## Waltzek: Gibson’s Paradox

As central banks from across the world continue to compete for historically low interest rates, those interested in gold investment are happily watching the gold price rise. But, as we all know this isn’t just a coincidence and Gibson’s Paradox goes some way to explain this.

In 1923 Alfred Herbert Gibson published a paper regarding the negative correlation between interest rates and inflation in Banker’s Magazine (White, 2011). John Maynard Keynes later coined the term Gibson’s Paradox in 1930 (Keynes, 1930). Unlike his contemporaries, Keynes embraced Gibson’s finding as one of the most established and profound in the field of economics. I concur Gibson’s Paradox deserves to be recognized as an economic law, not merely a theory.

Subsequent researchers proposed that Gibson’s Paradox explains much of the price movement in the gold market (Summers & Barsky, 1988). Research indicates that the gold price and real interest rates are highly negatively correlated – when rates go down, gold goes up. It has been rigorously back-tested and stands the test of time via not only theoretical evidence, but empirical research. In fact, regression analysis reveals a very high

f-statistic which adds statistical support to the notion – when real interest rates are below 2%, a bull market in gold is virtually certain.If experimental and experiential evidence validates Gibson’s Paradox, how come the theory isn’t widely recognized? It’s likely that the mainstream media and academia have been reticent to accept and assimilate Gibson’s Paradox due to a simple misconception. The generally accepted real interest rate or rate of return is not negative, and so a gold bull market is not anticipated.

How should analysts / economists determine the real interest rate? The real interest rate is the nominal rate that investors expect to receive, i.e. the long term treasury bond coupon or rate less the inflation rate. Since the U. S. Treasury earns 3% per annum, the real interest rate is 3% minus the annual rate of inflation. John Williams’ Shadowstats.com indicates a domestic inflation rate of 6-8%. To verify his work, one can calculate the annual growth rate in the Treasury Inflation Protected Securities TIPS ETF from the IPO date in 2004 until 2012. The TIPS ETF indicates a 6% (approximate) annual inflation rate, very close to John Williams’ figure. So to determine the real rate of return, the 6% inflation rate is subtracted from the 3% treasury yield, resulting with a real interest rate of -3%.

Next, Gibson’s Paradox offers a gold price forecast for the next 12 months (White, 2011). The rule states that for every percentage point the real interest rate (-3%) is below 2%, gold will increase in value by 8%. As calculated in the last paragraph, the real interest rate is assumed to be -3%. Since -3% is 5% below the 2% threshold, 5 percentage points times 8% provides the gold forecast for the next 12 months: 5 x 8% = 40% . The current gold price is near $1,700 – leading to a gold price forecast of: $1,700 x 1.40 = $2,380. Anecdotally, $2,380 coincides with the 1980 inflation adjusted, peak gold price.

Maintaining a healthy modicum of skepticism is wise for every investor. Next a very cursory back-test of Gibson’s Paradox is illustrated in Figure 1.1. Assuming that rates entered negative territory in 2001 and have remained there ever since, resulting with a constant real interest rate of -0.5%, gold should have performed as follows:

## Figure 1.1. Gibson’s Gold Law – Back-test:

2001: $300;

2002: $360;

2003: $432;

2004: $518;

2005: $622;

2006: $747;

2007: $895;

2008: $1074;

2009: $1289;

2010: $1547;

2011: $1857.Do the numbers above look familiar? Clearly the back-test shows a high correlation to the true bull market price advance – Gibson’s Paradox holds. Assuming the same negative real interest rate of -0.5% (2.5% below the threshold resulting with 2.5 x .08 = 20% growth per annum) Gibson’s Paradox provides a gold forecast in Figure 1.2 (White, 2011):

## Figure 1.2. Gibson’s Gold Law – Forecast:

2012: $1,700 x 1.2 = $2229;

2013: $2229 x 1.2 = $2675;

2014: $2675 x 1.2 = $3210;

2015: $3210 x 1.2 = $3851;

2016: $3851 x 1.2 = $4622;

2017: $4622 x 1.2 =$5,547.Therefore, if real interest rates remain even fractionally negative, given the precepts of Gibson’s Paradox, the price of gold should surpass

$5,500 by 2017. However, there are many factors that can skew the actual forecast outcomes. For instance, the real interest rate is volatile, which will result in varied annual gold price forecasts. The Gibson Gold Forecast is intended only as a guide. Nevertheless, gold investors are urged to regularly calculate the real, inflation adjusted interest rate to verify that it is below 2% and particularly that it remains below 0%, to satisfy the ideal conditions for higher gold prices.