# Why Gold Has A Real Return – The Definitive Gibson’s Paradox Solution

### Why Gold Has A Real Return – The Definitive Gibson’s Paradox Solution

Julian Van Erlach

Nexxus Wealth Technologies, Inc.

October 31, 2015

Abstract:

Gold is shown to obtain a real return in terms of global purchasing power per Troy oz. Whereas fiat money obtains a negative return equal to the inflation rate (loss of purchasing power) which is directly related to the excess of money stock growth to real GDP, gold obtains a real yield due to inherent above-ground stock growth below the rate of world real GDP growth. This effect has historically been masked by measuring the price of gold in currencies that have appreciated and not in global purchasing power. A novel solution of the Gold Standard Gibson’s Paradox proves that gold is valued according to a constant real yield.

### Why Gold Has A Real Return – The Definitive Gibson’s Paradox Solution – Introduction

This paper is a sub-section of a forth-coming paper that demonstrates how gold is valued globally as a function of a real yield that it obtains inherently. Thus, in terms of global purchasing power, gold is more than a real store of value, is sensitive to the global real after-tax intermediate and long term interest rate, and to changes in the expected fiat inflation rate. The author is a co-author of the 2005 Journal of Investing article: “The Price of Gold: A Global Required Yield Theory”.

### How Gold Gets Its Real Yield

Fiat money itself is not thought of as an investment asset for the simple reason that it loses purchasing power at the rate of inflation. Fiat money-based investment assets pay a return in fiat money – stocks and bonds for example – and must return, in fiat money, more than inflation after taxes to provide a real return in the form of capital gains, dividends and interest. The quantity theory of money (QTM) and its equation of exchange form can be used to describe inflation and purchasing power.

MVt = PtT Formula (1)

Where M is the total amount of money in circulation on average in an economy over a period t;

V is the transactional velocity of money for all transactions in an economy over time frame t;

P is price level;

T is an index of the aggregate real value of all transactions in an economy over a time frame;

This can be rewritten as Pt = MVt/T. The role of velocity and its contribution, if any, can be debated, as can the measures of money and transactions index. Fortunately, the theory can be put to a simple empirical test: the period 1981 – 2006 when the US M3 measure was collected and published. With no V term applied, figure 1 shows the indexed ratio of M3/real GDP (proxy for T) against the index of the CPI.

Figure 1: M3/Real GDP vs. CPI 1981 – 2006

The temporary negative divergence of M3/real GDP vs. the CPI during 1993-1999 was likely caused by the rapid growth in foreign investment in the U.S. during this period with sufficient magnitude in relation to GDP to push the CPI to the observed levels (Figure 2).

Figure 2: Net Direct Foreign Investment in the U.S. 1960-2012

The striking relationship offers empirical support for the QTM. The author has constructed a similar measure for gold, as a global asset, over a time period with reasonably good data for the total above ground world gold stock, world real GDP, and the world price level – the critical ingredients for the empirical test using World Gold Council gold stock and production data, and Angus Maddison world GDP and population data.

Figure 3: Pure Gold Standard World CPI vs. World Gold Stock/World Real GDP 1820- 1912

Over the 93 year period, the world price index (available from Barsky-Summers (1988)) clearly moves with the ratio of above ground gold stock to world real GDP. The divergences in the mid 1840’s and mid 1870’s correspond respectively to the U.S. banking crisis and depression and the UK Great Depression. Both historic and more recent gold mine production data (World Gold Council) show a clear and consistent pattern of above ground gold stock growth of about 1.2%; which closely matches world population growth. This of course means that world real GDP grows faster than world gold stock at the rate of real per capita productivity growth (GDP growth comprising inflation, population growth and per capita productivity growth).

The QTM indicates that gold, in its roles as a medium of exchange and investment should therefore gain in real purchasing power (in terms of a basket of goods and services) per unit at the rate of world real per capita productivity growth; in contrast to fiat money which loses purchasing power at the rate of inflation. Roy Jastram (1977) however, finds that gold appears to play the role of a constant rather than accretive store of value.

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