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I am STANCO 25 Professor of Finance, Emeritus at Stanford University and a recipient of the 1990 Nobel Prize in Economic Sciences. More than you will ever want to know about me can be found at my Stanford web site: www.stanford.edu/~wfsharpe

Sunday, August 18, 2019

The Four-fund Proxy for the Wold Bond Stock Fund

Chapter 7 of my ebook on retirement income suggests the use of a portfolio of four Vanguard mutual funds to serve as a proxy for the “World Bond Stock Fund”, which can serve as the “market portfolio” in analyses using the RISMAT software. This post will update the information needed for this approach. However, times have changed. It is now possible to approximate the world bond stock fund with only two funds. The next post will discuss this. Feel free to wait for it.

Now to the four-fund approach. The ticker symbols and names of the funds are:

VBTLX Vanguard Total Bond Market Index Fund (admiral shares)

VTABX Vanguard Total International Bond Index Fund (admiral shares)

VTSAX Vanguard Total Stock Market Index Fund (admiral shares)

VFWAX Vanguard FTSE All-World ex-US Index Fund (admiral shares)

In each case, the shares are of the “admiral” class which provide the same gross returns but with lower fees as “investor class” shares of the same fund. At the time the chapter was written in 2015. the minimum investment for admiral shares in each of the funds was $10,000. However, this has fallen as the funds have attracted more assets. As of this post in 2019, one can obtain admiral shares for any one of these funds for an investment of $3,000 or more.

The first and third funds invest in securities of United States companies, while the second and fourth hold only securities of companies based in other countries. In the mutual fund industry the term “international” generally means “non-U.S.” but I prefer to use the latter term for clarity. Funds that hold securities of U.S. and non-U.S. Companies are generally called “Global” – a convention that I will follow.

A fund's expense ratio indicates the proportion of one's investment that is deducted to cover the expenses of fund management. Is is generally expressed as an annual percent of value. Over the course of potentially many years in retirement such expenses, if high, can significantly effect one's standard of living. Here is a table from chapter 7 of the ebook showing the funds and their expense ratios in 2015:

VBTLX: 0.06% per year
VTABX: 0.14% per year
VTSAX: 0.05% per year
VFWAX: 0.13% per year

And here are the expense ratios today:

VBTLX: 0.05% per year
VTABX: 0.11% per year
VTSAX: 0.04% per year
VFWAX: 0.11% per year

Happily, all the expense ratios have decreased, presumably due to increased assets under management allowing fixed costs to be spread over larger pools of money.

In the ebook I suggested that the world bond/stock fund be proxied by a combination of these four funds, using the relative market values of the underlying securities in each of the four component sectors. But where to find such values? Ideally, for each fund we would find the market capitalization at some recent date of the index being tracked, then adjust the holdings of the four funds so that their relative values would have equaled those of the corresponding indices at that date.

Here are the indices tracked by the funds in 2015:

 Barclays U.S. Aggregate Float Adjusted Index

Barclays Global Aggregate ex-USD Float Adjusted Regulated Investment Company Index Currency Hedged

The Center for Research in Security Prices U.S. Total Stock Market Index

FTSE All-World ex U.S. Index

In 2019, the funds tracked were similar, although the name of the indices tracked by VBTLX and VTABX had been changed to reflect their acquisition by Bloomberg. Moreover, small changes had been made in their composition. The current names are:

 Bloomberg Barclays U.S. Aggregate Float Adjusted Index

Bloomberg Barclays Global Aggregate ex-USD Float Adjusted RIC Capped Index (USD Hedged).

At the time the book was written, Barclays bond index values were not available to the public at large, so I proposed using capitalization values from relatively similar funds provided by Citibank:

Citibank U.S. Broad Investment Grade Bond Index (USBIG)

Citibank World Investment Grade Bond Index (WorldBIG) minus the value of the USBIG Index.

Fact sheets for the Bloomberg Barclays bond indices are still not publicly available. The Citibank indices are now provided by FTSE, which does make fact sheets with capitalization values available to the general public.

Here are ways to find the fact sheets for the four indices. The search texts given will generally work but you might need to choose from multiple provided links. In most cases the desired fact sheet will appear in your browser, but a downloadable pdf file may be provided instead. As always with information on the web, things may change and some extra effort may be needed.

U.S. Bonds
    Search for: FTSE USBIG fact sheet

Global Bonds
     Search for: FTSE WorldBIG fact sheet

U.S. Stocks
     Search for: CRSP U.S. market fact sheet

Non-U.S. Stocks
      Search for: FTSE all world ex US fact sheet

The FTSE fact sheets provide market capitalizations as of the end of the most recent month but CRSP capitalization values are provided only as of the end of the most recent quarter.

Once you have index market capitalizations for the end of the most recent quarter you can update the desired values for the four funds using the approach given in the ebook for estimating current market values or, if you have access to the MATLAB language, the program given in chapter 7.

But instead you might want to use the two-fund approach. For this, see the next post.

Wednesday, June 12, 2019

Prior blogs

This blog was preceded by two others, neither of which will be updated in the future. However, each contains some information on retirement income analysis that may be of interest to readers of this blog.

The first contains posts from 2003 through 2013.
It can be found at: 


The second contains posts from 2013 through 2017.
It can be found at: