Dow Jones Tobacco vs. DJI: Portfolio VaR Analysis 2007–2010

Data Selection: Justifications and Discussion

Two separate major U.S. indexes were evaluated over a period extending from the beginning of 2007 to the beginning of 2010. The Dow Jones Industrial Average was selected as a broad indicator of overall U.S. economic health, while a more specific indicator — the Dow Jones U.S. Tobacco Index — was also selected to represent a more targeted industry analysis. Six phases of calculation were conducted and contrasted with various macroeconomic trends prevalent throughout this period. This provided evidence that the Dow Jones U.S. Tobacco Index was composed of companies that sold goods with a low price elasticity of demand, low income elasticity, or possibly some combination of both. Furthermore, a discussion was included recommending that future research be conducted over this period to further delineate factors and information that could potentially be used for future public health policy.

The macroeconomic environment from the beginning of 2007 to the beginning of 2010 is an interesting period to study. While the National Bureau of Economic Research (NBER) officially declared that the U.S. entered into a recessionary period in December of 2007, the economy as a whole showed signs of stress long before this date (MSNBC, 2008). The NBER later declared that the recession officially ended in June of 2009 (Isidore, 2010). However, considering only the official beginning and end dates paints only a small portion of the total picture. In fact, since the official end date passed, America saw a deterioration of over nine hundred thousand jobs as well as the slowest growth in the nine-month stretch following a post-war downturn (The Economist, 2010).

Unemployment rates at the beginning of the period being studied approximated about seven million people in the U.S., and the unemployment rate was under five percent (Bureau of Labor Statistics, 2007). By the end of the period being studied, unemployment had risen to ten percent and then dropped slightly to nine point seven percent (Hincha-Ownby, 2010). Both the unemployment rate and the total number of people unemployed more than doubled. Many economists believe that the high levels of unemployment created demand-side problems that will never be overcome by supply-side initiatives (Krugman, 2011). One factor that underlined many of the subsequent problems the U.S. economy faced during this time was the housing bubble peak, which was estimated to have occurred in 2005 (Byun, 2010). This phenomenon resulted in a subsequent unemployment effect estimated to range from 1.2 million to 1.7 million jobs, and cost U.S. homeowners billions in lost real estate wealth.

Index pricing data was selected for the period extending from January 1st, 2007 to January 1st, 2010. The first index chosen was the Dow Jones Industrial Average (DJI). The DJI represents a fairly broad economic indicator. It is composed of thirty stocks and is price-weighted among the largest blue-chip organizations traded on the New York Stock Exchange (NYSE) (Abbondante, 2010). While other indexes — such as the S&P 500 and the NASDAQ — contain a compilation of stocks, the DJI has been a widely recognized and reliable indicator of overall U.S. economic health. It should also be noted, however, that a small number of critics argue that since the companies included in the index are limited and subject to frequent changes, it may not be quite as reliable as most people are led to believe (Blodget, 2009).

An index representing a narrower industry segment was also chosen for analysis. Since the macroeconomic environment at the time represents a period fraught with volatility and uncertainty — including some considerations of systemic risk — the Dow Jones U.S. Tobacco Index seemed like an interesting secondary selection. Though the main stream press reports little on this industry index, a tremendous body of literature has been developed in journals over the last three decades concerning the price and income elasticity of tobacco products (Chaloupka, 2011). For example, in the late 1960s, researchers identified the price elasticity established by previous studies to range from -0.10 to -1.48 (Lyon & Simon, 1968).

Tobacco can serve as a classic example for the price elasticity of demand as well as income elasticity, since data are readily available both before and after state and federal tax policies have been implemented. Both the federal government and a majority of state governments have issued tax policies that have subsequently increased the purchase price for all consumers at given intervals (Tanzi & Zee, 2000). Although there appears to be a relative consensus that demand undoubtedly diminishes under such policy initiatives, the extent to which it does is highly contested. New models consider not only the basic underlying economic data — such as information on price and income levels — but also attempt to connect macro-social influences, such as various marketing campaigns, to the total body of knowledge (Chaloupka, 2011).

Daily frequency data were chosen to provide an accurate dataset with which to analyze each index, given the heavy volatility that occurred in markets throughout this period. Each dataset for the individual indices therefore consisted of 752 data points. Two potential macroeconomic influences were hypothesized to potentially affect the narrower industry-focused index: either the index would experience diminished returns due to the effects of an effective reduction of income in the economy, or the resulting recession would have no effect due to the marginal rate of tobacco's income elasticity. The data suggested that, on the whole, the tobacco index outperformed the broader market during this period.

Table 1 — Descriptive Statistics

Portfolio Analysis for Six Discrete Weight Combinations

The daily returns for each index were calculated based on the rate of continuously compounding interest that each index earned per day. The returns were compiled and the overall performance of each index was identified in terms of return as well as risk. A combination of various potential portfolios for the period was constructed at six discrete weightings ranging from 0% to 100% of each index. The risk and return figures were calculated for each possible portfolio weighting by multiplying the factors by their relevant portfolio weighting. Below are the individual figures for each portfolio as well as the performance of the combined portfolio possibilities under the constructed model.

Table 2 — Dow Jones Industrial Average Portfolio Contribution

Table 3 — Dow Jones U.S. Tobacco Index Portfolio Contributions

Table 4 — Total Portfolio Performance for Each Weighting Variation

The dominant portfolio that emerged from comparisons of the various weighting combinations was the portfolio that included the heaviest weight for the tobacco index. Since the tobacco index outperformed the broader index on the whole, it produced the most profitable outcome. The total returns for each portfolio combination are displayed in Table 4. As the data shows, the slope shifts slightly when the DJUSTB weights are at 80% and 90%. This is due to the fact that these two figures represent only a 10% incremental difference, while other combinations represent a 20% incremental increase. This shift further supports the conclusion that the dominant portfolio was the tobacco index.

VaR Compared to Actual Returns

For the period January 1st, 2007 to January 1st, 2010, a sample portfolio was constructed based on a hypothetical $100 million investment at the beginning of the period. The sample portfolio consists of 80% of the DJUSTB index and 20% of the DJI index. The standard deviation for each index was identified and weighted appropriately to represent the scenario. The actual returns generated by the portfolio were calculated to be $745,781.39, given the weighted returns that each index provided. The Value at Risk (VaR) was also calculated at the 95% confidence interval (1.64) by multiplying this figure by the total portfolio risk. The calculated VaR figure was nearly two and a half million dollars, compared to an actual return of well under one million dollars. It is therefore reasonable to speculate that investors were expecting a higher return than they received, since the amount of risk they were accepting was significantly greater.

Another way to consider the value at risk of a portfolio is that there is a one-in-twenty chance that this loss could be realized. Thus, with the advantage of hindsight, it is unlikely that investors would have been comfortable with this investment. Yet, at the time — considering that the broader index was also subject to significant risk, including systemic risk — this investment may have appeared as the lesser of two evils.

The actual returns of the tobacco index are significantly higher than those of the DJI in part because of the weakened value of the dollar relative to foreign currencies. This point is expanded upon in Part Six; however, it is relevant to note here that over two thirds of the tobacco industry's revenue streams come from developing markets, which are highly subject to fluctuations in exchange rates.

Table 6 — Sample Portfolio Risks and Returns

Table 7 — One-Day VaR Figure

Conclusion

While the issuance of the tax may explain tobacco's relatively poor performance up to its historical low, it does not fully explain the steady recovery from that point until the index reached its historic high in 2010. However, most people do not realize that over two thirds of tobacco sales originate from developing markets (Palos, 2009). Therefore, profits are ultimately more affected by the strength of the dollar compared to other currencies than by taxes issued in the domestic market. When the dollar strengthens, raw materials become effectively less expensive for American-based multinationals; however, at the same time, the company's revenue streams are also received in foreign currency. Therefore, a weaker dollar actually increases gross revenue. While almost counterintuitive, the model confirms this relationship.

As the U.S. slowly emerged from recession at an unimpressive pace, most of the developing world bounced back at a faster rate. As a result, foreign currencies were trading against the dollar from a stronger position. It is therefore reasonable to conclude that the slow recovery in the United States actually reduced the portfolio risks for the 2009–2010 sub-period compared to the entire period being studied. Future research should be conducted over this period to further delineate the factors at play and to generate information that could potentially inform future public health policy.

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