A reader requested a test of the following hypothesis from the article “Gold’s Bluff – Is a 30 Percent Drop Next?” [no longer available]: “Ironically, gold is more than just a hedge against market turmoil. Gold is actually one of the most accurate indicators of the stock market’s long-term direction. The Dow Jones measured in gold is a forward looking indicator.” To test this assertion, we examine relationships between the spot price of gold and the level of the Dow Jones Industrial Average (DJIA). Using monthly data for the spot price of gold in dollars per ounce and DJIA over the period January 1971 through January 2019 (577 months), *we find that:*

The following chart plots the ratio of the level of DJIA to the price of gold in dollars per ounce (DJIA/gold) over the full sample period. The ratio ranges from 1.3 at the end of January 1980 to 42.2 at the end of August 1999, with average 13.8 over the full sample period. Its value at the end of January 2019 is 18.9.

Also shown is the inception-to-date (ITD) average of DJIA/Gold, which ranges from 6.1 to 23.3. The wide variation in ITD average suggests the sample period is too short to determine a reliable average. In other words, this sample indicates no obvious “normal” value for the ratio.

To test predictive power, we first relate monthly level of DJIA/gold to next-month DJIA return.

The following scatter plot relates next-month return on DJIA to monthly value of DJIA/gold over the entire sample period. The Pearson correlation for the two series is -0.05 and the R-squared statistic 0.003, indicating that monthly level of DJIA/gold explains less than 1% of variation in DJIA the following month. In other words, the ratio of DJIA level to spot gold price appears not to be useful at a one-month horizon.

The Pearson correlation between next-month change in gold price and monthly value of DJIA/gold is 0.01 and the R-squared statistic 0.000, indicating no relationship.

To test for an exploitable non-linearity, we calculate average future DJIA and gold returns by ranked fifth (quintile) of DJIA/gold.

The next two charts summarize average next-month returns for DJIA (upper chart) and gold (lower chart) by quintile of DJIA/gold over the full sample period and two equal subperiods (break point at end of November 1993). There are 115 observations per quintile for the full sample.

Variation in average future DJIA monthly returns across quintiles is not systematic, but suggests that very low values of DJIA/gold are good for DJIA.

The DJIA/gold ratio quintiles show no ability to predict average future monthly returns for gold.

Note that these analyses are in-sample, meaning that an investor would need foresight through the end of the sample period to trade on this information during the sample period. A realistic (out-of-sample) scenario limits an investor to past data only, and the sample is scant from that perspective. For example, as shown in the first chart, an investor operating in the 1980s and 1990s would have calculated a much lower average for DJIA/gold than an investor operating since the mid-2000s.

Might DJIA/gold work more convincingly at an annual forecast horizon?

The next scatter plot relates next-year DJIA and gold returns to end-of-year DJIA/gold over the entire sample period (47 annual returns). The Pearson correlation for the two series is -0.20 and the R-squared statistic 0.04, indicating that end-of-year DJIA/gold explains about 4% of DJIA return the following year. In other words, a low (high) DJIA/gold is a little bit predictive of a strong (weak) stock market at a forecast horizon of one year.

The Pearson correlation for future gold returns is 0.00 and the R-squared statistic 0.00, indicating that end-of-year DJIA/gold explains none of gold return the following year. Stocks and not gold drive any reversion in DJIA/gold at an annual horizon.

The average annual return for DJIA for the 23 years with the lowest (24 years with the highest) values of DJIA/gold is 9.4% (7.6%). However, excluding either the best (1975) or the worst (2008) year for DJIA during the sample period makes returns for the highest and lowest values of DJIA/gold about the same. A single extreme year alters the conclusion, demonstrating unreliability of the suggested relationship.

Might the predictive horizon of DJIA/gold be longer than a year?

The final chart summarizes correlations between annual DJIA return or annual gold return and annual DJIA/gold for lead-lag relationships ranging from returns lead DJIA/gold by four years (-4) to DJIA/gold leads returns by four years (4). Results suggest that:

- Strong DJIA and weak gold returns over the past four years suggest (as would be expected) high DJIA/gold values this year. Conversely, weak DJIA and strong gold returns over the past four years suggest low DJIA/gold values this year.
- A high DJIA/gold this year suggests strong gold returns two to four years hence and weak DJIA returns one to four years hence. Conversely, a low DJIA/gold this year suggests weak gold returns two to four years hence and strong DJIA returns one to four years hence. These findings may persist beyond four years.

However, the sample is very short for this kind of analysis. The large peak in DJIA/gold in the late 1990s dominates findings. Also, the analysis is in-sample, so an investor operating in real time may have drawn different conclusions at different times.

In summary, *evidence from the past 47 years offers little support for belief that the ratio of DJIA to gold price reliably predicts stock market returns and no support for belief that the ratio predicts gold returns.*

Use of gold prices before 1971 would have little incremental value since: “On March 17, 1968, …the price of gold on the private market was allowed to fluctuate…[, and] in 1975…the price of gold was left to find its free-market level.”

Cautions regarding findings include:

- As noted, the available sample of free market gold prices may be too short to expose a reliable DJIA-gold relationship.
- Also as noted, the above analyses are in-sample. An investor operating in real time during the sample period would have drawn different conclusions at different points in time.
- A rolling historical window analysis (rather than ITD) may produce different results, but the dynamics of DJIA/gold indicate a very slow process, suggesting the need for a very long window.
- Because of weak/inconsistent evidence and the short sample, the above analyses test no trading strategies based on DJIA/gold.

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