Relationship Between Gold, Inflation, and Equities
Introduction:
No doubt you have often heard it stated as a matter of fact that gold is a hedge against inflation or, what may at first glance seem synonymous, that gold is correlated with inflation. Have you wondered to what degree this may be true, if it is true at all? Perhaps curiosity about gold has been piqued in light of recent record gold prices coupled with economic conditions in general.
In this first of two articles we will assemble and analyze data describing the statistical correlation between the monthly returns of gold, inflation, and equities. And in part2 of this study we will compare the long term price trends of gold, inflation, and equities.
Scope:
We will consider two specific questions within the context of the U.S. markets. The answers will impact the asset allocation decisions we make when managing an investment portfolio.
 Have gold returns after the end of the Bretton Woods agreement been correlated with actual inflation or with equity market returns? ^{1}
 Has there been a relationship between the long term price trends of gold, inflation, and equities? We will address this question in part2 of this study.
Definition of Terms:
Part of the problem is the ambiguity that arises due to the different usage of words. So let’s begin by defining some important terms. The S&P 500 index (SPX) monthly closing prices will act as the proxy for the equity market price. ^{2} And gold prices will be represented by the monthly closing US dollar price of one troy ounce. ^{3}
In this study inflation will be defined as a general rise the price level of goods and services due to monetary causes, i.e. due to the supply and demand dynamics of money and not of goods and services. Inflation will be represented by the U.S. Bureau of Labor Statistics’ Consumer Price Index for All Urban Consumers: All Items (CPIU). ^{4} Though I acknowledge that its adequacy as said measure is often debated, it is none the less what many investors reference when quoting inflation.
By “correlation” I mean the statistical definition of the word, and not its colloquial meanings. Correlation analysis verifies if returns are related, while regression analysis attempts to define the precise mathematical form of this relationship, such as y=mx+b.
Of specific interest is the sample linear correlation coefficient of monthly returns between two assets. This coefficient describes the degree to which the average variation of returns (deviation from the sample average return) between two assets is linearly related. Values range from 1 to +1, where zero means no linear relationship exists, and +/1 means a perfect linear relationship exists. Mathematically, the correlation coefficient is:
For example, if gold’s monthly return rises above (or declines below) its average value coincident with inflation rising above its average, then the correlation coefficient will be positive (negative). The more closely the variation of returns of one asset is synchronized with the other regardless of scale, ^{6} the closer the correlation coefficient approaches to +/1. The more random the relationship, then the closer correlation approaches zero.
Scatter plots help visualize the relationship and help determine if it is linear or nonlinear. A strong nonlinear correlation could result in a low linear correlation coefficient with misleading results. Always keep in mind that correlation does not imply causation, and it should be suspect in the absence of a reasonable basis.
Have Gold Returns Been Correlated With Inflation or Equity Returns?
We will attempt to answer this question by performing two exercises using monthly return data gathered from January 1979 through June 2011:
 Calculate and analyze the correlation coefficient between gold, the CPIU, and the SP500.
 Perform a linear crosssectional regression analysis, regressing gold against the CPIU and then against the SP500.
We can do this quite adequately using Microsoft Excel. Note in the following table that we are calculating correlation and regression using monthly price change in percent, as shown in the columns labeled “Gold%”, “CPIU%”, and “SPX%”, rather than using the raw prices.
Over the period from January 1979 through June 2011, correlation (in green) between monthly gold returns and inflation was a paltry 0.1252. Gold and equity returns correlated even less, a miniscule 0.0270. The fact that the “tcalc” values (in red) are all less than the critical value 2.8232, confirms that correlations are indeed all statistically insignificant or likely equal to zero at the 99% confidence level. Incidentally, the correlation between equities and inflation was only 0.0706.
The lack of significant linear correlations between gold, inflation and equity returns does not necessarily mean that there is no correlation at all. After all a strong nonlinear correlation could exist, producing low linear correlation values.
The following scatter plots will visually confirm the absence of strong linear and nonlinear correlations. Notice the randomness of these patterns – much like a shotgun blast. The first chart regresses gold against inflation and the second regresses gold against equities.
These regression charts can each be summarized as a table sometimes referred to as an ANOVA, or analysis of variance table. Notice in the table below that both coefficients of determination, R^{2}, are virtually zero. ^{5} On average, the variation in inflation returns explains 1.57% of the variation in gold returns, leaving more than 98% unexplained by inflation. The explanatory factor between gold and equities is even less, a mere 0.07%.
“The absence of significant correlation in monthly returns between gold and equities is a delectable fact of prime significance when analyzing the diversification role of gold in an investment portfolio’s asset allocation.”
But Have Gold Returns Been Correlated Over Shorter Periods?
What we have examined thus far is the correlation of returns over a secular ^{7} time frame, namely over three decades. But what about cyclical periods of say 13 years? A simple way to begin to answer this question is by plotting the data visually as in the following chart.
The red line represents 3year moving correlation between gold and inflation measured using the scale on the left. Each point on this line is correlation calculated for the preceding three years between monthly gold returns and the percentage change in inflation. The green and dashed blue lines represent gold and equity prices measured using the price scale on the right and are offered as a historical backdrop for the correlation line.
As the high rate of inflation of the 1970’s declined significantly in the early 1980’s, the 3year moving correlation between gold and inflation dropped suddenly from a positive .2505 to a negative .3963 in less than one year. This correlation then trended gradually to its highest level at .5222 in 1993 only to again decline sharply to a negative .3164 by late 1996.
Correlation treaded above zero during the cyclical bear then bull markets in equities between 2000 and late 2007. Then by late 2008, correlation rose swiftly to 0.4511 as the second cyclical bear market of the 2000 secular bear market was well underway. I will leave it to the reader to extrapolate a meaningful conclusion from this correlation data.
Conclusions:
The data presented here does not support a significant correlation between monthly gold returns and inflation or equities in the U.S.A. during the three decades since 1979. But the absence of significant correlation in monthly returns between gold and equities is a delectable fact of prime significance when analyzing the diversification role of gold in an investment portfolio’s asset allocation.
In part2 of this study, we will address the second question namely whether there has been a relationship between the long term price trends of gold, inflation, and equities.
Thank you for reading this article. Your comments are welcomed!
Related articles suggested for your reading:
A Technical Analysis of Gold’s Secular Uptrend
Adding Gold To An Equity Portfolio
Relationship Between Gold, Inflation, and Equities II
Merging Fundamental and Technical Analysis
Footnotes:
 Equity valuation theory and practice includes expected inflation in the required return estimate or discount rate.
 (Sep. 2011). In Yahoo! Finance. Retrieved from http://finance.yahoo.com/
 (Sep. 2011). In World Gold Council. Retrieved from http://www.gold.org/
 (Sep. 2011). In Federal Reserve Bank of St. Louis. Retrieved from http://stlouisfed.org/
 The coefficient of determination, Rsquared, is the percentage of the total variation explained by the regression equation, Y=mX + b. It is equal to SSreg/SStot, the variation explained by the regression as a proportion of the total variation, where SStot = SSreg + SSresid. In a simple (not multiple) linear regression, Rsquared is also equal to the square of the correlation coefficient.
 A hypothetical correlation coefficient of +1 does not mean that the dependent variable moves 1% for a 1% move in the independent variable. The dependent variable may for example be related by a factor or 1.2 and thus moves 1.2% for a 1% move in the independent variable.
 Secular trends last approximately 925 years. Several cyclical trends each approximately 13 years in duration can exist within one secular bull or bear trend. The cyclical bear from 2000 until early 2003, followed by the cyclical bull ending late 2007, and the second cyclical bear ending in early 2009 all comprise the same secular bear market which began in 2000 as measured by the S&P 500 index.
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Other Links to this Post

Relationship Between Gold, Inflation, and Equities II  Sargon Y. Zia, merging fundamental analysis with technical analysis — October 16, 2011 @ 3:04 pm

Adding Gold To An Equity Portfolio  Sargon Y. Zia, merging fundamental analysis with technical analysis — October 23, 2011 @ 11:28 pm

A Technical Analysis of Gold’s Secular Uptrend  Sargon Y. Zia, merging fundamental analysis with technical analysis — October 31, 2011 @ 9:39 pm
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