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Investing in the global stock market

I want to invest in a global capitalization weighted free float stock market index. Below I explain what I mean, who provides such indexes and how I would build such an index using just two funds.

1 Disclaimer

I am not in anyway qualified to give anyone financial advice. Furthermore the numbers in this article are based largely on guesses (the basis of which are detailed in the appendix) and I'm notoriously bad at algebra. So proceed at your own risk.

2 Defining the index I'm looking for

I'm looking for an index that covers all the equity assets on the planet and then weights them based on their market capitalization. Capitalization just means taking the stock price and multiplying it by the number of shares in the company. The idea being that the index reflects the evaluation of the world's investors in the world's companies.
A complication however is that the number of shares a company has issued is not the same thing as the number of shares available for purchase by the world's investors. Some companies have a chunk of their shares kept off the market by governments, by regulations or by families. So the 'real' value of the company isn't a blind multiplier of the value of the shares versus the number of the shares. Rather it's the value of the shares multiplied by the number of shares that are available for purchase. This difference is known as the free float and indexes that adjust for it are called 'free float' or 'free' indexes. I want to work based on such indexes.

3 Slicing the pie

Traditionally capitalization weighted free float equity indexes divide the world based on country. Each country is classified into three categories, developed, emerging and frontier. Within each country companies that are identified as being hosted in that country are classified into large capitalization, medium capitalization and small capitalization. There are also micro capitalization indexes but as I show below it takes enough effort to get the other 98.5% of the market so I'm not going to worry too much about them.
Note that I have also more or less given up for now in investing in Frontier countries. There are a few funds that go there but they tend to be very expensive and use odd indexes. My suspicion is that over the next few years we'll see some reasonably low cost main stream ETFs that cover this area, so I'll wait.

4 The contenders

There are a bunch of companies that produce capitalization weighted free float equity indexes including MSCI Barra, FTSE, S&P, Bloomberg, Morningstar, Dow Jones, etc. But of those the two most popular and comprehensive are the MSCI Barra and FTSE indexes. For more information on those indexes check out the appendix.
The big challenge for me has been getting data about these indexes. In the past some Indexes, notably FTSE and Dow Jones, published a ton of great data. Now only Dow Jones publishes a tiny bit and the rest publish nothing. For any information one has to pay literally thousands of dollars in subscription fees which is too rich for my blood. Thankfully Vanguard has substantially improved its offerings since I first got into international investing so I just don't need the same amount of data I used to need.
In terms of companies that produce funds that follow these indices there is, in my opinion, really only one player that truly matters - Vanguard. Their record of low costs and low tracking error (e.g. their funds return what the index returns) are without peer in the industry. So below I will just be looking at Vanguard funds. [Note: I have heard that Dimension Fund Adviser funds are also quite good but I don't have enough money to get direct access to them and I'm unwilling to pay an advisor.]

5 The two fund solution - 0.14% expense ratio

When it comes to covering every single stock from micro to large cap in the U.S. market the best in the business, near as I can tell anyway, is the Vanguard Total Stock Market ETF (or Admiral shares) with an expense ratio of 0.07%. This ETF follows the MSCI US Broad Market Index which is essentially identical to the Wilshire 5000 index or just about any U.S. whole market index. With this fund I can cover at absurdly low expense the entire U.S. market.
So now I just need to account for the rest of the world. And there is great news. Vanguard has a reasonably new fund called the Vanguard Total International Stock fund. It comes in investor shares, admiral shares and as an ETF. It covers the MSCI All Country World ex USA IMI. This means it covers everything from small to large cap and all markets from emerging through Europe and Asia. Everything but the U.S. But we have the Vanguard Total Stock Market fund to cover that. So with just two funds we can cover just about all investable assets on Earth (minor non-US micro and frontier countries).
Fund Name Expense Ratio Index Tracked
Vanguard Total Stock Market ETF 0.07% MSCI US Broad Market Index
Vanguard Total International Stock ETF 0.20% MSCI ACWI ex USA IMI
My assumptions are:
Market Split Percentage
% of all-world market accounted for by the US 45.7%
% of all-world market ex US 54.3%
So the math is:
45.7%*0.07% + 54.3%*0.20% ? 14%

6 Calculating the U.S./International Split

To execute the index strategy I need to know what percentage of the world total free float capitalization is taken up by the U.S. One way to get this data is to go to the Dow Jones website and look up the fact sheet for Down Jones Global Indexes. The last one I looked at had data dated 12/30/2011 and said that the U.S. is 44.81% of the world market. But I'm not sure if that's on a free float basis.
Another way to calculate this data is a bit trickier. I go to the Vanguard Total World Stock ETF, it's symbol is VT, on the Vanguard Website and look up the portfolio composition which says that as of 12/31/2011 'North America' made up 50.40% of the portfolio. There are a few problems here. First, this fund is based on a FTSE index not a MSCI index (which is what the funds I actually invest in use). Second, 'North America' covers all of North America, not just the U.S.
To adjust for this I go to the Vanguard FTSE All-World ex-US ETF (VEU) whose composition as of 12/31/2011 is 7.30% North America. This would be North American countries (like Canada) that aren't the U.S. I could have used the Vanguard Total International Stock ETF but I wanted to stick in the same index and the Vanguard Total International Stock ETF uses MSCI.
So now I have to adjust. The way I do this is kinda evil and probably wrong but I have to work with what I have. What I do is use proportions. I'm figuring that the value of say Europe in both funds should represent roughly the same amount of money. So I divide the portion of the portfolio taken up by Europe in the Vanguard FTSE All-World ex-US - 43.90% by the portion taken up by the Vanguard Total World Stock ETF - 23.30%. So now I just calculate 0.233/0.4390 = 0.531. That gives me the translation ratio. Now I can calculate the final adjustment: 0.504 - (0.073 * (0.233/0.4390)) = 0.465.
So this argues that the U.S. is roughly 46.5% of the total world market capitalization according to FTSE.
Of course Dow Jones and FTSE don't quite agree, FTSE says 46.5% and Dow Jones says 44.81%. But honestly that's close enough for my books and given the uncertainties as to what the Dow Jones numbers represent and the huge scary fudge factors in calculating the FTSE numbers this is about as good as I can expect.
One check is to use the conversion ratio on some other numbers. So let's look at say Emerging Markets. They are 13.50% of total world and 25% of FTSE All-World ex-US. So 0.25 * (0.233/0.4390) = 0.133. So 13.3% doesn't exactly equal 13.50% but it's about as close as I'm going to get without spending thousands of dollars to get access to index fund data.
So I'll just split the difference between the indexes and declare the U.S. to be (0.4481 + 0.465)/2 = 45.7% of the world market.

A MSCI Barra's view of the world

MSCI Barra divides the world into exactly the terms I used in Section 3? - developed, emerging and frontier.
Index Name What it covers Notes
MSCI All Country World Index Investable Market Index (ACWI IMI) All developed and emerging countries. All large, mid and small cap stocks in those countries. I can't find any ETFs or mutual funds that I can invest in that actually follow this index.
MSCI All Country World Index (ACWI) All developed and emerging countries. All large and mid cap stocks in those countries. iShares MSCI ACWI tracks this fund.
MSCI Global Small Cap Index All small cap stocks in developed and emerging countries. I can't find anyone with this exact index, just the countries in EAFE and Japan.
MSCI Frontier Index My guess is that this only covers large and mid cap stocks in those countries but I can't be sure. I can't find anyone who tracks this index.

B FTSE's view of the world

Like MSCI Barra, FTSE follows the same break down as I used in Section 3?.
Index Name What it covers Notes
FTSE All-World Index All developed and emerging countries. All large and mid cap stocks in those countries. Vanguard Total World Stock Market tracks this fund
FTSE Global Small Cap Index All small cap stocks in developed and emerging countries. Vanguard has a fund that tracks this fund minus U.S. small cap
FTSE Frontier 50 Index Frontier countries, not clear which capitalizations. I can't find anyone who tracks this

C Deep history

There were a lot of twists and turns that got me here. The sections below are completely out of date and I only include them here for my own historical reference.

C.1 The three fund solution - 0.19% expense ratio

Here there is good news and some small bad news. The good news is that it only takes two more funds to cover the rest of the world. The Vanguard FTSE All-World ex-US covers all developed and emerging markets in the world except the US (hence ex US in the name). It specifically covers all large and mid cap stocks. But this leaves small cap. For that I need one more fund, the Vanguard FTSE All-World ex-US Small Cap ETF which fills that hole.
The small bad news is that I'm mixing indices, MSCI for the U.S. and FTSE for the rest of the world. But given how well defined and consistently covered the U.S. market is I don't think in practice this will prove to be a problem.
Fund Name Expense Ratio Index Tracked
Vanguard Total Stock Market ETF 0.07% MSCI US Broad Market Index
Vanguard FTSE All-World ex-US ETF 0.25% No fair guessing
Vanguard FTSE All-World ex-US Small-Cap ETF 0.40% Oh come on
My assumptions are:
Market Split Percentage
% of all-world market accounted for by the US 41%
% of all-world accounted for by ex US large and mid cap 53%
% of all-world accounted for by ex US small cap 6.0%
So the math is:
41%*0.07% + 53%*0.25% + 6.0%*0.4% ? 0.19%

C.2 A four fund solution - 0.17% expense ratio

When I started to invest internationally in a serious way about five years ago I needed to find a way to hold international stocks in a taxable account. At the time there really weren't that many outstanding international stock index funds that had good behavior (in terms of distributions and capital gains). So I ended up in the Vanguard Tax Managed International fund which is an EAFE fund. EAFE is an index used by MSCI, in this case, and it stands for Europe, Australasia and the Far East. All things considered I wish I wasn't in the fund but I'm stuck with it. First, if I sell it I'll realize a ton of capital gains. Second, any funds withdrawn from the fund in less than 5 years realize a 1% redemeption fee. So the cost of exiting the fund is just too high.
So my plan is to keep the money and try to compensate. The thing about the EAFE fund is that it doesn't include emerging stocks the way the all world ex US fund does. So I had to also buy the Vanguard Emerging Markets ETF to fill out my portfolio. Most of my emerging ETF money is in tax exempt accounts so I can sell without capital gains. But some is taxable and it has appreciated a lot so the taxes would be pretty serious. So I need to hold those shares as well. Over time as stocks dip and as shares get beyond the 5 year limit I'll try to sell off shares. But until then I have to figure out how to integrate my existing shares into my ideal portfolio.
To do this I'll calculate the normal contribution that should go to all-world ex US and then I'll break that amount into money already in the EAFE and emerging that I can't sell. If the total money going to all-world ex US is less than what is in EAFE+emerging then I'm stuck and I'll just have to keep the shares and be out of balance. If however the amount is more than is already in EAFE and emerging then I'll use that money to buy ex US stock. If the balance between EAFE and emerging is off then I'll mostly live with it unless it gets too crazy in which case I'll have to decide if I want to either take a capital gains/fee hit or buy more stock and store up more problems.
Mixing indexes is bad. For example, EAFE doesn't include Canada while the all-world ex US does. Or the way that MSCI calculates small cap is different than FTSE so the EAFE and emerging funds don't include all the companies that the FTSE all-world does and the FTSE small-cap doesn't cover them either so they are just missing from my portfolio.
Fund Name Expense Ratio Index Tracked
Vanguard Total Stock Market ETF 0.07% MSCI US Broad Market Index
Vanguard Tax-Managed International Fund 0.20% MSCI EAFE Index
Vanguard Emerging Markets ETF 0.27% MSCI Emerging Markets Index
Vanguard FTSE All-World ex-US Small-Cap ETF 0.40% You get one guess
My assumptions are:
Market Split Percentage
% of all-world market accounted for by the US 41%
% of all-world accounted for by EAFE large & mid cap 41.9%
% of all-world accounted for by ex US small cap 6%
% of all-world accounted for by emerging stocks 11.1%
So the math is
41%*0.07% + 41.9%*0.20% + 6%*0.40% + 11.1%*0.27% = 0.17%
The 10.5% savings of this approach versus the other one is clearly, in my mind at least, not worth the dog's breakfast of index mixing and coverage holes. But I'm more or less stuck with it since I'm not willing to take the 1% haircut (not to mention capital gains taxes) on getting rid of my Vanguard Tax Managed fund. But if I was starting from scratch I certainly wouldn't have taken this approach.

C.3 Cooking the books

Previously I pulled a bunch of numbers out of the air and listed them as 'assumptions'. Below I explain where those numbers came from. Please fasten your seat belt, it's going to be a bumpy ride.

C.3.1 Percentage of world market accounted for by the US - 41%

MSCI no longer publishes much useful information publicly. I actually looked into buying access to their data but the most rock bottom subscription they said they offered was more than $3000. Too rich for my blood. So my primary source for market capitalization information is the FTSE All-World Index review published with Nomura [1]. I used the July 2010 edition for these numbers. I took the USA market capitalization ($10,606,743,000,000) and divided it by the All-World Index capitalization ($25,640,028,000,000) to get a US total market percentage of roughly 41%. But remember, the FTSE All-World Index doesn't include small cap stocks. So that 41% represents 41% of the Large/Mid Cap universe. However FTSE defines Small Cap as being 10% of the capitalization of the regional market so this means that the US is also 41% of the total world market across small, medium and large capitalizations.

C.3.2 Percentage of all-world accounted for by ex US Large and Mid Cap - 53%

If the U.S. is 41% of the world's market then by definition the rest of the world is 59%. But we can't forget to break things up into small cap and the rest. Also by definition Small Cap is 10% of the total regional value (according to FTSE). So this means that 90% of the 59% belongs to non-US large and mid-cap companies. Thus giving us roughly 53%.

C.3.3 Percentage of all-world accounted for by ex US Small Cap - 6.0%

By the same logic used previously this value is 10% of the 59% or 5.9%. Due to rounding errors however I am going to bump the percentage 0.1% to make everything add up to 100%.

C.3.4 Percentage of all-world accounted for by EAFE large and mid cap - 41.9%

The closest thing in FTSE land to MSCI's EAFE is developed markets ex US. But the comparison isn't exact. For one thing EAFE explicitly doesn't include Canada where as developed ex US does. I'll deal with this by rolling the Canada contribution into the EAFE dollars. Also the country memberships of developing versus emerging in FTSE land aren't exactly the same as developing versus emerging in MSCI land. So the whole thing is a mess. But I'm going to go with the FTSE numbers. So in this case I'll take a short cut. I already know from above that the developed world ex US accounts for 59% of the large and mid-cap market. I then look up the emerging market capitalization at $3,216,452,000,000 and divide it by the global capitalization at $25,640,028,000,000 and get 12.5%. So 59% - 12.5% = 46.5%. But remember the large/mid cap versus small cap 10% split so I need to adjust for that getting a final value of roughly 41.9%.

C.3.5 Percentage of all-world accounted for by Emerging Stocks - 11.1%

In the previous section I already calculated that emerging is 12.5% of the large/mid cap world so now I need to adjust by 10% to get its percentage of the whole world for 11.25%. I'm going to shave 0.15% off to make the numbers all add up nicely. The discrepency is due to previous rounding.
Is FTSE emerging a good stand in for MSCI emerging? I think so. Here's why
The way I tried to figure this out is a bit complex so hold on. I couldn't get good numbers for MSCI's numbers representing things like the US market cap so I had to go instead go to the iShares MSCI ACWI ETF which publishes a fact sheet [2] that lists the value of their stocks in each country. Then using software I can't even find anymore (I did this back in January of 2010) I calculated for each country what the total value of the stock the ETF held for that country was worth. Then I went to MSCI Barra's site for index membership and pulled down the membership list for EAFE. The combination of U.S., Canada and EAFE is all developed countries so remaining capitalization is by definition emerging. Of course this whole approach is suspect since the stocks held by the iShares ETF represent their replication of the index, not the index itself. But without a better source of information this was the best I could do. I did all of this back in January of 2010 so I pulled the December 2010 results for the Nomura/FTSE All-World review and calculated the table below.
Region % of large cap/mid cap capitalization using iShares MSCI ACWI ETF holdings % of large cap/mid cap capitalization using FTSE Index
U.S. 41.30% 41.02%
Canada 4.12% 3.56%
EAFE 40.59% 41.60%
Emerging 13.99% 13.82%
So given all the caveats it seems reasonable to use the FTSE emerging markets definition as a stand in for MSCI.

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