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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

Tuesday, September 24, 2019

A Two-fund Proxy for the World Bond Stock Fund

In the preceding post, I updated the material in my ebook that showed how to use four mutual funds to approximate a fund including all traded risky stocks and bonds in the world. I also suggested that it might be easier to approximate such a “world bond stock fund” (WBS) with two traded instruments. This post shows how this can be done.

Vanguard offers a number of exchange traded fund (ETFs) which invest in various types of bonds and stocks. The two of interest for our purposes are:

The Vanguard Total World Stock ETF (ticker symbol: VT)
The Vanguard Total World Bond ETF (ticker symbol: BNDW).

Following convention, I'll refer to them henceforth using ticker symbols.

I'll have more to say about ETFs in general and the particular approach utilized by BNDW. But first, let's consider the investments included in the funds and a way to determine the appropriate amounts to invest in each.

Here are the product summaries from the Vanguard website:


  • Invests in both foreign and U.S. stocks.
  • Seeks to track the performance of the FTSE Global All Cap Index, which covers both well-established and still-developing markets.
  • Has high potential for growth, but also high risk; share value may swing up and down more than U.S. or international stock funds.
  • Only appropriate for long-term goals.


  • Seeks to track the performance of the Bloomberg Barclays Global Aggregate Float Adjusted Composite Index.
  • Broad, diversified exposure to the global investment-grade bond market.
  • Unique ETF of ETFs structure.
  • Intermediate-duration portfolio, with exposure to short-, intermediate-, and long-term maturities.
  • Provides current income with high credit quality.

While these may not be perfect representatives for the overall world bond-stock market, they should provide a reasonable approximation. But how much to invest in each one? The market capitalization for the stocks covered by the FTSE Global All Cap Index can easily be found online. The fact sheet for the end of August 2019 showed a total value of $51,447,853 Million (roughly 51.5 Trillion US Dollars). But values for the bonds in Bloomberg Barclays indices are not available to the general public.

Not to worry. FTSE Russell graciously provides and maintains an Adaptive Asset Allocation Policy Calculator that allows investors or advisors to back-test and update strategies that adapt asset allocations to market proportions, using an approach that I presented in a paper published in the May/June 2010 issue of the Financial Analysts Journal.

For an investor wishing to hold market proportions of bonds and stocks, the approach simplifies to simply adjusting proportions of bond and stock holdings periodically as needed to approximate those of the market as a whole. Moreover, the FTSE AAAP site provides estimates of these proportions as of the last trading day of every month.

To access the site, go to: https://research.ftserussell.com/Analytics/AAAP/Home/Index. You will arrive at the home page for the calculator. The upper-left portion of the page looks like this:

Simply click the text “Calculator” to the right of the “Home” tab to obtain the page for the calculator. The top left-hand portion should look like this:

If the region shown is not Global , click the nearby arrows until it appears.

The text at the bottom of this section indicates the market capitalization proportions of global (world) equity and bonds at the end of the month shown as the current month. This information is generally updated from 7 to 10 days after the end of the each month.

To get a more precise indication of the bond and stock proportions, look at the graph to the right of this first bar. Initially, it will look like this:

The policy weights can be ignored – our interest is in the equity and bond market weights (the black and grey curves). As can be seen, these have varied substantially over the period covered (from December 2002 to the end of the prior month).

To obtain more detailed information, you can simply move your mouse to the diagram to obtain a dashed vertical grey line, then move it to any desired month . For our purposes, the final month (on the far right) is germane. Here is the diagram for the end of August, 2019:

The most recent proportions are shown at the upper right of the graph. In this case FTSE estimated that at the end of August 2019 equities consituted 47.699% of the market and bonds 53.301%.

FTSE makes these functions of the AAAP Calculator available without registration. Those who wish to analyze policies involving combinations of stocks and bonds other than those of the market as a whole need to register to obtain the full functionality of the adaptive asset allocation approach. But this is not needed for our purposes.

Once the proportions of world bonds and stocks at the end of the preceding month have been obtained it is straightforward to calculate the number of shares of one of the two ETFs that need to be sold and the number of shares of the other that need to be purchased in order to bring the portfolio proportions of bonds and stocks close to estimated current proportions.

The google spreadsheet below does the job. The values in green are required inputs, those in black are computed by the spreadsheet, and those in red indicate the number of shares of one ETF to purchase and the number of the other to sell as well as the associated estimated values. The information in column E indicates the sources of inputs (in green) and the computations utilized by the spreadsheet (in black). When constructing your own spreadsheet you will need to enter formulas in columns C and D for the rows in which there is a formula in black in column E.  Once you have done this you can just type in current values for the items in green for your portfolio and click “run” to obtain the appropriate values for the numbers in red.

Due to the need to trade in integer numbers of shares the proceeds proceeds generated from the sale of shares of one of the etf's is designed to exceed the cost of the shares of the other etf. However, if execution prices differ significantly from the prices input in line 4, this may not be the case. In any event, the total value of the holdings of the two assets is likely to change only slightly.

There is little reason to make frequent changes in holdings of the two funds. The majority of the changes in their relative values will result from changes in the prices of assets already held rather than new issues, redemptions, dividends, interest payments and the like. It should suffice to check the relative values of your holdings against those shown in the AAAP calculator every month or so, changing your portfolio holdings only when the differences are substantial.

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