Gold Price Explained
Gold's Movements in Relation to Other Assets
Alternative title: How to look at observable prices for other assets besides gold in real-time and infer the direction of the gold price?
Introduction
There is a relationship between the gold price (in US dollars) and all of the following: the US dollar, US real interest rates, and World inflation expectations. We can observe changes in the latter three and make inferences about how the gold price is likely to change.
I will present things in the form of a series of numbered items (so that I can come back and edit later as necessary).
List of revisions
Last revised on June 9, 2020 (Items 15.1, 24.2, 29.1, 30.1, 30.2, 32, 33 are new. Deleted Items 18, 19, 19.1 and replaced them with item 19.3. Revised Item 26.)
Previously revised on Jan. 12, 2020 (Item 22.1 is new.)
Previously revised on Dec. 29, 2019 (Items 16.1, 24.1 are new.)
Previously revised on Oct. 18, 2019 (Items 19.2, 30, 31 are new.)
Previously revised on June 21, 2019 (Item 4.05 is new.)
Previously revised on July 31, 2018 (Item 2.1 is new.)
Previously revised on March 14, 2018 (minor edits, the Introduction & items 11.1, 19.1, 28.2, 28.3 are new, modified 23, 24, 25, deleted 23.1)
Previously revised on Feb. 28, 2018. (Item 25.3 is new)
Previously revised on Jan. 22, 2018. (Items 25.1, 25.2, 28.1 (all new items))
Previously revised on Jan. 21, 2018. (Items 25, 27)
Previously revised on Jan. 15, 2018. (Items 4.1, 18, 19, 23.2, 26)
1---
All along, I assume we're talking about the gold price in US DOLLARS, i.e. from a US investor viewpoint.
2--- USDJPY
GOLD & CURRENCY
Gold tends to move inversely to USDJPY.
When the yen STRENGTHENS (USDJPY goes down, i.e. the dollar WEAKENS or goes down), gold tends to move up.
2.1--- USDCNY, USDCNH
In the summer of 2018, gold has traded inversely to the Chinese Yuan. The onshore version of this currency is USDCNY whereas its offshore version is USDCNH. The website investing.com provides real-times quotes of both. Reference: @GlobalProTrader on Twitter.
The relationship between USDJPY and Gold seems to have broken down. This may be temporary. It is believed that the BOJ has been ramping the Japanese Yen (i.e. higher USDJPY) in order to prevent the S&P 500 from falling. Reference: @BamaBroker on Twitter.
3---
Same thing as saying that
"A weak US dollar is bullish for gold."
3.1---
Notation $A -- this is the dollar symbol followed by a single or multiple letters represented by 'A' here.
$A represents something that can be entered for a ticker (or symbol) into stockcharts.com to get back a chart.
If 'A' represents a stock or ETF ticker, then stockcharts doesn't require preceding it with the '$' character. E.g. The stock Amazon is entered as AMZN because AMZN is a stock ticker, but the currency exchange rate USDJYP has to be entered as $USDJPY because USDJPY is not a ticker.
Also, both $A and #A have special meanings in Twitter. They are hashtags.
4---
GOLD & INTEREST RATES
Gold tends to move inversely to REAL interest rates. (That's US rates!)
The TIP is a bond that moves inversely to REAL rates.
TIP = Treasury Inflation-protected Bond.
Learn about TIP at https://www.treasurydirect.gov/indiv/products/prod_tips_glance.htm
Learn about the TIP ETF at http://www.etf.com/TIP
4.05---
Chart showing Gold's inverse movement relative to US REAL interest rates.
4.1---
The TIP ETF has a duration of 7.75 years as of this writing. This means that it can be thought of as a bond whose maturity is 7.75 years.
5---
When REAL rates go down, gold tends to move up.
Do we observe the direction of real rates by looking at the TIP ETF or what?
6---
Notation A:B -- this is the quantities 'A' and 'B' with a colon symbol in between them.
A:B means the ratio of A to B, also written as A/B, A/B ratio, or A:B ratio.
Stockcharts.com allows the user to plot charts by entering "A:B" where 'A' and 'B' represent two tickers.
We'll see an example below.
7--- TIP:SHY ratio
@Bamabroker looks at the TIP:SHY ratio to determine the direction of REAL interest rates.
A FALLING ratio means RISING real rates.
A RISING ratio means FALLING real rates, which is bullish for gold.
(Stockcharts.com recognizes both TIP and SHY without them being preceded by '$'.)
8---
When REAL interest rates go down (i.e. TIP:SHY ratio goes up), gold tends to move up.
9---
Same thing as saying that
"Falling REAL interest rates are bullish for gold."
9.1---
SHY represents the ticker for the 1-3 year Treasury bond ETF.
10---
To summarize things up to this point, we've said that gold tends to move up when the dollar goes down, and we've said gold tends to move up when real rates go down.
These earlier Tweets also suggest that what's also relevant is the relationship between the US dollar and REAL interest rates in US.
11---
It is actually true that the US dollar going down coincides with US real interest rates going down, usually. (Also, dollar up <=> real rates up.)
This makes good economic sense ... (Pause and think!)
11.1---
When US real interest rates go up, it makes non-US investors more interested in purchasing US dollars in order to benefit from these higher rates. Their buying action drives up the US dollar.
Similarly, when US real interest rates go down, the US dollar follows and goes down.
12---
What about the effect of inflation on the price of gold? Hmmm ...
13---
GOLD & INFLATION
@Bamabroker says US inflation does NOT affect the price of gold!
However, @hussmanjp says that WORLD inflation coincides with the price of gold moving in the same direction, i.e. rising WORLD inflation <=> gold goes up.
14--- Hussman's Model
@hussmanjp also says the same thing as above about the effect of US dollar and US real interest rates on the price of gold.
His equation for the gold price is:
$/ounce of gold = $/FC x FC/ounce of gold,
where FC stands for "foreign currency", and
'$/ounce of gold' = gold price in US dollars,
'$/FC' = value of Foreign Currency expressed in US dollars,
'FC/ounce of gold' = gold price in Foreign Currency.
Observe that all he has done to obtain the right-hand side is to introduce FC/FC which is nothing but 1 into '$/ounce of gold'.
Note that when the US dollar weakens, '$/FC' goes up.
Source: https://www.hussmanfunds.com/html/gold.htm (publication date unknown)
15---
When the US dollar goes down (i.e. USDJPY goes down), or when US real interest rates go down (i.e. TIP:SHY ratio goes up), '$/FC' goes up. Therefore, '$/ounce of gold', which is the gold price, goes up.
MAJOR STATEMENT!
(My earlier Tweets are consistent with both @hussmanjp and @bamabroker.)
15.1--- Hussman's Model in terms of Recognizable Variables
I usually remember variables more easily than English sentences. So, I will cast item #15 in algebraic form.
Gold Price ($/ounce) is proportional to: i_w / (r * USDXYZ) ,
where
i_w = world inflation rate (see Item 20),
r = US real interest rates,
USDXYZ = value of US dollar = amount of foreign currency "XYZ" that can be exchanged for one US dollar.
The reason for the symbol USDXYZ is to capture the way that foreign currencies are quoted. For example, USDJPY represents the value of one dollar in terms of Japanese Yen. The units of USDJPY are Japanese Yen per Dollar. This was also addressed in item 2.
16---
Compare this past statement to @TruthGundlach who had put up a chart showing the copper:gold ratio moving in lockstep with the 10-year US Treasury yield, TNX.
Note: TNX represents NOMINAL interest rates, which are approximately the sum of REAL interest rates and inflation expectations.
(To view the chart for TNX in stockcharts.com, you need to enter it as $TNX.)
16.1--- Chart of Copper:Gold Ratio & 10-Year US Treasury Yield
We see two periods (2012-2013 and 2018) when $TNX moved away from Copper:Gold in a major way but then was "pulled" back toward that ratio. In 2014, it was the ratio that moved somewhat away from $TNX but was then pulled toward it. Something to think about ...
17--- Copper:TNX ratio
Rearranging Gundlach's equation, we have him saying that copper:TNX ratio moves in lockstep with the gold price.
This looks very different from my earlier Tweets! Or does it really?
(To view the chart for copper in stockcharts.com, you need to enter it as $copper. To view the ratio copper:TNX, you need to enter them as $copper:$TNX. Lower or upper case doesn't matter.)
I decided to delete this section on June 9, 2020 and replace it with Item 19.3.
I haven't worked this out fully, but the starting point seems to be as follows.
(a) We could assume that the copper price moves in proportion to WORLD inflation expressed in dollars. (This makes intuitive sense.)
(b) We could then model the fact that TNX moves in proportion to both US REAL interest rates and US inflation expectations.
I am unclear as to whether the above assumptions lead to the movement of the copper:TNX ratio being proportional to simply 1/r or i/r, where 'r' represents US real interest rates and 'i' represents inflation (and I am being vague by not distinguishing between WORLD inflation and US inflation expectations ...). However, I suspect that the right answer is probably
19---
I decided to delete this section on June 9, 2020 and replace it with Item 19.3.
The observation that the TIP:SHY ratio and the Copper:TNX ratio are highly (but certainly not perfectly) correlated should drive our thinking under item 18. This is explored in the next item.
19.1---
I decided to delete this section on June 9, 2020 and replace it with Item 19.3.
19.2--- Copper tells the story of Economic Growth whereas Gold tells the story of Lack of Economic Growth
Chart showing Gold's inverse movement relative to US REAL interest rates (which we had previously seen under Item 4.05) and newly, Copper's inverse movement relative to China NOMINAL interest rates. Source.
The story of Copper seems to be tied to global economic growth ...
I will derive a model for Copper based on Gold and TNX.
A model for each of TNX (10-year US Treasury yield) and Gold Price is as follows.
TNX = (1 + r) * (1 + i) - 1 = r + i + r*i
Gold = k * i_w / (r * USDXYZ)
The notation is the same as in Item 15.1 but also
i = US inflation rate,
k = proportionality constant.
(Side note: in TNX, most people ignore the term r*i because it is negligible, but I'll keep it in there because it is more precise.)
Because of Gundlach's observation that Copper / Gold Ratio moves in lockstep with TNX, we can write
Copper / Gold = k_2 * TNX,
where k_2 is another proportionality constant.
Rearranging and then substituting, we have
Copper = k_2 * Gold * TNX
= k * k_2 * (r + i + r*i) * i_w / (r * USDXYZ)
In words, here's what this means. The movement of Copper is
a) directly proportional to World inflation and US inflation, because of i_w and i + r*i, respectively.
b) inversely proportional to US dollar, because of 1 / USDXYZ.
c) "complicated" (yet inversely proportional) with respect to US real interest rates, because of (r + i + r*i) / r.
Some preliminary thoughts on item 'c':
Let's modify the model for gold by replacing the r term by r^a where a is some positive number (that's most likely less than 1 or maybe greater than 1). The case of a=1 corresponds to the model prior to modification. After modification, the model would looks like this.
Gold = k * i_w / (r^a * USDXYZ)
Then, in the expression for Copper, the term (r + i + r*i) / r becomes (r + i + r*i) / r^a, which can be rewritten as (1 + i) * r^(1-a) + i / r^a ...
From here on, I used Excel to experiment numerically. I found out that if we assume that a < 1, then the function (1 + i) * r^(1-a) + i / r^a is convex in r. As r increases (with a set to 0.5), the function will at first decrease and then there will come a point where it will increase, which is convexity. The minimum point of this convex function moves to the right as i increases. The part where the function is decreasing in r -- the left part -- is short (small r range) and steep (high slope). The right part is long and shallow.
If we assume that a > 1 or a = 1, the function (1 + i) * r^(1-a) + i / r^a becomes decreasing in r. I don't think this would be consistent with economic sense because r is directly proportional to economic growth meaning that we would expect Copper to increase with higher economic growth.
If we assume that a > 1 or a = 1, the function (1 + i) * r^(1-a) + i / r^a becomes decreasing in r. I don't think this would be consistent with economic sense because r is directly proportional to economic growth meaning that we would expect Copper to increase with higher economic growth.
20--- World Inflation
Back to @hussmanjp's gold equation and the subject of inflation's effect on the gold price.
Repeating his equation,
$/ounce of gold = $/FC x FC/ounce of gold.
When there is rising WORLD inflation (not US inflation), 'FC/ounce of gold' goes up. Therefore, the gold price goes up.
21---
Question: How would we observe WORLD inflation?
Question 2: How is WORLD inflation related to US inflation? Hmmm ... Are they correlated or independent? What if central bank policy differs across countries?
22---
A clue for the answer may come from Gundlach's chart showing the correlation of copper:TNX ratio and gold price.
Copper may be correlated with WORLD inflation. (It makes intuitive sense, and which is what I have already explored under items 17 - 19.1.)
Ignore copper:TNX ratio for now ...
22.1---
Calculating WORLD inflation is easy even though observing it may be more difficult. To calculate it, we would first measure inflation in each country. For example, in the US it would be done via the CPI Index or PCE Index. Once we had a measure of inflation by country, we would then form their weighted average in order to arrive at WORLD inflation. What would the weights depend on? Perhaps a GDP weighting would make sense.
As a practical matter, we could ignore countries with very small GDPs.
When thinking about things in this framework, it's likely that US inflation could serve as a crude proxy for WORLD inflation.
23--- TIP:TLT ratio
Coming at it differently,
To the extent that WORLD inflation is correlated with US inflation, we can observe US inflation through the TIP:TLT ratio.
TIP is inversely proportional to US real interest rates.
TLT is inversely proportional to US NOMINAL interest rates, which in turn are proportional to US real interest rates and US inflation expectations.
So their ratio (TIP/TLT) is proportional to US inflation expectations.
(When working with the ratio TIP/TLT, The effect of US real interest rates on the TIP cancels out the effect of US real interest rates on TLT; this can be shown more rigorously by modeling the price of a bond as F/(1+r)^n, where F is the bond's face value payable in year n and r is the bond's yield. Furthermore, for a bond that's priced off of a nominal yield, we would model its price as F/((1+r)*(1+i))^n, where r represents a real yield and i represents an inflation rate.)
(Stockcharts.com recognizes TLT without it being preceded by '$'.)
23.1---
TLT represents the ticker for the 20+ year Treasury bond ETF.
Readers should tread lightly. This item needs more work, which may affect item items 23, 24, & 25 ...
24---
When US inflation expectations go up, TIP:TLT ratio goes up.
24.1--- Alternate Measure of Inflation: !PRII:!PRDI Ratio
!PRII stands for Pring Inflation Index while !PRDI stands for Pring Deflation Index. Both are available at Stockcharts.com; you will need to enter the '!' character.
To measure inflation, one would plot their ratio.
Here's an article from Stockcharts describing them (and an article from their creator). PRII is sensitive to mining, energy, basic industry, steel, and chemical stocks and rises when they rise. PRDI is sensitive to banking, insurance, and utility stocks and rises when they rise.
Here's a nice long-term chart from Stockcharts.com. (If this link stops working, the aforementioned article should contain links to live charts.)
Reference: I learnt about PRII and PRDI from @stebottaioli on Twitter. Link to the Tweet that did it.
24.2--- Comparison of !PRII:!PRDI Ratio to TIP:TLT Ratio
These Tweets provide such a comparison. Both ratios (are supposed to) rise with rising inflation.
25--- Ratio charts example
Note. It is indeed possible and observable for TIP:TLT ratio to go down (marking
This happened in 2017. See next two charts. Look at the trend from Jan. 2017 through Dec. 2017.
25.1--- Pure charts, not ratio charts
Appearing below are the charts for TIP, TLT, and SHY. These aren't ratio charts. As such, they may provide additional insight as to how the above ratio charts have come about.
Observe that the dominant trend from Jan. 2017 through Dec 2017 was that both the TIP and TLT rose (implying that the respective rates driving each ETF -- i.e. real rates in the case of TIP and nominal rates in the case of TLT) -- were falling. The ratio charts tell us that not only were real rates falling, but also that inflation expectations were falling.
During the same period, the SHY chart shows that from Jan. 2017 through Aug. 2017, SHY rose (implying that the rate driving it fell). Then, for the rest of 2017, SHY fell (implying that the rate driving it rose).
25.2--- Which looks better: TIP:TLT or TLT:TIP?
It's not clear to me whether there is a difference in looking at the TIP:TLT ratio chart or the TLT:TIP ratio chart. Mathematically, there is no difference, but there may be a difference from a technical analysis viewpoint. (Something to be explored later.) Meanwhile, the charts for both of these ratios appears below.
To my naked idea, the TLT:TIP chart looks better because it shows the flattening of inflation expectations which occurred in the second half of 2017 more clearly than the TIP:TLT chart.
(My rationale for presenting the TIP:TLT chart was that in conjunction with the TIP:SHY chart, we would have TIP as the numerator in both charts. However, now that I think of it, it may have been better to work with the TLT:TIP chart than the TIP:TLT chart because a rising TLT:TIP chart corresponds to falling inflation expectations. So, it is a more natural way to view things. Likewise, a rising TIP:SHY chart would correspond to falling real rates.)
25.3 --- Rationale for working with TIP:TLT instead of TLT:TIP
People who like to work with the TIP:TLT ratio like the fact that a rising TIP:TLT chart corresponds to rising inflation expectations and a falling TIP:TLT chart corresponds to falling inflation expectations. I.e. the chart moves in the same direction as inflation expectations.
(Personally, I like to work with TLT:TIP because in conjunction with TIP:SHY, things make sense as follows. To look at inflation expectations, I know I need to work with TLT whereas to look at real rates, I know I need to look at TIP. When looking at TLT, in order to remove the effect of real rates, I know that I need to normalize by TIP. When looking at TIP, in order to remove the effect of short term rates, I know I need to normalize by SHY. Hence, I end up with TLT:TIP and TIP:SHY as the things I need to be looking at. Next, I keep in mind that both ratios move in the opposite direction of the variable of interest. I.e. TLT:TIP moves in the opposite direction of inflation expectations and TIP:SHY moves in the opposite direction of real rates. Remembering that each movement is in the "opposite direction" is easy to remember because when dealing with a bond, its price always moves in the opposite direction of its yield. Here, we are dealing with specific types of bonds.)
26---
SUMMARY, version 1
For gold to go up in US dollar terms, we want to see
a) USDJPY go down (bearish US dollar)
b) TIP:SHY ratio go up (falling US real interest rates)
b') Copper:TNX ratio go up
Please see Item 30.1 for SUMMARY, version 2.
27---
We shouldn't care about
d) TIP:TLT ratio going up (rising US inflation),
unless we can establish that it is correlated with WORLD inflation.
28---
Next task: How to observe WORLD inflation via observations on asset prices or otherwise?
Unfinished work. I've made some inroads in Items 22 and 22.1.
28.1--- Intuition
My goal isn't to derive the fundamentals all the way to the deepest level possible, but to show enough of the fundamental underpinnings associated with observable market prices to allow one to interpret charts in order to understand what they mean. An academician might call my analysis a little sloppy and I might agree.
So, the TLT:TIP ratio uses the TIP to get rid of the real interest rate component of TLT while leaving behind its inflation expectations component.
Likewise, the TIP:SHY ratio uses the SHY to get rid of something (???) so as to leave behind a purer measure of real interest rates than would have been captured by TIP alone. (@Bamabroker could explain this better, as this ratio is what he uses to monitor the movement of real interest rates.)
28.2---
IEF is the 7-10 year Treasury bond ETF.
I wonder why @Bamabroker works with TLT:TIP instead of IEF:TIP. TLT has a duration of 20+ years whereas the TIP has a duration of 7.75 years. So, the durations of TIP and IEF are about the same whereas the durations of TLT and TIP are not. (It may be because the impact of inflation expectations on TLT is more pronounced than on IEF ...)
28.3---
Question: Why do we measure the strength or weakness of the US dollar against the Japanese Yen and not against some other currency or the US dollar index (a currency basket)?
Answer: Empirical studies must have shown the correlation of the gold price to be highest when measured against the USDJPY exchange rate as opposed to any other candidates ...
29---
References: @hussmanjp, @Bamabroker, @TruthGundlach on Twitter.
29.1---
@Bamabroker is no longer on Twitter. Apparently, his employer (Morgan Stanley?) didn't approve of his Twitter activity.
30---
Additional Reading:
1) Lyn Alden provides two valuation models for gold.
The first model plots gold on the same chart as US per-capita money supply (measured in the US as M2 divided by US population). The idea here is that M2 may be growing at 5-6% p.a. whereas population would be growing at around 1% p.a. (The supply of gold above ground is also growing around the same rate as population ...)
The second model plots gold's annual rate of change in price on the same chart as real interest rates.
In summary, gold tracks per-capita money supply and inversely real interest rates.
https://twitter.com/haditaheri/status/1181581470114209796
Interesting side comment: There is about 1 ounce of gold for each person on earth.
30.1--- Enhancing Haussman's Model with Alden's Model
SUMMARY, version 2
Reference: Haussman Model (Item 15.1)
Gold Price ($/ounce) is proportional to: i_w / (r * USDXYZ)
Gold Price ($/ounce) is prop. to: (M / Pop) / r,
where
M = US money supply (Alden suggests M2, Richard Wiener has used MZM),
Pop = US population,
r = US real interest rates (as before).
Haussman Alden Hybrid Model:
Gold Price ($/ounce) is prop. to: i_w * (M / Pop) / (r * USDXYZ).
30.2--- How can Gold not rise despite a growing Money Supply?
The combined Hussman Alden model shows that the way to keep Gold (priced in $) from rising despite a growing Money Supply is for the Dollar to remain strong.
2) David Jensen makes the case for gold price manipulation. ("If inflation is under-stated, then real yields are perceived to be higher than they really are, which implies that people will think that it's fair for gold's price to be lower than where it ought to be.")
https://twitter.com/haditaheri/status/1013597527428349952
3) Willem Middelkoop argues that gold could play a role if there's a reset in the global monetary system. ("The world faces two major financial problems that have yet to be solved.")
https://twitter.com/haditaheri/status/1184526919099920384
32-- What's clear and what's not
Reference: Haussman Alden Hybrid Model (Item 30.1)
Gold Price ($/ounce) is prop. to: i_w * (M / Pop) / (r * USDXYZ).
What's not clear is the direction of the US Dollar (USDXYZ). There are good arguments in favor of both. US Dollar liquidity shortages and a world marching toward crisis (whereby the dollar would act as safe haven) both point to a stronger dollar. On the other hand, Ray Dalio's perspective on the long-term debt cycle and the presence of excessive debt in the US (not to mention the entire world) point to a weaker dollar.
The variables that take a back seat are World Inflation (i_w) and US Population Growth (Pop). Population growth may march on as it has previously done, so I don't expect it to cause any abrupt shifts in the Gold Price. The last remaining variable is World Inflation. In a world where most countries have engaged in and continue to engage in expansionary monetary policy (e.g. QE, NIRP), I feel that the effect of this variable on the Gold Price is upward. However, I believe that my write-up is weak on its treatment of World Inflation ...
It seems that at the end of the day, it's the US Dollar that will determine the fate of the Gold Price.
33--- Incomplete work
$WIP vs $TIP ...
(For the US, we have TIP:TLT ratio for observing real interest rates. Q: Is there an analog for the World? We have WIP instead of TIP, but what is there instead of TLT?)
Author is also on Twitter
