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A research paper entitled ‘The Price of Gold: A Global Required Yield Theory’ (RYT) holds that “since gold fulfills the unique function of a global store of value, its yield must vary inversely to the yield required by any financial asset class, thus providing a hedge in the case where such assets are losing value. Our theory explains about 88% of actual $USD gold prices and 92% of actual gold returns on a quarterly basis, including the peak prices of gold, over the 1979-2002 period.”

The original article, as written by Christophe Faugère & Julian Van Erlach MBA, is presented below in a slightly edited ([ ]) and abridged (…) format by the editorial team at munKNEE.com to ensure the reader with a fast and easy read.

Assessing the fair value of gold largely remains a mystery in Finance. While in some instances the existing literature has found empirical relationships between gold prices and macroeconomic variables such as inflation and exchange rates, little evidence has been offered for connections between gold and other asset classes. [Up until now there has been] no comprehensive theory of gold valuation showing how inflation, exchange rates and other asset classes may together affect gold pricing; or how gold and other asset classes may be affected by common underlying factors.

In this paper, we offer a gold asset pricing theory that treats gold as a store of wealth. We demonstrate a theoretical and empirical link between gold price, inflation, and foreign exchange rates and the general valuation of the stock market. Gold is a store of value, that is, a hedging instrument against inflation and the collapse of the value of other asset classes.

Throughout the history of civilization, gold has been the single most important global store of value. To this day, it fulfills this unique function. For the purpose of extending Required Yield Theory to gold pricing, we postulate the following:

1) The global real price of gold essentially is a real P/E ratio for gold, where “earnings” represent purchasing power or a global price index.

2) The global real price of gold must vary inversely to all other main financial asset classes’ real P/E to preserve the real value of any investor’s capital against adverse movements in the values of financial asset classes.

3) Law of One Price: exchange rate fluctuations must impact local currency-denominated gold prices to eliminate potential international gold arbitrages.

4) Mining supply must be stable in relation to supply movements in the aboveground stock and the worldwide stock of gold per capita should not increase in the long run.

Condition 1) recognizes that even though gold does not produce actual earnings, its primary purpose is to provide a stream of services by maintaining real purchasing power over time. The same unit of gold can serve to purchase a representative basket of economic goods repeatedly. We define the forward P/E for gold as the price of gold divided by expected next period’s GDP deflator. It is easy to check that the real price of gold is the same as the real forward gold P/E ratio.

Condition 2) insures that gold behaves as a store of value, that is: capital flows to gold are dictated by changes in the minimum expected return achievable by other asset classes. It is important to emphasize that gold per-se does not require the same yield as other assets, as it stands outside of the conventional realm of investment goals, and acts mostly as a global hedging tool against financial downturns, and inflation.

Hence, our theory postulates that movements in the global real price occur because of the precautionary demand for gold, which largely depends on changes in the inverse real P/E (or required yield) of other assets classes combined. A consequence of this postulate is that a decline in the value of the stock market index does not necessarily entail flight to gold when, for example, expected stock earnings are also falling to maintain a constant real P/E ratio. On the other hand, flight to gold will happen when stock market prices are dropping faster than expected earnings due to acceleration of inflation for example.

In condition 3) we state that since gold is a global homogeneous durable commodity its price must be equalized across countries after currency conversion.

Condition 4) states that the supply of gold must be stable so that investors’ precautionary motive is fulfilled without major price movements driven by supply shocks. Indeed this condition seems to be characteristic of the precious metal mining industry.

A preliminary empirical investigation of the price of gold reveals a non-trivial connection between real gold prices and the US stock market. Gold’s real price varies inversely to the S&P 500 P/E, and thus with the earnings-to-price ratio.

The theory we develop below predicts and explains this high level of correlation based on viewing gold as a global store of value.

We have extended the Required Yield Theory (RYT) developed by Faugere-Van Erlach [2003] to value gold and to determine its return. RYT states that since global assets are priced to yield a global constant real return, and since gold is a global store of value, its price will vary directly with the global required yield and the global inflation rate. In the course of developing this asset valuation model we introduced a new exchange rule parity based on required yields comparisons across countries.

Specific predictions include:

1) the real price of gold varies proportionately to the change in long-term economic productivity as measured by GDP/capita growth.

2) Real gold prices vary proportionately to changes in the foreign exchange rate (direct quotation) when the domestic required yield is constant.

3) When the foreign exchange rate is constant and there are no major geopolitical or natural crises, real domestic gold price increases with domestic inflation.

4) When our new exchange rate parity rule holds, then effectively the real domestic price of gold is mostly determined by the domestic required yield. This entails that foreign exchange effects will impact the domestic real gold price to the extent that equalization of required yields is not taking place worldwide and/or that PPP is violated as well.

5) In the long-term, the gold per-capita supply remains constant.

6) The average long-term absolute price of gold is marked-up cost where the profit margin is given by the global average long-term per-capita rate of GDP growth.

While we suspect that central bank activities, hedging activities, supply/demand fluctuations, global real GDP growth changes or changes in global income and capital gains tax rates, affect gold prices as well, the valuation approach developed here performs very well absent these factors, with over 92% accuracy in predicting US Gold returns over a 23-year period.

As for the practical implications of these findings:

1. In the long run, the gold mining industry’s real profit margin is constant and equals the real per capita productivity.

2. The price of gold, on average, must be the average production cost plus a constant mark-up.

3. Furthermore, in order for the real value of gold to be maintained on a per investor basis, the stock of gold has to grow at a rate that can be no greater than population growth in the long-term. If the supply of gold grew at a lesser rate than population growth for reasons other than depletion of the exhaustible ore, gold price would grow faster than inflation and the quantity demanded for gold would drop.

4. Eventually the supply of mined gold will dwindle, which will drive prices up unless world population experiences zero growth in the foreseeable future. In that circumstance, far off in the future, a substitute medium of storing value may be discovered and used.

Another prediction of our theory of gold pricing is that the decrease in proportion of gold total value as compared to world wealth is explained by the Required Yield Theory in the fact that relative to financial assets, the long-term nominal value of gold must increase at the inflation rate, whereas the value of other assets rise with inflation plus real productivity. Thus, the proportion of investable wealth declines at an annual rate equal to real per share earnings growth or GDP/capita growth.

While we are certain that this paper’s findings will not even bring the massive divide between gold fans and pessimists even an inch closer, having a solid, reproducible basis in which to reproduce the authors’ results could be sufficient for some crazy quant to put together a HFT algo which will trade gold based on the postulates presented herein.

With an 88% prediction rate (absent major outliers events), we are confident that this could be an appropriate problem to reverse engineer (if it hasn’t been already).