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A reader posed the following question:
"What does recent outperformance of gold and steel mining sector and agricultural sector mean for the stock market in general and is there any correlation with other sectors in the following 3 to 12 months as common wisdom on the business cycle would suggest?"
To enable a sample that is long enough to support inference, we use the chemicals industry to represent agriculture and the precious metals and mining industry to represent gold and steel mining. We use the Fidelity Select Chemicals (FSCHX) fund as a tradable proxy for the chemicals industry and the Vanguard Precious Metals and Mining (VGPMX) fund as a tradable proxy for the precious metals and mining industry. To keep the analysis manageable, we relate the performances of these two funds to that of the S&P 500 index (and not the performances of other industries). Using daily return data for the funds and the index from 7/15/87 (the earliest all three are available) through 3/7/08, we find that...
Since we are investigating quarterly relationships, we first thin the sample by selecting every 63rd trading day so that quarterly test intervals are independent of one another. The thinned sample consists of 82 quarterly observations.
The following scatter plot relates quarterly changes in the S&P 500 index to changes in FSCHX for the same quarters. The Pearson correlation for the relationship is 0.68 and the R-squared statistic is 0.46, offering fairly strong evidence that the two series move together. The quarterly variation in FSCHX explains about half the variation in the S&P 500 index. Elimination of the outlier in the lower right (from the fourth quarter of 2000) increases the R-squared statistic to 0.56.
Is there any evidence that FSCHX leads or lags the S&P 500 index?
The next chart summarizes the correlations between quarterly returns for FSCHX and the S&P 500 index for various lead/lag relationships, ranging from the S&P 500 index leads by eight quarters to FSCHX leads by eight quarters. Sample sizes range from 74 to 82 quarterly observations, depending on the magnitude of the lead/lag interval. The correlation for the coincident relationship, as mapped in the preceding scatter plot, stands out. Correlations for lead/lag relationships other than zero appear to be noise.
For example, the assumption that FSCHX leads the S&P 500 index by one quarter ("1") yields a Pearson correlation of -0.33 and an R-squared statistic of 0.11, somewhat stronger than the quarterly reversion indicated by comparing the S&P 500 index to itself. These results suggest that the S&P 500 index next quarter has a modest tendency to move opposite the direction that FSCHX moved last quarter, with 11% of the variation in the index explained by the prior-month variation in FSCHX.
Is the story similar for precious metals and mining?
The next scatter plot relates quarterly changes in the S&P 500 index to changes in VGPMX for the same quarters. The Pearson correlation for the relationship is 0.13 and the R-squared statistic is 0.02, offering no evidence that the two series move together. In other words, quarterly returns for VGPMX have practically nothing to do with contemporaneous returns for the broad U.S. stock market.
Is there any evidence that VGPMX leads or lags the S&P 500 index?
The final chart summarizes the correlations between quarterly returns for VGPMX and the S&P 500 index for various lead/lag relationships, ranging from the S&P 500 index leads by eight quarters to VGPMX leads by eight quarters. Sample sizes again range from 74 to 82 quarterly observations depending on the magnitude of the lead/lag interval. Correlations for all the lead/lag relationships appear to be noise.
For example, the assumption that VGPMX leads the S&P 500 index by one quarter ("1") yields a Pearson correlation of -0.25 and an R-squared statistic of 0.06, somewhat stronger than the quarterly reversion indicated by comparing the S&P 500 index to itself. These results suggest that the S&P 500 index next quarter has a slight tendency to move opposite the direction of VGPMX last quarter, with 6% of the variation in the index explained by the prior-month variation in FSCHX.
In summary, evidence from simple tests indicates that the chemicals industry and the precious metals and mining industry do not reliably lead or lag the broad U.S. equity market. Chemicals (precious metals and mining) tend to move with (independently of) the broad stock market on a quarterly basis.
For related research, see Blog Synthesis: The Economy and the Stock Market. See especially our blog entries of 7/10/07 and 6/7/06.
