Does The ‘Shadow Price’ Of Gold Hold The Key To Its True Value?

If we can take this trend reversal as evidence that central banks consider the merits of the yellow metal to be anything but obsolete, this does raise the question of what role gold plays in a fiat money global financial system.

For us, however, rather than look at the role gold has as a component of central bank reserves, the more interesting question is what, if any does the link between the monetary base and gold reserves have to say for the potential intrinsic or shadow price of gold.

On this subject, principals Paul Brodsky and Lee Quaintance of QB Asset Management described in an investor letter written in 2011 how a “shadow price of gold” can be calculated by dividing the US monetary base by the official US gold reserves. The concept is relatively simple and dates back to the time when the monetary base (i.e. the dollar) was fully backed by gold.

While the direct link between the gold price and the monetary base is now something of a distant memory (the US having abandoned gold backing of the dollar in 1963), we believe there remains some merit in examining the relationship between gold reserves and the monetary base as an indicator of the implied price of gold. Using the same methodology as Brodsky and Quaintance (2011), we have extended the calculation to include the period from 2011 to 2018.

Using the adjusted monetary base figure provided by the Federal Reserve Bank of St Louis ($3.7 trillion as of May 2018) and US official Gold Reserves of 8,134 tonnes (0.261bn troy oz), the implied shadow gold price from our calculations is approximately $14,100. This compares to a spot gold price of c$1,2801. In effect, the implied price being c.11x higher than the current spot price.

Before jumping to conclusions regarding a ‘fair price’ for gold, we need to consider two potential issues with this analysis. Firstly, how has the relationship between the actual and shadow price varied over time (i.e. how well has the shadow price predicted the actual price). Secondly, given the expansion of the monetary base since the gold standard was abandoned (see figure 5), how does the shadow price vary with the level of assumed gold backing of the monetary base.

The shadow price over time

On the first issue, figure 1 plots the actual and estimated shadow price (based on 100% monetary backing) between 1970 and 2018 and shows that since the late 1980s there has been a significant divergence between the two. Figure 3 uses the same data but expresses the relationship as the actual gold price as a percentage of the shadow price in order to give a clearer idea when the two have converged and diverged.

As can be seen from the figure, the actual price of gold approximated the theoretical shadow price of gold in only two years out of the sample period of 48 years.

Interestingly, these two years happened to be 1979 and 1980, where the actual price of gold was 102% and 108% respectively of the shadow gold price. These two years, as we show in figure 4 which plots the year-on-year of US CPI inflation, were also stand out years for inflation.

We could be tempted to conclude, that for the actual gold price to converge with the shadow gold price (and our methodology to have merit) it requires extreme CPI inflation rates (for example, over two standard deviations above mean). However, the experience of 1974 when inflation met this criterion, but the actual gold price only reached 53% of the shadow gold price would tend to refute this. Prior to 1975, however, gold could not be easily traded as this was before the introduction of exchange-traded gold futures contracts in the US2. Hence, there is some justification to argue that the 1974 experience was not representative given the lack of the tradability of gold.

However, even stripping out 1974, using the assumption of 100% backing by gold, simply plotting the data over time does not say a great deal in favour of the shadow price as a predictor of the spot gold price. For the period as a whole, the average percentage rate is less than 30%.

But as we have already highlighted, during the post gold standard period the monetary base has significantly expanded. Figure 5, plots the US monetary base in both nominal and real terms (1983 being the base year for the real series) and shows the substantial growth over the period. The rate of expansion increased dramatically in the post financial crisis period as the Federal Reserve flooded the market with liquidity.

Given this expansion, using a 100% backing of the monetary base could be seen as an extreme level and so it is not surprising that it has relatively low predictive power. Addressing our second issue of assumed level of monetary backing, therefore, we repeat the analysis with an assumed level of 25%.

Figure 6 plots the resulting shadow price based on the lower assumed backing level. While, there remains significant deviations, the average percentage for the period increases from less than 30% (for 100% backing) to just over 100% using the 25% backing assumption.

Relationship with inflation

Given this closer relationship when using the lower backing assumption, we take the analysis further by splitting the comparisons of the actual gold price to the shadow price into discrete ten-year time periods. Table 1 compares the average actual-to-shadow ratio for each period, along with the average CPI inflation rate for the same period.

What our analysis shows is that on the assumption of a 25% monetary backing, the differential between the actual gold price and the shadow gold price is at its largest during periods of high inflation and at is smallest in periods of low inflation.

Given this relationship, the question arises of whether what we have shown is simply the actual gold price being a proxy for inflation or expressed in investment terms; an inflation hedge.

Academic work is inconclusive

On this issue there has been a considerable amount of academic work which has looked at the relationship between gold and inflation. In an early study, Jastram (1977) finds that gold is a poor hedge for inflation in the short run, though a good hedge in the long run. In a more recent study Aye, Chang and Gupta (2016) using data between 1833 and 2013 find that gold is a good inflation hedge in the long run, but the relationship breaks down during certain periods for various reasons. Iqbal (2017) using shorter term data between 1990 and 2013 finds that gold hedges inflation risk in the US but only during average and bearish conditions for gold markets and not in bull market times. Erb and Harvey (2012), however, find that gold is not a good hedge of inflation in the long run if the long run is defined as periods of 10 years or more.

If the relationship between the actual gold price and inflation is not as close as some would claim, what conclusions can be drawn from our analysis looking at the relationship between the actual and shadow gold price and the level of inflation?

Our key conclusion

Our key conclusion is that while the actual gold price may not be the perfect hedge for inflation, when measured over longer periods (i.e. ten years) we find the quantum of the differential between the actual and the shadow price of gold is closely related to inflation. At high levels of inflation, the actual price “over-shoots” the shadow price and at low levels of inflation the opposite is true. Moreover, in a period when the average inflation rate was close to the long-run average (i.e. 4%), namely the 1990s, the actual gold price was 85% of the shadow price.

Given this relationship between the actual and shadow price and inflation, all things being equal, we could conjecture that we do not need to return to the days of hyperinflation for the actual-shadow price differential to dramatically reduce (i.e. by a rise in the actual gold price). For example, with an inflation rate of just 3% (the average for the 1990s), we could see the actual gold price more than doubling if the differential converged to the 85% actual/shadow ratio from the current ratio of below 40%.

The shadow price of silver

This shadow price methodology does not have to be confined to gold. For those who have a greater interest in silver as an investment, we can use the above methodology in tandem with an average historic gold-silver ratio (spot gold price/spot silver srice) to derive a shadow price of silver.

Figure 7 above plots the historic gold-silver price ratio between 1975 and 2018. The average ratio for the whole period is 56.6. By dividing the shadow price of gold by this ratio the shadow price of silver for different monetary backing assumptions is shown in table 2. As shown in the third column of the table, using the 25% backing assumption the shadow silver price is calculated to be $62. At the time of writing this is almost four times the spot silver price of $16.43.

In summary

As a non-cashflow-generating/non-yielding asset, the absence of a numerator (such as a dividend, earnings or cash flows in the case of equities, or a coupon in the case of bonds) means that traditional valuation approaches are of little use when trying to determine a fair value for gold. The shadow price methodology discussed in this analysis which derives an implied price by dividing the US monetary base by the US official gold reserves offers a potential approach to this valuation problem.

Over the past half-century, on average an adjusted shadow gold price assuming 25% backing of the monetary base possesses reasonable explanatory power for the actual gold price, although large differentials have existed over extended periods of time.

Comparing the actual-shadow price differential over discrete ten-year periods reveals a close relationship with the inflation rate. For those who believe that inflation is not dead, relatively low levels of inflation compared to long run averages would appear to be sufficient to bridge much of the gap between the actual gold price and the adjusted shadow gold price. A relatively limited rise in inflation to 3% could lead to a significant reduction in the existing differential between the actual gold and the implied gold price. Which all things being equal implies a gold price of more than double the current spot price.

Using the same methodology for silver and comparing this to the long-run gold-silver price ratio implies an even greater upside for silver.

While history never repeats exactly, and academics continue to disagree about the role gold has to play as an inflation hedge, our analysis indicates that gold and silver prices have great potential and can play a valid role in a well-diversified portfolio.

By Matt Fletcher & Scott Evans

Matt Fletcher is a private investor based in Athens, Greece. His former roles include being a senor equity analyst for Eclectica Asset Management, Pioneer Investments, Merrill Lynch and a fund manager for Legal & General Investment Management.

Scott Evans is a researcher at London Business School (LBS) and is co-author of the Numis Smaller Companies index. Prior to LBS, Scott has held academic positions at the University of Oxford (UK), University of Birmingham (UK) and Brunel University London.

Seal Advisors

References

Erb, C.B & Harvey, C.R (2013), The Golden Dilemma, Financial Analysts Journal, CFA Institute.

Aye, G.C, Chang, T. and Gupta, R (2016), Is gold an inflation-hedge? Evidence from an interrupted Markov-switching cointegration model, Resources Policy, Volume 48, Elsevier.

Jastram, R (1977), The Golden Constant – The English and American Experience 1560- 1976, John Wiley and Sons.

Javed, I. (2017), Does gold hedge stock market, inflation and exchange rate risks? An econometric investigation, International Review of Economics and Finance, Volume 48, Elsevier.

Disclaimer<

SEAL Advisors is wholly owned subsidiary of Scott Evans Associates Ltd. All communications originating from Scott Evans Associates Ltd, however disseminated do not constitute a solicitation for the purchase or sale of any commodities, bonds, securities or investments of any kind. All information compiled in our communications are produced to the best of our ability, its accuracy is not guaranteed. Any persons using material published by Scott Evans Associates do so solely at their own risk and Scott Evans Associates Ltd shall be under no liability whatsoever in respect thereof. Users accept that all intellectual property rights (including copyright, patents, trade marks) whether registered, or not, on the communication shall remain the property of Scott Evans Associates Ltd and no customer, or other person shall, or shall attempt to obtain any title to such rights. Information appearing on this communication is the copyright of Scott Evans Associates Ltd and must not be reproduced in any medium without licence. Users are permitted to copy some material for their personal use as private individuals only. Users must not republish any part of the data either on another website, or in any other medium, print, electronic or otherwise, or as part of any commercial service without the prior written permission of a Director of Scott Evans Associates Ltd. Neither Scott Evans Associates Ltd, nor any of its suppliers, make any warranties expressed or implied, as to the accuracy, adequacy, quality or fitness for any particular purpose of the information or the services for a particular purpose or use and all such warranties are expressly excluded to the fullest extent that such warranties may be excluded by law. You bear all risks from any uses or results of using any information. You are responsible for validating the integrity of any information received over the internet. Due to the number of sources from which Scott Evans Associates Ltd obtains content Scott Evans Associates shall not have any liability (whether in contract or tort) for any losses, costs or damages resulting from or related to use of or inability to use any information contained in the publications or the web site of Scott Evans Associates Ltd. In no event shall Scott Evans Associates Ltd be liable to you for lost profits or for indirect, incidental, special, punitive or consequential damages arising out of or in relation to the provision of information in any publications however published.