What Makes for a Happy Life?

Excerpts from This Article

The not-so-obvious lessons:

Successful aging means giving to others joyously whenever one is able, receiving from others gratefully whenever one needs it, and being greedy enough to develop one’s own self in between.

Mature methods of coping include altruism, sublimation, suppression and humor.

These four mature coping strategies are not only associated with maturity, but they can be reframed as virtues. Such virtues can include doing as one would be done by (altruism); artistic creation to resolve conflict and spinning straw into gold (sublimation); a stiff upper lip, patience, seeing the bright side (suppression); and the ability not to take oneself too seriously (humor).

Blaming others, being passive-aggressive, living in denial, acting out and retreating into fantasy are all maladaptive coping mechanisms associated with poor outcomes.

When we're no longer young, the best way to selfishly improve your life is to be unselfish and focus on helping those around you.

Author is also on Twitter

Gianni Agnelli

Gianni Agnelli (1921, 2003), the charismatic Italian industrialist and principal shareholder of FIAT. Also known as L'Avvocato.

When he died, 500,000 people came to view his casket in Turin. His son committed suicide 3 years prior at the age of 46; he jumped from a 100 meter bridge to prove his courage to a father who never believed in his son’s courage.

• HBO documentary (in Italian), 99 mins: https://youtu.be/BROIUWAGZXs
• Section of it (in English), 31 mins: https://youtu.be/EbZuDD3PvB4

I found the documentary interesting because the social unrest (or rather, national terrorism) of the 1970s seems to be traceable back to declining economic growth in Italy.

L’Avvocato’s financial success must have been due, to a good extent, to Italy’s phenomenal economic growth in the 25 years following the 2nd World War. (However, this is not to dismiss L'Avvocato's skills and talents, plus his central role and influence in Italy's economy.)

Here's a chart of Italy's annual GDP growth rate. (I'm guessing that this would be a nominal growth rate as opposed to real. In other words, it includes inflation.) Italy's GDP growth rate has been on a steady decline since 1950.

References

1. The Economic Miracle, https://www.britannica.com/place/Italy/The-economic-miracle
2. 150 years of the Italian economy, 1861–2010, https://www.tandfonline.com/doi/full/10.1080/13545710903465507
3. The Italian Economic Crises of the 1970's - Federal Reserve Bank, https://www.federalreserve.gov/pubs/ifdp/1978/120/ifdp120.pdf
4. Gianni Agnelli, Wikipedia, https://en.wikipedia.org/wiki/Gianni_Agnelli 

Author is also on Twitter

Selected Slides from Mary Meeker's 2018 Internet Report

(with Commentary)

I excerpted the slides below from Mary Meeker's slide deck from May 2018 which can be found here. Update (June 6, 2020): This link doesn't work anymore. Here's a link that works and provides access to reports from all years.

I have preceded each slide with my own commentary. 

I've also included some predictions based on what the data is telling me. In so doing, we will see in due time whether and to what extent I may have made a fool out of myself! You can find them by looking for the word "predict" highlighted in yellow.

List of revisions:

Aug. 3, 2018: I have commented on the first 9 slides alone. 32 more slides to go. Proof-reading pending. 

June 5, 2020: I never commented on the remaining 32 slides. However, I did make all slides X-large for more easy viewing.

----------

Global Technology Private Financing

The next chart shows how technology private financing seems to have undergone a regime change in 2014. Its dollar amount somewhat doubled from the preceding 3 years. 

From 2009 (NASDAQ low point) to 2013, the stock market more than doubled. My hypothesis is that investors took their profits from the stock market and in 2014, stepped up their pace of investment in the private markets.

The lesson from 2000 is seen to be that while the stock market fell through 2002, private technology financing also fell, and it fell for one more year beyond 2002. Today, this should serve as a warning sign to private companies expecting to raise private funds in the event that the public stock markets turn sour.

USA Public Company R&D + Capital Expenditures

The next chart shows the massive amount of capital spent by US public companies on R&D plus Capital Expenditures in a single year. The figures run in the tens of billions of dollars on a per-company basis and the aggregate amount is almost $300 billion.

Also observe how Facebook falls short relative to other high tech names most of which are the FAANG stocks.

Square

The next slide is about Square, ticker SQ. Its global active seller count was 2.8 million estimated as of 2017.

The average GPV (Gross Payment Volume) per seller works out to $23,000 rounded for the year 2017. (These are small sellers.)

Shopify

The next slide is about Shopify, ticker SHOP. Its global active merchant count was 609,000 estimated as of 2017.

The average GMV (Gross Merchandise Value) per merchant was $40,000 rounded for the year 2017. (These are small merchants.)

Mobile App Session Growth

The following chart shows Mobile App Session Growth by App Type.

Shopping-related app sessions exhibit the fastest one-year growth. (A single year might be too short to establish a long-term trend, perhaps.)

The footnote says that the results are based on tracking 1 million apps across 2.6 billion mobile devices.

E-commerce Sales

The next chart is about e-commerce sales level and growth. The level is at $450 billion in 2017, up from half that level 5 years prior. This implies a 5-year growth rate of 15% per year, which is in line with the displayed growth rate.

Physical Retail Sales

The next chart is about physical retails sales level and growth. (If we've looked at e-commerce sales, it would be relevant to look at physical retail sales because of all the talk that e-commerce is eating away at retail.)

The level here is displayed as $3 billion in 2017 (but I'm guessing that there's an error in the scale and that it's really "trillion" and not "billion". For supporting evidence, see here).

The more crucial point is that retail sales growth has been less than 3% per year whereas e-commerce sales growth has been 15% per year or 5 times higher growth rate.

However, e-commerce's 15% growth rate is based on a smaller base than retails 3% growth rate, meaning that e-commerce's 15% growth rate translated into $62 billion of sales growth whereas retail's 3% growth rate translated into $152 billion. (Looking only at growth rates did not provide a complete picture!)

The final thing to notice is that retail's growth rate is decelerating. (Note the downward sloping trend line in red.) I'm not convinced that e-commerce's growth rate is decelerating. By looking at data at the other referenced source, I note that under a constant growth rate, since the level of sales increases year over year, the dollar amount of sales growth has been increasing year over year. To drive home the point, the retailer needs more resources to handle a 15% sales growth rate in year N+5 than in year N, say.)

E-commerce vs Physical Retails Sales

The next chart shows that e-commerce sales is growing relative to retail sales. In the 10 years from 2007 to 2017, e-commerce sales grew from 5% of retail sales to 13%.

At the same pace, it will take 11 more years before e-commerce sales reach the level of retail sales. (Let me do a sanity check on this. We have e-commerce sales at $450B in 2017 and retails sales at a level that's in the trillions. Using the other source referenced above, I back out a figure of $4.5 trillion for annual retail sales. I ask, what is the growth rate associated with going from $450B to $4.5T in 11 years? This is a 1000X increase! Answer: 87% per year. However, in the 5 years ending in 2017, e-commerce's growth rate has been 15%. So, is it possible that this growth will accelerate and rise to 87% per year? I doubt it. I think what will happen is that the $4.5T associated with retail sales will fall after the 11 years are up. Think about it. The consumers in the US have a limited capacity for consuming. It's this consumption that corresponds to e-commerce and retail sales. Today, their aggregate consumption amounts to the sum of e-commerce sales plus retail sales, a figure which equal $450B + $.5T i.e. $4.95 trillion or $5 trillion rounded. Now, in 11 years time, we might end up in a situation where e-commerce sales represent 100% of retail sales, but with the added case that e-commerce sales amount to half of the $5T figure i.e. $2.5T and with retail sales also amounting to the same amount. In this case, e-commerce sales will have to grow from $450B to $2.5T in 11 years. The growth rate associated with this happens to be ... 77% per year. This 77% growth rate is still too high to be realistic, I think. So, I'm going to make a prediction, and in so doing, perhaps make a fool out of myself. I predict that if the trends from the 5 years ending with 2017 were to continue, it would take longer than 11 years for e-commerce sales to reach the same level as retail sales. Let's come back in 11 years, i.e. 2029, and check to see what happened.)

Amazon & Alibaba

The next slide shows two behemoths next to one another. They are in the same space but in different geographic regions. Amazon and Alibaba.

Alibaba's higher GMV-to-Revenue ratio relative to Amazon's means that there are more third-party sellers on Alibaba than Amazon.

I checked their P/S ratio (price-to-sales) and stock prices. They are as follows.

AMZN P/S = 4.3 vs BABA at 12.5. The market sees more revenue growth potential in BABA. (I take this back! It seems misleading to work with "Revenue" given that Revenue doesn't capture "GMV". I'll pick this up a few lines below.)

AMZN stock price = $1,821 vs BABA at $180. 

AMZN market cap = $880 Bn vs BABA at $468 Bn. 

As of Aug. 3, 2018.

Picking up where I left off a few lines above, the interesting question is, which stock is cheaper? Both seems to have similar growth rates, with Alibaba's being slightly better. Let's assume that this trend continues, which means that growth won't cause any difference in valuation.

We could look at the ratio of market cap to GMV, in which case Alibaba comes out cheaper. Alternatively, we could look at the ratio of market cap to Free Cash Flow. Again, Alibaba comes out cheaper. So, I'll make the following prediction.

Barring the impact of currency on stock returns (i.e. assuming that we hedge away currency risk), I predict that Alibaba's stock price will outperform Amazon's stock price over, say, the next 5-10 years.

P.s. I think I need to qualify / modify my prediction by taking into account any differences in their R&D budgets ...

Author is also on Twitter

How to choose among Vanguard's 

Money Market and Money-market-like Funds?

Alternate Title: Is a bond fund's Yield worth its Duration?

Overview

I will look at bond fund yield and duration and explain how to select a bond fund based on these attributes. I will also use the Sherman Ratio as a handy tool.

Problem statement

Given (what I perceive to be) Vanguard's safest choices for cash investments, how should one choose among them?

(Readers who are just interested in the answer may jump straight to the Summary section at the bottom while glancing at the only table below.)

Data

Vanguard's list of mutual funds may be found here. The ones that are of interest to us here are as follows:

1. Vanguard Federal Money Market Fund (ticker: VMFXX)
2. Vanguard Prime Money Market Fund (VMMXX)
3. Vanguard Ultra-Short-Term Bond Fund Investor Shares (VUBFX)
4. Vanguard Short-Term Treasury Index Fund Admiral Shares (VSBSX)
5. Vanguard Short-Term Treasury Fund Investor Shares (VFISX)
6. Vanguard Short-Term Federal Fund Investor Shares (VSGBX)

I will compare them in what I believe is the "right way". (By the way, this method of analysis applies to other types of bonds funds as well and not just these ones; see Footnotes section however.)

Vanguard List of Money Market Funds and Closest Substitutes

Fund	Ticker	Average  Duration	SEC   Yield	Price   Range	Comments	Sherman Ratio
1	VMFXX	76 days	1.63%	constant		7.8
2	VMMXX	91 days	1.85%	constant		7.4
3	VUBFX	1.0 year	2.29%	0.80%		2.3
4	VSBSX	1.9 years	2.42%	1.96%		1.3
5	VFISX	2.0 years	2.10%	2.50%	Dominated by 4	1.1
6	VSGBX	2.2 years	2.32%	2.39%	Dominated by 4	1.1

Table-related Notes

• All data except the last two columns was copied from Vanguard, as of May 15, 2018.
• For VMFXX & VMMXX (the first two entries), what is listed under "Average Duration" is actually "Weighted Average Life". Vanguard doesn't quote a duration for them.
• "SEC Yield" represents the current estimate of annualized yield, as of May 15, 2018.
• "Price Range" denotes the percentage difference in the 52-week high and low prices, as calculated by Vanguard (not me).
• "Sherman Ratio" was calculated by me by using the formula given by 100 x SEC yield / Average Duration expressed in years.

Definitions

• Yield is another name for interest income.
• Duration is an approximate measure of a bond's price sensitivity to changes in interest rates. If a bond has a duration of 6 years, for example, its price will rise about 6% if its yield drops by a percentage point (100 basis points), and its price will fall by about 6% if its yield rises by that amount. (Source: Google)

Analysis

Typically, one would like to maximize yield. (Yield represents interest income.) If this were the only concern, one would pick fund 4 (VSBSX) with an SEC yield of 2.42%. 

However, more yield typically comes with more risk. To minimize risk, one ought to pick the fund with the least Average Duration. This will minimize the possibility of loss of principal due to rising interest rates. Note that I have presented the fund with the lowest duration first and in order of increasing duration. So, VMFXX has the lowest interest rate risk while VSGBX has the highest interest rate risk.

If minimizing duration was the only concern, one would pick fund 1 (VMFXX), but this comes at the expense of sacrificing yield. The SEC yield of VMFXX is 1.63% which is less than that of VSBSX that was selected two paragraphs above.

We immediately see that funds 5 and 6 are inferior to fund 4 because even though their Average Duration is greater than fund 4, their SEC yield is not higher. (This may be a short-term, transient anomaly in the data, as "SEC yield" can change daily. If it's not an anomaly, then my comment stands, which means that funds 5 and 6 ought to be avoided in favor of fund 4.)

The extent to which one can lose principal is captured in the 3rd column from the right which is labelled "Price Range", which means the following. If the future is going to be a repeat of the past 52 weeks, and if the fund in question is bought at its 52-week high price and sold at its 52-week low price, then the amount of loss would be what's displayed in this column. It's the most extreme loss, in all likelihood. We see that fund 5 (VFISX) has had the biggest price range and is therefore the worst fund in this aspect. But we shouldn't really care that much about fund 5 because it is dominated by fund 4. More importantly, we see that as we progress from fund 1 to fund 4, i.e. as duration increases, the Price Range also increases. This is to be expected and confirms the theory (which is something that's not being covered here).

We are now done with the analysis.

Decision Time

How to pick among funds 1-4? (We ignore funds 5 & 6 because they are dominated by fund 4, as explained above.)

The investor who cannot and doesn't wish to tolerate any additional risk ought to pick fund 1. This fund has the lowest Average Duration (safest), something which comes at the expense of having the lowest yield.

The investor who wishes to maximize yield and is willing and able to tolerate additional risk ought to pick fund 4. This fund has the higher SEC yield, which comes at the expense of having the highest duration (riskiest). How much risk would this investor really be taking? Here, the Price Range comes in handy and suggests that if the future were to be a repeat of the past, this investor would lose at most 1.96% in principal in conjunction to earning 2.42% in yield over one year. His net earnings would be 2.42% minus at most 1.96% which equals 0.46% or higher. In other words, the prospect of earning a 2.42% yield comes with the possibility of this yield shrinking to 0.46% over one year.

We can easily repeat the calculation in the above paragraph for fund 3 as well. However, we can also turn to the Sherman Ratio which captures the trade-off between yield and duration in a single number. The Sherman Ratio was created by DoubleLine Funds and Jeffrey Gundlach's team. It is the ratio of yield to duration. Qualitatively, it is the ratio of "benefit" to "risk", so the higher the better. We can think of this ratio as duration-adjusted yield. We can also think of this ratio as "slope" in a two-dimensional graph where yield is plotted on the y-axis and duration is plotted on the x-axis; it is the slope of the line connecting the origin to a specific fund's yield and duration. 

The Sherman Ratios for funds 1-6 appear in the right-most column. The Sherman Ratios indicate that funds 1 and 2 (with Sherman Ratios in the 7-8 range) have substantially higher duration-adjusted yield than funds 3 and 4 (whose Sherman Ratios are in the 1-2.5 range).

Before having looked at the Sherman Ratios, I would have probably chosen fund 3, but now that I've seen the Sherman Ratios and noticed the large difference in the Sherman Ratios of funds 3 and 2, I would probably opt for fund 2.

When comparing two funds, one needs to assess for oneself whether the incremental yield increase (in going from the lower yielding fund to the higher yielding fund) is worth the incremental increase in duration. For example, in going from fund 1 to fund 2, the incremental yield increase is 13% (i.e. (1.85% - 1.63%) / 1.63% = 0.13 = 13%) while the incremental increase in duration is 20% (i.e. (91 - 76) / 76 = 0.20 = 20%). Personally, I would make this jump because the Sherman Ratios are very close (7.8 and 7.4).

Other factors

Other factors not considered here but which may be worthy of consideration are as follows:

• Expense Ratio
• Fund size, also known as "Assets Under Management" (AUM)
• Other factors

In general, expense ratio is to be minimized. Too small of a fund size might be a sign of a young or neglected fund.

For the above set of funds, I did look at these other factors but judged them as secondary.

Afterthoughts

Question: What happens in a rising interest rate environment? (We are currently living through a rising interest rate environment because the U.S. Federal Reserve has been raising interest rates.)

Answer: The yields on funds 1 and 2 are likely to increase with increasing interest rates. So are the yields on funds 3-6. However, funds 3-6 are likely to suffer a loss of principal too.

Footnotes

Here are some fine points for more advanced readers.

SEC Yield

The important question is whether this quantity is before or after fund expenses. Ideally, we ought to base our comparison on after-fee yield. I believe the SEC yield is an after-fee quantity based on my interpretation of this quote from Vanguard's website: "The SEC yield for a money market fund is calculated by annualizing its daily income distributions for the previous 7 days." The key word is "distribution" which has the meaning of a cash payment from the fund to the fund shareholder.

Average Duration

1. For funds 1 and 2, there was no reported Average Duration and I had used their Weighted Average Life when calculating Sherman Ratios. This may be possibly incorrect theoretically, but I'm pretty much convinced that my thinking is correct from a practical point of view.
2. I have used the terms "Average Duration" and "Duration" interchangeably. Let me clarify the difference. A single bond has a duration. The duration of a bond fund is a function of its bond holdings' durations and it is this quantity that's called Average Duration. The right way to calculate this Average Duration is to calculate a weighted average where the weights are proportional to the amount of capital invested in each bond. For a crude analysis, an equally-weighted average would probably do.

Duration as a Concept

1. If we wish to know a bond's duration very approximately, we can say that it is the same as the bond's maturity. I.e. a bond maturing in 10 years has a duration of 10 years, crudely speaking.
2. The starting point for a quantitative understanding of Duration is (1) to write the expression for the price P of a hypothetical bond which has one cash flow F at future time T, and then (2) to differentiate it with respect to interest rate 'r' (i.e. calculate dP/dr), and then (3) to write an expression for dP/P by rearranging terms. The expression in step 1 is 
P = F / (1 + r)^T 



Duration in the way that I have explained it in the previous step is also known as "Modified Duration". It is described in Wikipedia here. There's also another kind of duration known as "Macaulay Duration" (also described in the same Wikipedia article). They are close cousins of one another and almost the same. So, for practical purposes it doesn't matter which one we use. (I like Modified Duration better because it has a well defined meaning which is dP/P. So, which definition is Vanguard using? Based on their comments when I searched their website for "duration", I think they are using Modified Duration.)

Credit Rating

If you are comparing bond funds (or bonds) with differing credit ratings (e.g. Treasury vs. corporate vs. investment grade vs high yield), it would be a mistake to blindly maximize Sherman Ratio. The right thing to do would be to adjust the Sherman Ratios for differences in credit rating.

The bond funds which are the subject of this discourse have similar if not identical credit ratings.

Summary

In this essay, we looked at a group of ultra short-term and short-term bond funds. (These funds just happened to be from Vanguard and just happened to be the safest choices for cash investments, in my opinion.)

We worked our way through a procedure for selecting the most appropriate fund based on (a) yield and (b) duration. Yield is a measure of income while duration is a measure of risk. All else being equal, yield is to be maximized and duration is to be minimized.

The Sherman Ratio is the ratio of yield to duration and may also be called duration-adjusted yield. It may be used to rank bond funds, with the highest Sherman Ratio fund usually being the most desirable.

Which fund would I have chosen? Fund 2. It has the second highest Sherman Ratio. I was willing to forego the highest Sherman Ratio fund because I felt the additional yield was worth the additional duration risk.


Disclaimer: This analysis is not meant to be advice, only educational. By relying on it, you are implicitly agreeing to assume full responsibility for its consequences and hold me harmless from any and all liability. If you don't think you have understood it, please do not use it.

Author is also on Twitter

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.)

18---

I decided to delete this section on June 9, 2020 and replace it with Item 19.3.

How should we interpret Gundlach's copper:TNX ratio?

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

(1 + i_w) / ((1 + i)*(1 + r)) 

with 'i_w' representing WORLD inflation and 'i' representing US inflation expectations.

So, Gundlach would be saying that (a) the gold price moves in direct proportion to WORLD inflation, and in inverse proportion to both (b) US real interest rates and (c) US inflation expectations. Items (a) and (b) are consistent with what was said earlier (item 15), while item (c) is a sore point.

Next, I explore this matter further.

19---

I decided to delete this section on June 9, 2020 and replace it with Item 19.3.

Question: Is the Copper:TNX ratio similar to any other quantity that we know of?

We know from item 7 that the TIP:SHY ratio is inversely proportional to real interest rates.

In stockcharts.com, a visual inspection of the TIP:SHY ratio and the Copper:TNX ratio suggests that the two ratios are highly correlated (and more so than TIP:TLT vs Copper:TNX). See item 23 for a discussion of TIP:TLT. 

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.

What does it mean when we observe that the TIP:SHY ratio and the Copper:TNX ratio are highly correlated?

The TIP:SHY ratio lets us make a statement about US real interest rates. So perhaps the Copper:TNX ratio is also making a statement about the same quantity. If that were the case, it would mean that the 'i_w' term and the 'i' term in

(1 + i_w) / ((1 + i)*(1 + r)) 

are almost equal and hence cancel out, thereby leaving us with 

1 / (1 + r)

Note that I mentioned that the correlation between TIP:SHY and COPPER:TNX is not perfect by any means. We need to think some more about

(1 + i_w) / ((1 + i)*(1 + r)) 

Perhaps we should be thinking of

(1 + i_w) / (1 + i)

as WORLD inflation net of US inflation ...

To be explored further at a later date ... See next item.

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 ...

19.3--- Copper:Gold Ratio and TNX

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.

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.

23.2---

I am undecided as to whether the movement in the TIP:TLT ratio is proportional to i/r or only i, where 'r' represents real interest rates and 'i' represents inflation expectations.

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 rising falling inflation) while the TIP:SHY goes up (marking falling real rates).

This happened in 2017. See next two charts. Look at the trend from Jan. 2017 through Dec. 2017.

Note that "rising inflation relative to real rates" is the same thing as "falling real rates relative to inflation". Think of it as the ratio i/r where 'i' represents inflation expectations and 'r' represents real interest rates. So to the extent that a relative movement is being captured, there is some ambiguity in what is revealed by the TIP:TLT ratio ...

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) 

Alden Model: 

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.

31--- David Jensen & Willem Middelkoop

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).

We live in a world where US Money Supply (M) has been increasing and continues to increase at an accelerated pace relative to recent and not so recent history. US real economic growth is expected to be on the low side. This can be attributed to low growth rate in the labor force as well as at-best lukewarm expectations for productivity. Therefore, US real interest rates (r), which are highly correlated with real economic growth, are expected to experience downward pressure and remain low. Both of these factors are bullish for the Gold Price.

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