The Golden Constant Hypothesis And Its Implications For Future Real Gold Returns

by: Radovan Vojtko


A "golden constant" hypothesis by Erb and Harvey considers inflation as a fundamental driver of the price of gold.

There exists some support of the claim that gold holds its value, but only in the very very long periods (centuries).

In the short term (decades), while inflation exhibited only mild volatility (over 10-year periods), the nominal price of gold, on the contrary, was very volatile.

The actual theoretical "fair" price, following the golden constant hypothesis, is approximately $825, which is much lower than the actual price.

Gold There are several theories attempting to explain either value or movements in the price of gold, with differing views on fundamental economic and political forces behind them (it is a very popular topic for conspiracy theorists too). The recent paper on "golden constant" hypothesis by Erb and Harvey considers inflation as a fundamental driver of the price of gold, and therefore suggests that the primary motive for investing in gold is to hedge against inflation. According to the hypothesis, the purchasing power of gold does not change significantly over the long term and any deviations in the gold price relative to inflation will be corrected. All of these statements lead to a common conclusion, that gold on its own is expected to generate practically zero real return in the long run. These findings have important implications for investors in popular gold ETFs like the SPDR Gold Trust ETF ( GLD or IAU.

In this article we will summarize the findings by Erb and Harvey (2015), who analyzed the historical prices of gold, compared them to theoretical prices under the golden constant hypothesis, and attempted to predict real returns from gold over the next 10 years, coming to some interesting results. After that we will take a quick look at Van Erlach's (2015) paper, who offered a different, but no less interesting, perspective on the matter.

The price of gold in July 2015 (the end of the paper's sample period) was $1096 per ounce. The theoretical "fair" price calculated by the authors, following the golden constant hypothesis, was approximately $825, which is much lower than the actual price. Erb and Harvey first calculated the average real price of gold over the period from January 1975 to June 2015 as an average of the nominal price of gold divided by the U.S. Consumer Price Index. Multiplying it back by the CPI in June 2015, they obtained the result of $825. The fact is, that the price of gold has fluctuated around the golden constant considerably over the 1975-2015 sample period, which divided the investors into two groups - those who believe that gold is still a reliable inflation hedge in the long run, and those who think the actual values are too far from the theoretical to agree with the previous group.

Note: If the average real gold price rises in the future, gold generates return higher than just compensation for inflation, and, vice versa, if it falls over time, the return will be lower than inflation rate, and thus gold would fail to fulfill investors' expectations as an inflation hedge.

With the current price of gold (January 8th, 2015) at around $1100 per ounce, the gold is still far from the theoretical price line. But the golden constant value is not to be considered the bottom. To reach the period's minimum real price from the beginning of this century, the price of gold based on the CPI from June 2015 could go as low as $350 per ounce (as shown in Figure 1).

Figure 1: Theoretical "fair", low, and high prices of gold; 1975-2015

Theoretical fair price Click to enlarge
Source: Erb and Harvey, 2015

Furthermore, no one can say with certainty that the real price of gold will not reach its new high or low in a foreseeable future. That is because, as Erb and Harvey point out themselves, golden constant hypothesis is not a fact. The golden constant hypothesis would expect the real price of gold to remain constant. Therefore, the current above-average real price of gold would be expected to "mean revert". Even though the graph predicts such development, future might be different - as the authors quote the words of Henry Ford: "history is more or less bunk".

Assuming that golden constant hypothesis will hold in the future, Erb and Harvey finally turned their attention on the analysis of real returns from gold. Based on the historical relation between the real price of gold and the subsequent real gold returns, which showed that an above-average real price of gold presupposes below-average 10 year real gold returns (and vice versa), the real gold returns are expected to be below-average over the next 10 years.

The authors forecasted a 10-year return, assuming an inflation rate of 2%, which would lead to an increase in "fair" - golden constant - price from $825 to $1006 per ounce. Compared to the actual current price of around $1100, it translates into a negative nominal and real return of -0.9% and -2.8% per year, respectively. If the price fell to the new low after 10 years (extreme case), which increased from $350 to $427 per ounce, the nominal and real annual returns would be -9.0% and -10.8%, respectively. What is interesting is that after changing the inflation rate from 2% to 0% and subsequently to 1%, the annual real return in both scenarios (both from actual to fair price and from actual to low price) remained unchanged (the nominal return naturally differed by exactly the difference between inflation rates).

Eventually, the authors found that being able to perfectly forecast future inflation is of no help at all in forecasting the future gold nominal returns. It is because while inflation exhibited only mild volatility (over 10-year periods), the nominal price of gold, on the contrary, was very volatile. However, they provide some interesting evidence, which supports the claim that gold holds its value, but only in the very long period(!): e.g. the wage of a Roman centurion measured in gold was barely different from what a U.S. Army captain is paid; the price of bread in gold terms was approximately the same thousands of years ago as it is today. It does not hold for short periods, not even 10 years, because the price of gold is too volatile.

Van Erlach's perspective

Van Erlach (2015) modified the traditional quantitative theory of money to measure purchasing power of gold over time - price level in terms of gold calculated as a ratio of above ground gold stock to world real GDP. Price level obtained this way was closely correlated to the world price index in the 19th century. Over the 1820-1913 period, the above ground gold stock grew rather consistently at the rate of 1.2% per annum, which was lower than the real GDP growth. Thus, the real purchasing power of gold increased over the period in global terms (see Figure 2).

Figure 2: World Gold Stock / World GDP vs. World Price Index; 1820-1913

World Gold Stock Click to enlarge
Source: Van Erlach, 2015

The phenomenon was concealed by expressing the price of gold in currencies of major economies, which appreciated over the period, making the real price of gold seem, more or less, constant until the abandonment of gold standard (as shown in Figure 3).

Figure 3: Real Price of Gold (Nominal price of gold in USD / U.S. CPI); 1820-2000

Real Price of Gold
Source: Data from and

Thus, Van Erlach's findings suggest, as opposed to golden constant hypothesis, that gold should be thought of as more than just a constant store of value - it should be thought of as an asset earning a real yield, which is a function of world gold stock to world GDP ratio.


The two articles looked at gold from different perspectives. Erb and Harvey showed us what a fair price of gold could be according to the golden constant hypothesis ($825 in June 2015 CPI), how low could it go to reach the bottom real price from the beginning of 2000s ($350 in June 2015 CPI) and what the real return would be over the next 10 years, assuming that the price gold will reflect its fair value at the end of the period (-2.8% per annum). Different rates of inflation did not affect the real return over the period. Eventually, they provide evidence, that gold might protect against inflation, but only over a very long term.

Van Erlach found that gold has historically obtained a real return in terms of the real purchasing power of gold, but the effect has not been visible when measured in major currencies that have appreciated over time.


  1. ERB, C. B. - HARVEY, C. R. 2015. The Golden Constant (Working paper)
  2. VAN ERLACH, J. 2015. Why Gold Has a Real Return - The Definitive Gibson's Paradox Solution (Working paper)

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