weighted index. Therefore, while the index did not adjust for the marginally dilutive effects of stock dividends, it did account for major changes such as stock splits. As the companies in the index changed, Mr. Dow also replaced the old companies with new companies in a manner that maintained the weighting scheme. For example, if the company to be replaced was 1/29.5th of the index, he balanced the new company in the index to exactly match 1/29.5th of the index Based on the above understanding, we reasoned the following: Our

numerator would consist of per share amounts of the 30 companies, which were summed into a DJIA dollar amount, such as DJIA earnings. This reflected that fact that Charles Dow simply added his 30 stock prices together in his original numerator. Ideally, our denominator would consist of the actual divisors used by the DJIA. However, since the actual DJIA divisors were available only on a periodic basis and not on a quarterly basis, we had to estimate quarterly divisors. We therefore solved for the DJIA divisor by summing our companies’ stock prices and divided by the index. This would account for Dow Jones’ fairly subjective divisor calculation. Survivorship Bias and Data Completeness Issues Survivorship bias was a significant concern for our project. The composition of the DJIA changes from time to time to reflect the changing nature of the economy. Since 1979, 3 Source: http://www.doksinet there have been four major changes in the composition of the DJIA index. We therefore

constructed our stock database to include only those stocks that were included in the index in the appropriate years, thus eliminating survivorship bias. We also accounted for mergers and acquisitions in the event that a new entity was added to the DJIA through consolidation. Additionally, we were unable to obtain stock data for two companies in the 1979 period: International Harvester and Johns-Manville. Due to this inability, we compensated our divisor by multiplying it by 30/28 in the years in which these companies were missing since they were both from the same period. (We now note that the numerator should also be multiplied by 30/28; this insight was not included in our results.) Results Scatterplot Test We plotted the three yields with the lagged returns as follows: Plot of DJIAreturns vs divlag 0.37 lot of DJIAreturns vs earnlag DJIAreturns DJIAreturns 0.37 0.27 0.27 0.17 0.17 0.07 0.07 -0.03 9 12 15 18 21 24 27 (X 0.001) divlag -0.03 -0.1-008 -0.06 -0.04 -0.02 0

002 earnlag Plot of DJIAreturns vs ebitlag DJIAreturns 0.37 0.27 0.17 0.07 -0.03 -0.07-004 -0.01002005008011 ebitlag We then calculated DJIA yields as of 4th quarter 1999 as follows: 4 Source: http://www.doksinet Dividend Yield: 2.571% (note that the scale on the dividends plot is x0001) Earnings Yield: 1.56% EBITDA Yield: 8.50% Based on these calculations and the three scatterplots, it appears that the current yield levels of the three measurements are all within general historic levels. As such, it appears that all three measurements are relevant for current use within the context of the DJIA. As a sidenote, earlier studies about dividend yields of the S&P500 are criticized because the current level of S&P500 yields is extremely low. Since the current level of S&P500 dividend yields is well outside historic levels, any sort of extrapolation on what the S&P500 itself might do is very tenuous. We believe that our calculated dividend yield is within historic

levels since DJIA companies tend to be larger, more established companies that issue regular dividends, unlike those in the S&P500. ARCH1 Regression R2 Test For ex-post analysis, we utilized DJIA data up to Q3 1999. The last independent variable observations for the same analysis was Q3 1996. Using an ARCH (1,1) methodology, we forecasted ex-ante the DJIA from Q4 1999 onwards. Dow Jones Annual Returns Over next three years = DJIA returns = ((DJIA t+12 /DJIA t )(1/3))-1 The basic model we used can be stated as the following: DJIA returns t+1 = α t1 + α t1 * credit spread t1 + α t1 term spread t1 + α t1 Treasury yld t1 + α t1 DJIA yld t1 + ε t1 As required by the ARCH1 methodology, we regressed the residual error against itself to attempt to forecast the next period’s error term and added this forecast error into our model. More specifically, our regression models were calculated as follows: DJIAreturns = - 0.054 - 5016*CrSprdLag + 2.273*TrmSprdLag + 1.255*TyldLag +

5.966*DivLag DJIAreturns = 0.067 - 4639*CrSprdLag + 2.479*TrmSprdLag + 0.788*TyldLag + 0.924*EarnLag DJIAreturns = 0.008 - 4018*CrSprdLag + 2.449*TrmSprdLag + 1.014*TyldLag + 1.002*EbitLag Dividend Model Earning Model EBITDA Model p-Values 0.0071 0.1034 0.0078 Adj. R2 28.60% 22.90% 28.50% Based on these results, we note that the EBITDA model has approximately the same adjusted R2 as the dividend model, but the earnings model has a lower R2 than either. Ceteris paribus, we conclude that surprisingly, EBITDA appears to be no better than dividends in minimizing residual error, and that earnings is significantly worse than either. 5 Source: http://www.doksinet 6 Source: http://www.doksinet ARCH1 Regression Predictions and Out-of-Sample Results Our forecast results were as follows: In-Sample Forecast: 10,000 9,000 Observed DJIA Div Yld Model Earn Yld Model EBITDA Yld Model 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 98 97 19 96 19 95 19 94 19 93 19 92 19 91

19 90 19 89 19 88 19 87 19 86 19 85 19 84 19 83 19 82 19 81 19 80 19 19 19 79 - Out-of-Sample Forecast: 19,000 17,000 15,000 13,000 11,000 9,000 Observed DJIA Div Yld Model Earn Yld Model 7,000 EBITDA Yld Model 5,000 1999 2000 2001 2002 7 Source: http://www.doksinet Out of Sample Quantitative Results: Year 1999 1999 1999 1999 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 Qtr 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 DJIA 9,786.16 10,970.80 10,336.95 11,497.13 10,921.92 10,447.89 10,650.92 10,787.99 ? ? ? ? ? ? ? ? Average Error (Out of Sample) Std Dev Error (Out of Sample) Average Error (In Sample) Std Dev Error (In Sample) dividends 7,699.42 9,765.49 9,788.58 10,376.00 10,251.22 11,450.60 13,114.32 13,365.21 12,268.89 13,763.93 13,109.57 11,994.21 13,555.18 16,051.91 18,333.22 18,161.85 earnings 8,224.58 9,652.13 9,571.32 10,007.50 10,899.67 11,430.18 13,001.59 12,608.34 12,593.53 13,908.06 13,082.48 11,153.23 14,018.10 15,973.96

17,837.76 16,873.83 EBITDA 8,221.07 9,495.56 9,751.18 Validation 10,224.64 10,749.67 11,439.66 13,210.25 13,055.61 13,107.81 14,277.05 13,411.68 Prediction 12,035.90 15,017.11 17,311.32 19,516.48 18,803.44 51.38 1,752.93 (0.56) 1,548.61 93.48 1,657.19 195.86 735.98 182.68 730.14 202.65 741.00 Based on these results, we note that both in-sample and out-of-sample results show that there is little discernable difference between the three models’ forecasting ability. Interestingly enough, we also note that all three models appear to have significantly over forecast the market in the validation period. Conclusions Our results do not appear to support the hypothesis that it is possible to improve the dividend yield model by “going up” the income statement. Had our data supported our hypothesis, we believe the earnings yield model would have had more predictive power than the dividend yield model, and the EBITDA model would have had even more predictive power still. This was

not the case; our results showed little meaningful difference between the three models. Subsequent investigations into this issue might orthogonalize the measurements; i.e, test for reasons that may explain consistent differences between EBITDA and dividend yield models. We also note that our inclusion of macroeconomic variables may have distorted the results; a pure model built from the three yields alone might have proven more concrete results. 8 Source: http://www.doksinet Indeed, our tentative conclusion, were we to draw any, is that earnings yield appears slightly less powerful than either dividends or EBITDA. We speculate that this may have to do with the fact that earnings per share is often subject to intense management scrutiny. This may alter its own validity as a barometer of corporate health 9