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In investing, I have a heavy focus on reinsurance companies, and I enjoy learning how to value their investment portfolio and underwriting ability, taking inspiration from the reinsurance companies that Warren Buffett used to help build Berkshire Hathaway's investing empire. The other focused... More
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  • Are Commodities A Leading Or Lagging Predictor Of Equity Prices? 0 comments
    Dec 29, 2012 11:59 PM | about stocks: SPY

    (This analysis was performed in 2006)

    EXECUTIVE SUMMARY

    There have been many attempts to accurately forecast the direction of public equity markets. Because of the number of participants in these markets, any true predictive relationships tend to be extremely short-lived and self-correcting, through a process known as arbitrage in financial parlance. The Dow Jones Industrial Average of 30 leading industrial companies is one of the most widely followed equity indices in the world. Commodity prices are an important factor in the cost of industrial production and thus are expected to affect the profitability of industrial companies, and possibly the valuation of industrial companies in the equity markets. Other factors that may be associated with the economy, such as Consumer Price Index (CPI) and the National Bureau of Economic Research (NBER) economic cycles, could also affect the profitability and equity valuation of industrial companies.

    This analysis analyzed potential associations with the DJIA and the Commodity Producer Price Index (Commodity-PPI). Initial analysis revealed a significant but relatively weak positive linear association between the Commodity-PPI and the next month's DJIA performance. Additional variables that were included in further modeling included CPI, NBER economic cycle periods, and pre/post-1970 era analysis. Inclusion of the NBER economic cycle in the model strengthened the predictive power of the Commodity-PPI and next month DJIA by identifying that this relationship existed only during months of economic contractions (from peak to trough of the economic cycle). Further analysis revealed that this relationship existed only in the months prior to 1970 and not subsequently. A potentially confounding effect was identified between CPI and Commodity-PPI.

    To account for all of these factors, a complex multiple regression model was constructed including all of the variables mentioned above. The strongest association in this model was between the Commodity-PPI and DJIA. However, the association between Commodity-PPI and CPI could not be excluded as a confounding factor. Another complicating factor was that a fair number of outlier extreme values in the DJIA could not be accounted for in the multiple regression model. This was felt to be an artifact of kurtosis, a phenomenon previously described in equity market performance with the occurrence of much larger events than would be anticipated statistically.

    Potential areas for future study are discussed, including the use of a more modern equity market index of commodity-intensive industrial companies, since changes in the DJIA component companies could explain the fact that the strong correlation between Commodity-PPI and DJIA during contracting economies appeared to breakdown sometime subsequent to 1970. Also, better indicators of inflation could be included, such as M2 money supply and interest rates, to help offset the potentially confounding influence of monetary inflation on the variables in this analysis

    INTRODUCTION

    Background

    The economy in capitalist societies is typified by boom and bust cycles of various periodicities. Despite intense study, few experts have been able to predict the secular trends of growth and contraction. Economists have proven to be notoriously unreliable at predicting the onset of economic recessions accurately, for example.1

    Thus, it is not surprising that predictions of equity market performance are even worse in accuracy. A successful model of macroeconomic leading indicators might be able to assist portfolio managers in repositioning investment portfolios to avoid losses and to take advantage of gains in different asset classes.

    The Macroeconomic Business Cycle

    Recessions are described as period of economic contraction, in which previous mal-investments are corrected through revaluation of asset prices and even bankruptcies. Expansion cycles are characterized by economic growth and increased borrowing for build-out of capacity. Historical data of "official" business cycles are collected by the National Bureau of Economic Research (NBER).2

    Macroeconomic input factors of production are tracked in order to explain the short-term economic cycles of expansion and contraction. These inputs consist of labor, borrowed capital, and raw materials. Economic indicators measuring these input factors are divided into coincident, leading, and lagging indicators, depending on how the number peaks are in or out of phase with the economic expansion/contraction cycle.3 Coincident indicators include payroll data. Leading indicators include average work hours, durable goods orders, M2 money supply, new housing starts, and consumer expectations.4

    The stock market itself has sometimes been viewed as a leading indicator for the economy.5,6 Examples of lagging indicators include unemployment rate and changes in the consumer price index.

    One difficulty of interpreting leading indicators is that they are by definition out of phase with the current economy. It is not uncommon for many business leaders and investors alike to ignore or mis-read leading indicators. For example, businesses suffering through a recession are often reluctant to reposition for growth when leading indicators show an upcoming turnaround. Similar things are observed at the peaks of economic cycles, when businesses and investors may inappropriately extrapolate the recent wonderful growth in profits for years into the future. An awareness of these flawed emotional tendencies may allow astute investors to profit at important inflection points in the economic cycle.

    The equity market as a proxy for macroeconomic performance

    For the purposes of this analysis, I am attempting to use the stock market index returns of industrial companies as proxies for macroeconomic performance. Obviously, stock markets may not reflect macroeconomic output over the short run, which I will arbitrarily define as 2 years or less. This is likely due to inherent biases among investors and corporate management, including overconfidence and inappropriate extrapolation of recent news.7 However, over the long term (10 years or more) such performance should be highly correlated with macroeconomic output, given the size of the United States public equity markets. If it were otherwise, then the stock market could be severely mis-priced and result in large potential opportunities for arbitrage8 to attempt to bring valuations back in line. Basically, this is a major premise of the efficient market hypothesis and of capitalism theory itself - that any short lived price anomaly serves as an opportunity for an astute investor, and will be corrected in the long run.9

    In summary, the capital markets can be irrational or inefficient over short periods of time, but over longer periods the performance should be driven by fundamental value rather than the whims of investor emotions. Since commodity prices are one of the major determinants of the cost of production of industrial companies (such as those within the Dow Jones Industrial Average), commodity prices may provide important signals about the macroeconomy. Because the public equity markets represent the overwhelming majority of value of United States firms, the fate of equities should reflect the overall fate of the macroeconomy.

    Definition of the problem

    This analysis will test whether the commodity producer price index has correlations with equity performance, and if so, whether they are a leading or lagging indicator.

    DATA

    Data were collected from a variety of public sources (see variable table and references). I personally downloaded each data series from publicly available websites. Monthly data series for a variety of indicators were obtained and collated into a single spreadsheet file. Data were verified for completeness and proper data transfer. After collection, data were transferred to a JMP data sheet. After verifying accurate transfer of data, additional data columns were generated for the derived and calculated fields, as described below.

    Another categorical data series was added to indicate the NBER-defined months of economic contraction (from peak to trough of the economic cycle) and expansion (trough to peak); there were 21 complete cycles from 1990-2006, and we are currently still in the midst of an expansionary phase at the time of this writing in December 2006 (although some leading indicators appear to have trended downward).

    Variables

    The proposed analysis will use multiple regression of monthly time series data. The primary response variable will be the Dow Jones Industrial Average (DJI) monthly % change, which is a continuous variable. This was derived from the DJI data series, which is a continuous metric variable with units of nominal US dollars.

    The predictor variables in the regression analyses will consist of the following:

    1. Commodity-PPI, monthly percentage change of the commodities segment of the producer price index (PPI), continuous variable. The Commodity Producer Price Index (Commodity-PPI) is a monthly government report of the approximate price of a "basket" containing various commodities. I predicted that stock indices may have negative correlations to all of the producer price index components since these factors represent costs to companies, and periods of high monthly changes in commodities may represent periods of impaired corporate profitability and thus decrease stock valuations.
    2. Commodity lag 1,3,6 month. These are computed continuous variables, which is simply the Commodity-PPI monthly percentage change (above) lagged by 1,3, or 6 months. I predicted that Commodity-PPI and stock index monthly changes would be negatively correlated, and the strongest statistical significance would be observed with 6-month lagged Commodity-PPI. I believed the 6 month lag is important because commodity prices take time to work their way through the production and inventory and distribution system, and also corporate reporting occurs at quarterly intervals, so 6 months will be needed for large commodity price changes to negatively impact corporate earnings and presumably stock prices.
    3. Commodity lead 1, 2, 3, 6 month - for these data series, I used -1, -2, -3, or -6 values for the lagging time frame, which shifted the data set forward relative to the original commodity-PPI data series. This will be used in the regression analysis to test whether monthly commodities price changes are a leading indicator of monthly equity market returns.
    4. CPI MOM (Consumer Price Index, monthly percentage change). The primary data series is a continuous variable. It is obtained from the US Bureau of Labor Statistics (for references, see table below). I believed the CPI would be relatively positively correlated with equity index returns and with commodity PPI returns. This variable was also lagged for various time periods to determine the time frame with strongest association with DJIA performance.
    5. NBER contraction. This is a categorical variable describing whether the listed month was within an expansionary (0) or contractionary (1) phase of the economic cycle, according to NBER data. The peak of the economic cycle occurs during the "topping out" part of a growing economy, while the trough occurs when a recession is showing signs of turning around. These time point do not coincide the defined periods of economic growth and recessions; in fact, they are 90 degrees out of phase with these other terms, if the economic cycle is viewed as a sine wave. Contractionary months are defined as months in which the economy, as measured by unemployment statistics and other monthly figures, from the peak of the economic cycle to the trough. A more detailed outline of the NBER methodology is available on their website.10

    Table 1. Variables

    Monthly Data series

    Date range

    Source Reference

    Response variable:

      

    DJIA, real (month-end closing prices)

    1900-2006

    11

       

    Predictor variables:

      

    CPI, nominal

    1913-2006

    12

    CPI, monthly % change

    (calculated)

    (calculated)

    Commodity-PPI, monthly % changes

    1913-2006

    13

       

    NBER Economic Contraction (0=no, 1=yes)

    1900-2006

     

    Limitations of the data

    For the stock market indices, the foremost weakness of analyzing long-term data is that the stock indices have changed over the years. Reasons for changes in the index components can be due to mergers or bankruptcies. Since bankrupt companies have been removed from the indices and replaced with healthier ones, this introduces a survivorship bias and may overstate long term equity market returns; this is inherent in any long term equity market index analysis. This is a limitation of all available indices and there is effectively no way to avoid it.

    Another potential confounding factor for the predictor and response variables is the influence of inflation. While beyond the scope of discussion, inflation is generally a monetary phenomenon, whereby increasing amount of money are placed into circulation through the fiat currency process of fractional reserve lending. In order to offset the long-term trend for fiat currencies to lose purchasing power through inflation, the prices of assets generally rise over time. This would be expected to cause concurrent increases in CPI, PPI, and Dow Jones. Even if inflation is an underlying factor behind increases in Commodity-PPI and the DJIA, it is possible that a slight investment advantage could be gained if the optimum leading and lagging time period could be identified.

    Another limitation of the data is that equity index returns have been described as having kurtosis.14 This phenomenon occurs when a variable exhibits a form of non-normal distribution, resulting in "fat tails". In other words, although the majority of time periods appear to follow a normal distribution, extreme values (<5 and >95th percentile) occur at a much high frequency than would be predicted by a normal distribution. The issue of market kurtosis was the subject of an entire recent popular book.15 Kurtosis is a difficult problem to deal with in financial market analysis, and has been the cause of demise of multiple hedge funds that initially exhibited strong performance until becoming overwhelmed by statistically rare events that resulted in much larger losses than predicted by the computed model.16,17

    Finally, the data are limited by a lack of granularity. The statistics that are publicly released are often limited to the tenth of a percent. This results in a large cluster of events between -0.5 and +0.5%, with a number of outliers. While transformation may help result in a more normal distribution, it may also amplify the limited granularity of the data. A related issue is that the producer price index often reports a zero percent change in many months, since many months contain rather small changes in prices that round to zero, potentially hiding tiny directional movements in prices.

    METHODS

    First, each of these data series were analyzed for normal distributions using summary statistics, histograms, and normal quantile plots. Non-normal data were considered for transformation when appropriate. The time frames used were March, 1926 through October, 2006, since this was the time frame for which data for all variables were available.

    Response variable, summary statistics

    As shown in Figure 1, the monthly percentage changes of the Dow Jones Industrial Average (DJIA) do not follow a normal distribution. The distribution of monthly changes shows a sharp peak, but with an increased number of events outside the two standard deviation bands. Further analysis reveals a heavy clustering of values within -1% and +1%. The mode of +0.3% is approximately equal to the mean.

    As expected, the DJIA monthly changes exhibit kurtosis, or fat tails. For examples, the negative 23.2% change for the month of October 1987, is 4.3 standard deviations from the median monthly change. A change of this magnitude should occur less than 0.00007% of months. However, October 1987 is not even the largest drop. The largest monthly drop during the analyzed time period occurred during September 1931 (-30.7%, 5.7 standard deviations). A change of this magnitude is expected to occur less than 0.00000006% of months, if returns followed a statistically normal distribution. Thus, during the 968 months under observation, 0.000058 months of this magnitude of a monthly change in DJIA would have been expected had the results followed a normal distribution. Thus, a data set of over 206,000 years would be needed!!

    Several procedures were attempted to produce a more normal distribution, in order to facilitate further analysis. Other transformations that were attempted include: natural logarithm, base 10 logarithmic, exponential transformation, reciprocal, reciprocal of the natural logarithm, square root, and quartic root of DJIA. The quartic root of DJIA appeared to produce the most normal distribution with the smallest number of outlier events (Figure 2). However, the use of the quartic root would have obscured the directional sign of the monthly changes in DJIA, which is the primary focus of the analysis. Thus, untransformed DJIA data were used for subsequent analysis.

    Figure 1. Dow Jones Industrials, monthly changes (%): Summary Statistics

    (click to enlarge)

    Figure 2. Transformation: Quartic Root(DJIA)

    (click to enlarge)

    Predictor variable, summary statistics

    The Commodity-PPI variable is the primary predictor under consideration in this analysis. The raw data of monthly percentage changes in Commodity-PPI are shown in Figure 3. The data do not have a normal distribution, as shown in the normal quantile plot. Among the transformations tested, the natural logarithm produced a slightly more normal distribution as judged by the normal quantile plot. The histogram appears to be both rightward skewed with outliers and also with an exaggerated peak to the left of the mean. Thus, subsequent analysis used the raw, untransformed data for commodity-PPI. The rationale for this is that part of the non-normality of the data was due to an increased number of months with zero percent reported change. There should be no directional bias from these zero-change months when comparing to the DJIA monthly changes, so the statistical model under development would be expected to be underpowered to detect a meaningful correlation (type one error). This was felt to be preferable to the risk of introducing a type 2 error (in describing a non-existent correlation), which might have occurred if excessive transformation of non-granular data were performed.

    Figure 3. Commodity-PPI, monthly % change, Summary Statistics

    (click to enlarge)

    Linear regression analysis of Commodity-PPI and next month DJIA.

    The first testing focused on comparing the commodity-PPI monthly changes (predictor variable) with DJIA monthly changes (response variable). Untransformed data series were used for each variable. When same month data were used, no significant relationship was identified by linear regression (correlation coefficient=0.003, p =0.081), as shown in Figure 4.

    The commodity producer price index (PPI) was lagged for 1, 3, and 6 months, and also advanced by 1, 2, 3, and 6 months relative to DJIA. The commodity PPI is composed of a basket of common commodities. Because the hypothesis was that Commodity-PPI might serve as a leading or lagging predictor of DJIA performance, various leading and lagging periods for Commodity-PPI were tested. Linear regression statistics from these analyses are summarized in Table 2. To summarize these findings, the strongest correlation coefficient and statistical significance were identified when the Commodity-PPI had a lead time of one month compared to the DJIA. With a one month lead time, the linear regression analysis identified a correlation coefficient of 0.011, with p=0.0009.

    Table 2. Linear regression statistics with various leading and lagging time period of Commodity-PPI, when compared to DJIA monthly changes.

    Commodity-PPI

    r-squared

    slope

    P value

    Lag 6 months

    0.000144

    0.00402

    P=0.7106

    Lag 3 months

    0.000031

    0.00039

    P=0.8631

    Lag 1 months

    0.000095

    0.00067

    P=0.7628

    Same month

    0.003

    0.00388

    P=0.0812

    Lead 1 months

    0.011

    0.00739

    P=0.0009

    Lead 2 months

    0.00456

    0.00469

    P=0.036

    Lead 3 months

    0.00455

    0.00467

    P=0.0364

    Lead 6 months

    0.000037

    -0.00042

    P=0.8500

    Figure 4. DJIA by Commodity-PPI, one month leading

    Further analysis was performed to see if different relationships existed during expansionary, contractionary, or both types of months of the NBER economic cycles. The summary statistics for the monthly changes of Commodity-PPI by type of NBER month are shown in Figure 5. Nonparametric tests (Wilcoxon, Median, and Van der Waerden tests) showed significant differences in the Commodity-PPI during contractionary months, which were lower in magnitude, compared to expansionary months (data not shown). Linear regression slope statistics for these analyses are summarized in Table 3. During expansionary economic phases, there is no significant relationship with Commodity-PPI and next month DJIA returns. However, during contractionary months there appears to be an association of Commodity-PPI with DJIA (Figure 6). The slope is higher on this linear regression analysis, as is the correlation coefficient, compared to the expansionary months and the non-segregated data Commodity-PPI data set. This suggested that the association of Commodity-PPI and next month DJIA (identified above) is primarily limited to the contractionary months of the economic cycles.

    Table 3. Linear regression statistics with Commodity-PPI and next-month DJIA monthly changes, according to NBER economic cycle phase.

    Commodity-PPI

    NBER cycle

    r-squared

    slope

    P value

    Lead 1 month

    All months

    0.0114

    0.00739

    P=0.0009

    Lead 1 month

    Contractionary months

    0.0384

    0.0203

    P=0.0034

    Lead 1 month

    Expansionary months

    0.00006

    0.00154

    P=0.44

    Figure 5. Commodity-PPI monthly changes, by NBER economic cycle phase.

    (click to enlarge)

    Figure 6. DJIA by Commodity-PPI during contractionary economic cycles

    Consumer Price Index monthly changes

    The Consumer Price Index (CPI) was analyzed due to the likely confounding effects of consumer inflation over the long time period being analyzed. As with other data sets, the summary statistics for CPI showed a slight kurtosis, although the means and median values are similar, the histogram shows no perceptible skewing, and the data points nearly follow a normal distribution on the normal quantile plot (data not shown). Thus, non-transformed data were used with non-parametric tests for statistical comparisons with other data series.

    Preliminary analysis for underlying influence of consumer-led inflation, as measured by the monthly percentage changes in the CPI, was performed. A number of leading and lagging time frames (CPI lagged by +6, +3, +2, +1, 0, -1, -2, -3, and -6 months) were tested. A two month leading time from for CPI relative to DJIA resulted in the only statistically significant positive association on linear regression analysis, as shown in Figure 7. Despite the statistical significance of this relationship (p=0.0048), the relationship is not of large magnitude, with a slope of 0.0016 and a correlation coefficient of 0.008. The other leading and lagging time periods tested showed no significant relationship at all between DJIA and CPI, which further indicating that there was not any pervasive association between the two measurements.

    Figure 7. DJIA by CPI (leading, two months)

    To assess for a confounding relationship between CPI and Commodity-PPI, a linear regression analysis was performed on these two variables. As shown in Figure 8, there was a positive linear relationship between these two variables. Also, note that the time frames with the strongest association with DJIA were used in this and subsequent analyses (Commodity-PPI leading one month, and CPI leading 2 months)

    Figure 8, Linear regression of Commodity-PPI (leading one month) and CPI (leading two months)

    Because NBER economic cycles were found to affect the strength of the linear relationship between DJIA and Commodity-PPI, further analysis was performed. Figures 9a and 9b show the results of linear regression between CPI and Commodity-PPI in expansionary and contractionary months, respectively. While significant positive linear correlations were found in each series, the slope was higher in the contractionary months (1.03) compared to expansionary months (0.65). This indicated that the confounding relationship between CPI and Commodity-PPI is sensitive to the economic cycle and is most profound during times of economic slowing.

    Figure 9a. Commodity-PPI by CPI during expansionary economic cycles

    Figure 9b.Commodity-PPI by CPI during contractionary economic cycles

    Performance during expansionary and contractionary economic cycles

    Evaluation of DJIA monthly performance according to NBER economic phase revealed no significant differences using nonparametric testing (data not shown). However, closer analysis revealed the standard deviation of monthly changes during months of a contractionary economy (0.108%) was twice that of expansionary months (0.057%). The fact that equity returns were not significantly lower during a contracting economy at first appears to be counterintuitive, but actually is consistent with many claims that the equity markets often anticipate the subsequent performance of the economy. This is also consistent with the commonly-held belief that equity markets are more volatile during a less favorable economy.

    Similar analyses were performed for the CPI and commodity-PPI monthly changes. Unlike DJIA, both variables were found to be significantly lower during months labeled by NBER as contractionary, as shown in Figures 10a and 10b. These results are as expected, as consumer and producer price inflations are generally lower during contractionary months. Also, the standard deviations for both variables were slightly higher during the contractionary months (although less than 20% higher, in contrast to the DJIA which had twice the standard deviation during these economic periods). Thus, a contracting economy resulted in lower monthly changes in CPI and Commodity-PPI but not DJIA. However, the opposite was true in terms of volatility, as measured by standard deviation, which was much higher in DJIA during a contracting economy, while being nearly unchanged for CPI and Commodity-PPI.

    Figure 10a. Analysis of commodity-PPI monthly changes according to NBER economic cycle.

    Figure 10b. Analysis of CPI monthly changes according to NBER economic cycle.

    Subsequent analysis was performed to determine whether the significant relationship between commodity-PPI and DJIA was present during pre- and post-1970 era. (Note that this time point was arbitrarily chosen.) These results indicated a significant association between DJIA and Commodity-PPI was present only during the pre-1970 era, with no relationship at all in the post-1970 era (data not shown). To incorporate this finding into the model under development, the effects of Commodity-PPI on next-month DJIA were analyzed by linear regression according to both NBER economic cycle and pre vs post-1970 era. In this analysis, only the pre-1970 contractionary months revealed any significant relationship (figure 11). In these months, there was a significant positive relationship between Commodity-PPI and next-month DJIA monthly changes. The slope for this linear regression was 4.3% with a correlation coefficient of 0.21. This compares favorably with the earlier linear regression analysis (Table 2) and suggests that by narrowing down the time frame to pre-1970 contractionary economic months, a stronger association between commodity prices and DJIA performance has been identified.

    Figure 11. Linear regression analysis for DJIA according to Commodity-PPI (leading one month), for contractionary economic months prior to 1970.

    A multiple regression model was constructed to combine the variables discussed above. In this model, the DJIA was the response variable. The predictor variables included the continuous data series, Consumer-PPI and CPI, since both variables were shown to have relationships with the DJIA. NBER contraction and pre-1970 were used as categorical predictor variables, since they had been shown to identify time periods during which the other variables had a stronger relationship with DJIA. The results of leverage plots for each variable are shown in Figure 12a. The multivariate model statistics are shown in Figure 12b. It is important to note that multicollinearity is present due to the presence of the identified strong relationship between Commodity-PPI and CPI, and future analyses would require a better accounting for the potentially confounding effects of inflation among all of these variables. While the CPI has a linear relationship with Consumer-PPI, it is not a statistically significant predictor of DJIA within this multiple regression model. The only significant independent predictors of DJIA performance in this model appear to be Commodity-PPI (leading one month) and NBER contraction months, as indicated with p values of 0.0218 and 0.0314 respectively.

    Residual analysis from this multiple regression model reveals a somewhat sigmoidal-shaped normal quantile data plot with a few outliers outside the normal distribution, as shown in figure 12c. Figure 12d shows a time series model of the multiple regression residuals that reveals no apparent trends in residuals, but occasional large outliers appear to be scattered randomly throughout the data series. Figure 12e shows a residual versus predicted plot, which reveals no apparent curvilinearity but a possibility heteroskedasticity, with a higher density of points in the central portion of the plot. This could represent an effect of the outlying fat tails, represented by the single dots, which appear far outside the very dense portion where most points are found. This could be an artifact of the kurtosis in many of the data series that was discussed earlier. Figure 12f shows the histogram of Cook's D analysis of residuals from this model, which shows a number of influential outliers. Again, this is consistent with the hypothesis that kurtosis of the variables produces outlier months with exceptionally large monthly changes that are difficult to account for within a multiple regression model. Finally, figure 12g shows studentized residuals and hat analysis for the multiple regression model. The studentized residuals show a fair number of outliers, reflecting the kurtosis mentioned above. In summary, residual analysis reveals a possible influential effect of some of the extreme value outliers. While removal of the outliers would likely improve the correlations in the multiple regression model, it would also render it useless as a predictive tool.

    Figure 12a. Leverage plots of predictor variables in multiple regression model of DJIA

    (click to enlarge)

    Figure 12b. Multiple regression model for DJIA, by Consumer-PPI, CPI, NBER economic phase, and pre/post-1970 eras.

    Figure 12c. Residual analysis for the multiple regression model.

    (click to enlarge)

    Figure 12d. Time series plot of residuals from the multiple regression model.

    Figure12e. Residual by predicted plot for the multiple regression model.

    Figure 12f. Histogram of Cook's D Influence of Multiple Regression model residuals.

    Figure 12g. Studentized residuals and hat values of multiple regression model residuals.

    (click to enlarge)

    DISCUSSION AND CONCLUSIONS

    A positive linear relationship was identified between Commodity-PPI and DJIA from 1926 and 2006. While statistically significant, it was relatively weak in terms of magnitude, as measured by slope and correlation coefficient on linear regression analysis. By analyzing multiple factors, a stronger relationship was uncovered between these variables for pre-1970 months during periods of economic contraction.

    A multiple regression model was constructed to test whether the factors shown to be individually important factors of DJIA performance could be combined in a more complex model. The residual analysis of the multiple regression model indicates that a significant effect of outliers creates difficulties in using this regression model for predictions. While removal of outliers would very likely strengthen the correlation coefficient, it would also render the model useless as a predictive tool. The effects of kurtosis have created multi-billion dollar losses for highly leveraged hedge funds that ignored the outlying fat tail events in their statistical models.

    Multicollinearity is a difficult problem to deal with in this analysis. Because inflation raises the prices of essentially all assets (including equities), inflation likely remains a major lurking variable that influences DJIA, Commodity-PPI, and CPI. Thus, subsequent analysis could include other measurements of inflation, such as interest rates and M2 money supply in an attempt to normalize for the effects of inflation.

    These results highlight the complexity of attempting to predict equity market performance. Given the large number of professionals working to identify value with low risk, or "alpha" as described by the hedge fund industry, it is not surprising that relatively simple comparison of commodity price charts would fail to identify major correlations, or that correlations may be present in only certain time periods. Market experts might argue that the large number of mutual and hedge funds serve to immediately arbitrage any significant price anomalies. In fact, that any significant relationship at all was observed may be viewed as slightly remarkable, and further work could be performed to see if a modern relationship still exists between Commodity-PPI and the performance of equity index averages.

    Unfortunately for the initial hypothesis, the predictive value of Commodity-PPI for next-month DJIA performance appears to have diminished since 1970. Several reasons could explain this apparent change in a previous significant relationship. One major reason could be a change in the types of companies included in the Dow Jones Industrials index. Modern companies that have been added to this index include the addition of more technology companies, including software companies (Microsoft), computer component companies (Hewlett Packard, Intel), and telecommunications (Verizon). These types of companies are expected to be less dependent on commodity prices and more dependent on intellectual property and brand equity. While these types of companies were added to DJIA to better reflect the composition of American production, it has also resulted in a shift away from commodity-intensive industries toward softer, knowledge-based high-tech industries.

    Another interesting finding is the increase in volatility of DJIA monthly performance during a contracting economy. Our models do not account for an effect of volatility. However, many modern financial derivatives such as futures, options, and swaps do include volatility as a component of price. The same is true for many value at risk (VaR) calculations. This represents another potential avenue of investigation, since the increase in volatility could cause an increase in market instability or a market meltdown even in the absence of price changes, due to the way volatility is priced as a risk factor by many derivative models.

    Further analysis could concentrate on identifying the best cut-off time frame, or on analyzing individual commodity prices to see which, if any, individual commodities might be most associated with DJIA performance. However, the observation that the association is significant only prior to 1970 suggests that little if any predictive role is likely to be found to aid in portfolio management decisions. If the diminution of predictive value of Commodity-PPI was due to changes in the DJIA index, however, alternative indices of pure "hard manufacturing" companies could be analyzed to see whether Commodity-PPI still has predictive value for these commodity-consuming industries.

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    13http://www.bls.gov/ppi/home.htm (Accessed November 3, 2006)

    14en.wikipedia.org/wiki/Kurtosis

    15 Mandelbrot B, Hudson RL. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward; Basic Books, 2004; ISBN 0-465-04355-0

    16en.wikipedia.org/wiki/Long-Term_Capital_Management

    17 finance.yahoo.com/columnist/article/futu.../10116

    Disclosure: I am long SPY.

    Themes: commodities, asset allocation Stocks: SPY
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