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?)

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Why was LIBOR rigged?

This blog post dovetails a BBC documentary dated April 2017 which I had Tweeted about.

There seems to have been two motives for LIBOR rigging. One was financial stability and the other was profit.

Motive #1

Here's what happened. Banks agreed to lend to one another at lower than fair market interest rates, something called "low-balling."

For example, a LIBOR trader who knew that borrowing banks out there were riskier than perceived would bid a lower interest rate at which he was willing to lend out his own bank's capital.

This signaled the following to third parties: The borrowing bank's creditworthiness was sounder than it actually was.

This in turn signaled the following:

1. The banking system was more stable than it actually was.
2. Things were closer to normal than they really were.

In my opinion, the intent of all this signaling may have been to prevent something like a bank run and system-wide financial collapse.

Motive #2

Barclays Bank set up an investment fund named the Ricardo Master Fund. This was under CEO Bob Diamond, the very CEO who has denied knowing anything about LIBOR rigging at his bank. This fund stood to profit if LIBOR fell. Barclays itself invested $100Mn in this fund and made a $100Mn profit, according to the BBC documentary.

There is strong evidence of LIBOR rigging dated Sept 2007 and October 2008, according to the same documentary. However, according to @davidenrich's Spider Network book, LIBOR was widely known to be manipulated to suit banks' positions as early as 1991.

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Bloomberg Debate at 

Davos 2017 World Economic Forum:

Comments by Ray Dalio & Larry Summers

Bloomberg recently held its annual debate at Davos, bringing together figures from politics, government, and finance. The debate was moderated by Bloomberg anchor Francine Laqua. This was part of the 2017 World Economic Forum.

Larry Summers and Ray Dalio were panel members. Here's the 50-minute video of that debate.

This blog is about comments made by Summers and Dalio that I'd personally like to take away and record for future reference.

Overview

• Populism as a new, worrisome trend
• U.S. economic success under Trump
• U.S. economic policy recommendations

Ray Dalio

Dalio highlighted the following:

• Rising trend of populism at a global scale 
• Very similar to 1930's. 
• Brexit, Italian referendum, Trump election are all examples.
• Populism means 
• Protectionism
• Nationalism
• Anti-globalization. 
• Risk of polarization at a global scale. 
• "Populism scares me."
• Globalization & wealth gap 
• The globalization that started in the 90's ...
• Increased trade and 
• Reduced the wealth gap between rich & poor countries, but 
• Increased it within countries. 
• We may now be at the end of globalization.

Larry Summers

Paraphrasing Summers: The lesson from history is that populist policies will hurt those very people in whose name those policies are carried out. "Those people" = the middle class.


U.S Economic Success under Trump

Dalio thought that U.S. economic success under Trump was a complicated question. The positive aspects were "economic confidence" and the unleashing of "animal spirits" that seems to be occurring. Dalio noted that we live in a world where capital is very mobile and can easily relocate to where the environment was more pro business. He further noted that the U.S. was known for the "rule of law" and "protection of property".

Both Dalio and Summers were in agreement that populism was a big negative.

I should put the above comments into context by noting (from elsewhere) that Trump has signaled the willingness to reduce regulation and taxes. He is also willing to raise trade barriers on imports. Reducing regulation and taxes is what unleashes animal spirits. Raising trade barriers is how populism manifests itself and possibly polarizes countries.

Elsewhere on Dec. 19, 2016, Dalio had blogged that there's little doubt that Trump is an aggressive leader. He had written that the question was whether he'll be aggressive and thoughtful or aggressive and reckless. Reference.


U.S. Economic Policy

Summers offered the following guidelines for U.S. economic policy.

He said the slogan ought to be "Make America greater than before" instead of making it "great again" as Trump has said.

Summers' three major policy recommendations for the US were:

1) Public investment on an adequate scale, starting from infrastructure, but also embracing technology and education.

2) Global strategy focused on making global integration work for ordinary people, starting with addressing "capital mobility and control".

(I'm not sure what he went by "capital mobility and control," as it could mean something dark and restrictive of freedom, so I went back and listened to previous sections of the video and discovered that he made comments indicating being in favor of eliminating "tax arbitration" and "regulatory arbitration" across countries. For example, a company operating in country X shouldn't be allowed to register in country Y because country Y offers lower taxes than country X.)

3) Enabling the dreams of young American people, by addressing issues of (a) education, (b) improving the school-to-work transition for those not pursuing higher education, and (c) ability to purchase a first home.

(He means (a) improving the quality of education and reducing its cost, (b) making low-income jobs more readily available in a world where automation and technology are moving these jobs toward obsolescence, (c) making homes more affordable for first-time home buyers. To make homes more affordable, they'd have to offer this group low mortgage rates, provide tax incentives such as keeping mortgage interest payments tax deductible, etc.

Summers' recommendation on point #3 are rooted in the 30-40 year trend that fewer children are earning more than their parents. I had Tweeted about this here.)

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Dismal Future Financial Asset Returns:

Commentary by J.P. Morgan Asset Management

Revised on Dec. 5, 2016 as follows: In addition to the reference to John Hussman (see below at the very end), I added references to Robert Shiller and Fama & French.

On page 12 of the Nov. 28, 2016 issue of the magazine Pensions & Investments was printed an article authored by John Bilton, the London-based managing director and global head of multi-asset strategy at J. P. Morgan Asset Management. The article caught my attenion.

The article's title was "Asset owners face daunting path from continuing central bank challenges." Below are some salient excerpts. Emphasis mine.

"The extremely accommodative central bank policy of recent years may well have prevented economic Armageddon, but it also drove asset returns far in excess of underlying economic growth. In the past 50 years, U.S. stocks have, on average, outrun gross domestic product growth threefold during phases of economic expansion. In this post-financial crisis expansion, U.S. stock markets have outstripped the U.S. economy by almost eight times. Absenting a remarkable sustained and successful period of fiscal stimulus, an inescapable conclusion is that this extended period of policy largesse -- designed to stabilize the economy -- resulted in asset returns being borrowed from the future, and now that future is here."

Some comments for readers who may be less familiar with facets of what's being said: 

• The "accommodative central bank policy" and "period of policy largesse" both refer to policies of quantitative easing since the Great Financial Crisis of 2008/2009.
• The author is making the valid comparison between stock market growth rates and growth rates in the real economy. Think of it in these steps: (1) The real economy grows. (2) Company earnings grow. (3) Stock prices rise. Withouth (1), (3) is not based on fundamentals but on what we can call investor sentiment or risk tolerance.
• The author's mention of "fiscal stimulus" is reference to president-elect Donald Trump's intention to spend $1 trillion on infrastructure projects over a 10-year period. (The media has reported on this at the following sources: Washington Post, CNN, CNN Money, Politico, FiscalTimes, BusinessInsider)
• The author wants readers to understand that equity markets cannot go up forever and that if they have already gone up too much, they are likely to either not go up for a while or worse, drop.
• Personally, I found the contrast between a "threefold" increase from history and the "almost eight times" increase in the current cycle jaw-dropping.

----------------------------------------

On to the next excerpt. Emphasis mine.

"We find ourselves caught in an uncomfortable, but potentially enduring equilibrium: growth is unlikely to be strong enough to support a sharp rise in interest rates, yet at the same time the exuberance and excess that often mark the end stage of an economic cycle are palpably absent. Some may call this a "Goldilocks" scenario; but if it is, then it's a rather bleak read of the fairytale [sic]. Poor demographics and weak productivity combine to peg the long-term outlook for developed market real growth at just 1.5% over the next decade. This translates to a significantly slower and shallower path of global interest rate increases, and lower terminal rates for both the cash rate and 10-year yields. In turn, any hope asset owners have for higher yields or better growth is likely to be a long time coming."

My comments:

• If the current situation is indeed an equilibrium, meaning that if we believe that it will persist, it characterizes quite a strange world because of the following. (A) Economic growth is anemic and as a result, interest rates won't be able to go up, but still, the Fed intends to raise them. (B) Despite the fact that we are most likely at the end of a business cycle, sentiment among people and investors is not one of exuberance and excess.
• The fact of the matter is that we face a future characterized by "poor demographics" and "weak economic productivity", neither of which signals strong economic growth. Therefore, we should expect a slow path of interest rate increases across the globe.
• The bottom line is that bond investors hoping for "higher yields" (in order to buy bonds) should restrain their hope. So should equity investors hoping for higher stock prices based on "better growth".

----------------------------------------

On to the next excerpt. Emphasis mine.

"A future in which returns are expected to be muted means that reaching the hurdle rate to meet long-term objectives -- like the increasingly elusive but still psychologically powerful 8% annual return target historically considered achievable for a balanced, moderate risk portfolio -- is going to require a lot more creative thinking and much more active diversification."

My comments:

• It is a mathematical fact that at 8% annual growth, capital doubles every 9 years. In contrast, at a 1.5% annual growth rate, capital doubles every 47 years! (Assuming annual compounding) There is a generation of difference between 9 years and 47 years.
• The future does not look good for investors. This includes pension funds and insurance companies! It should also be a wake-up call for retirees and those approaching retirement age.

----------------------------------------

On to the next excerpt. Emphasis mine.

"Based on a multidecade [sic] set of assumptions that underscores the economic and capital market estimates we have been compiling for the past 21 years, on a 10- to 15-year outlook, ... real assets are likely to hold up best in a world of challenged growth and lackluster returns."

My comments:

• The author's observations about "real assets" is based on historical data. It is not an opinion. (However, one could argue that 21 years is too short of a look-back period, and especially given the strange nature of the "current equilibirum," that we ought to be looking back all the way to the 1929 Great Depression and even further back ... This is easier said that done because it is certainly not be easy to obtain the data. Some have tried, successfully. E.g. (1) quantitative equity manager John Hussman, (2) Robert Shiller, (3) Fama & French.)
• "Real assets" consist of the following, which is not necessarily exhaustive list: real estate, infrastructure (toll roads and bridges, oil & gas pipelines), timberland, farmland, precious metals, fine art, and collectibles.

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US Interest Rate Forecasts:

On Eve of Rate Hike #2 since 2008/2009

Back in early 2015 or about 3 months shy of 2 years ago, I blogged about the Fed's intentions to raise rates through the end of 2017. (Here's the link to that blog post).

In this blog, I will state what has occurred so far. But first, let me reiterate the Fed's plans from back in early 2015.

Back in early 2015, the Fed had projected the following rate increases:

• 0.5% increase by 2015 year end,
• 1.25% increase by 2016 year end, 
• 1.25% increase by 2017 year end.

Back in early 2015, the futures market had the following expectations for rate increases:

• 0.38% increase by 2015 year end,
• 0.75% increase  by 2016 year end,
• 0.6% increase by 2017 year end.

So, what transpired?

1) The Fed raised rates by 0.25% in December 2015. They are now 0.5%; see this source or this other source. (With time, the data at these sources may change and become irrelevant ...)

2) The Fed is expected to raise rates by another 0.25% when it meets later this month on Dec. 13 and 14.  See this source. The futures market is predicting with almost certainty that this raise will occur.

It is noteworthy that so far, the Fed has fallen short of not only its own projections but also the futures market's smaller projections.

What does this mean? I think it means that the economy is not strong enough to handle a higher interest rate.

For future reference, the following Wikipedia article documents the history of Fed's actions.

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The Part of Life We Really Live

On July 31, 2016, Northman Trader, whom I follow on Twitter, wrote: One of my favorite historical writers is Seneca the Younger. He, like all of us, was a flawed human being but I appreciate his wisdom, realism and philosophical musings. Born in Spain he became a personal tutor and advisor to Emperor Nero and had a front row seat to power in Rome during some of its glory days and time of madness. In the “Shortness of Life” he, a man in his own time, wrote among other things:

“The part of life we really live is small….Consider how much of your time was taken up with a moneylender, how much with a mistress, how much with a patron, how much with a client, how much in wrangling with your wife, how much in punishing your slaves, how much in rushing about the city on social duties. Add the diseases which we have caused by our own acts, add, too, the time that has lain idle and unused; you will see that you have fewer years to your credit than you count. You will hear many men saying: “After my fiftieth year I shall retire into leisure, my sixtieth year shall release me from public duties.” And what guarantee, pray, have you that your life will last longer? Who will suffer your course to be just as you plan it? Are you not ashamed to reserve for yourself only the remnant of life, and to set apart for wisdom only that time which cannot be devoted to any business? How late it is to begin to live just when we must cease to live! What foolish forgetfulness of mortality to postpone wholesome plans to the fiftieth and sixtieth year, and to intend to begin life at a point to which few have attained!”

Excerpted from the following Tweet: https://twitter.com/northmantrader/status/759700492691787776  

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