World Bond/Stock Portfolio

 is a portfolio proposed by William F. Sharpe.

Construction
The World Bond/Stock (WBS) portfolio consists of the following four asset classes held in market proportions:


 * 1) U.S. Bonds
 * 2) Non-U.S. Bonds
 * 3) U.S. Stocks
 * 4) Non-U.S. Stocks

Many index providers do not publish market cap numbers; but there some that do so in their quarterly fact sheets. In RISMAT-7, Sharpe identified the following indexes as a close approximation for each of the four asset classes:
 * The Citibank US Broad Investment-Grade Bonds Index (USBIG) for U.S. Bonds
 * The Citibank World Broad Investment-Grade Bond Index (WorldBIG) for U.S. Bonds and Non-U.S. Bonds
 * The CRSP U.S. Equity indices for U.S. Stocks
 * The FTSE equity indices for Non-U.S. Stocks

Furthermore, he selected the following four Vanguard index funds as a proxy for constructing the WBS:

The table below shows representative indexes and corresponding funds that track the four asset classes:
 * VBTLX: Vanguard Total Bond Market Index Fund Admiral Shares
 * VTABX: Vanguard Total International Bond Index Admiral Shares
 * VTSAX: Vanguard Total Stock Market Index Admiral Shares
 * VFWAX: Vanguard FTSE All-World ex-U.S. Admiral Shares

It should be noted that the indices that VBTLX and VTABX track do not publish market cap numbers and, as a result, the Citibank indices are used. Sharpe has advocated that these should be reasonably close between the two index providers.

Rebalancing
Because the major index suppliers typically only release quarterly market cap numbers, Sharpe augments the last reported market cap numbers by the difference in adjusted closing values for funds that track the indexes.

To start, we must determine the market cap values of the four indices. As of 07/30/2017, the numbers are as follows:

Dividing by the totals will give the proportions for the WBS on 07/30/2017:

To account for drift in the market capitalization numbers, we can use the difference in adjusted closing prices for funds between now and the last quarter. This is easily done with data from the Yahoo Finance site: use the ticker symbol and select historical prices, then find the “Adj(usted) Close” prices forthe end of the prior quarter and the most recent date available. These will be the same as the unadjusted prices for the latest date but may differ for earlier dates, to allow for dividends and distributions. The ratio of the two prices will be the ratio of values of the holdings at the two dates for an investor who chooses to reinvest a fund's dividends and distributions in the same fund.

Equations for determining the adjusted percentages are as follows:


 * Price Ratio = Ending Price / Starting Price
 * Adjusted % = (Market Cap) x (Price Ratio) / ( Sum ( (Market Cap) x (Price Ratio) ) )

Applying this technique using numbers from 07/30/2017 to 08/18/2017, we can adjust the market cap numbers by the start/end price ratios by calculating the following for each asset class as follows:

Adaptive Asset Allocation
An adaptive asset allocation can be applied to the WBS portfolio, in which an asset allocation policy adapts as markets move, taking into account changes in the outstanding market values of major asset classes. An example of such a policy is given by Sharpe in his paper entitled "Adaptive Asset Allocation Policies" :

"“The fund’s Asset Allocation Policy is to have 80% invested in stocks and the remainder in bonds when the market value of stocks is 60% of the total value of stocks and bonds, with the proportions to be determined each period using the adaptive asset allocation formula.”"

In this manner, the overall asset allocation will trend with the overall WBS, but limits are applied based on an individual's risk tolerance or other circumstances. To determine the actual percentage of bonds-to-stocks, the following formulas can be applied:


 * desired asset % = ( (desired initial asset %) x (current asset's market %) / (initial asset's market %) ) / ( Sum( all desired asset % ) )

Taking the policy statement above, we can apply the formula using example values. Using the percentage of stocks/bonds in the WBS as of 07/30/2017, the result of applying the above stated policy would be: