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# Estimating the expected return of a stock index

Tactical asset class allocation is an investment strategy where a portfolio’s long-term allocation is adjusted based off of the expected return of each asset class.  One approach to estimating an asset class’s expected return is to apply a valuation model to an index fund representative of that asset class. Here the primary difficulty is obtaining enough years of historical earnings data for each of the index’s constituents to allow creating a time series of the index’s historical earnings that is representative of the index’s collective demonstrated earnings power. The reason why one (or even several) year’s of earnings are not enough is that a single year’s earnings can be impacted by cyclic factors – for more on this topic, see this article:  seekingalpha.com/article/139168-how-to-determine-the-demonstrated-earnings-power-of-a-cyclical-company-like-caterpillar

Once we have an estimate of the index’s collective earnings power, we can use a simple valuation model (see seekingalpha.com/article/140593-a-simple-valuation-model-for-large-cap-stocks) to estimate the index’s intrinsic value, and use this and the current market price to estimate the index’s expected rate of return. If this expected return is higher than the asset class’s long-term expected return, then that asset class’s allocation could be bumped up, and vice versa.  Two approaches to this adjustment algorithm will be discussed later; first let’s see how to estimate an index’s collective earnings power and intrinsic value by looking at three examples.

Small Cap Domestic Stocks:

To estimate this asset class’s intrinsic value and expected return, I used Standard and Poor’s Small Cap 600 index as a proxy for the small cap domestic stock (SCDS) asset class, as they have this index’s constituent list (in ticker format) conveniently downloadable as a spreadsheet.  To implement this asset class in a portfolio, I would probably use Vanguard’s NAESX index fund.

My first step in analyzing this index is to bring up the Investing Toolbox’s Portfolio Tool, put the tool in Asset Class Modeling Mode, and then import the tickers of the Small Cap 600 index by copying them from the spreadsheet and using Menu->Import->Ticker List function. I then have the tool automatically download (from Morningstar) each constituent’s industry, ten-years of earnings data, and current market capitalization.  This information is used to generate each constituent’s real (inflation-adjusted) expected return, and also generates a covariance matrix (600 X 600 in this case) which is used to estimate the index’s standard deviation of returns.  The index’s real arithmetic return is calculated as a market-cap weighted average of each constituent’s expected return, as estimated using the valuation model discussed in “The Patient Investor”.  A small sample of this portfolio as shown entered into the tool is shown below:

As you can see, the tool estimates the index’s real expected arithmetic average return to be 8.5%, with a standard deviation of 32.5%. Although the standard deviation of returns is close to the historical long-term average, the expected return is a lower than the long-term historical average of 10.6%.

Large Cap Foreign Stocks:

Modeling the expected return of the large cap foreign stock index (LCFS) presents the issue of where to find ten-years of earnings data.  Although most foreign companies do present English language financial reports, these reports are not to be found in a standardized format that lends itself to automatic download.  My solution is to use Standard and Poor’s ADR index, since a market cap weighted average of this index would be a good proxy for a large cap foreign stock index.  And since these companies all have shares listed as American Depository Receipts, Morningstar’s database has ten-years of financial data in standardized format.  To implement this asset class as an index fund, I would probably use Vanguard’s VGTSX index fund.

The next step is to import a ticker list of the ADR index’s constituents into the Portfolio Tool, and then following the same procedure as for the SCDS asset class.  Doing so, we find that the tool estimate’s the index’s real expected arithmetic average return to be 7.9%, with a standard deviation of 19.1%.  This can be compared to my estimate of this asset class’s long-term historical return of 6.7% with a standard deviation of 18%.

Large Cap Domestic Stocks:

For our final example, let’s look at large cap domestic stocks (LCDS). Here an obvious proxy is the SP500 index, which has actual operating earnings data downloadable from Standard and Poor’s, which means we can plug an earnings time series directly into our valuation model.  This gives an estimated intrinsic value of \$915, which can be compared to the current index value of \$1027 implies an expected real geometric return of 4.9% (see this article  seekingalpha.com/article/142838-s-p-500-... for an example of this calculation). Here the expected return is approximated as the ratio of estimated intrinsic value to market value, multiplied by the 5.5% real discount rate (the long-term expected geometric return used for this asset class).  See my book “The Patient Investor” for the rationale for this calculation, which takes into account mean reversion.  Converting this geometric return to an arithmetic mean using this asset class’s long-term standard deviation of 17% gives an expected average return of 6.85%.

To compare this to the approach used for the LCFS and SCDS asset classes, I imported the SP500 constituents into the portfolio tool, and analyzed the portfolio, which showed an expected average return equal to 6.6% and a 17.5% standard deviation, pretty close to the numbers found by directly analyzing operating earnings, which in my opinion give a more accurate picture of sustainable earnings.

Adjusting a Portfolio’s Allocation using Expected Returns:

The amount by which you adjust each asset class depends on the tactical asset class allocation strategy.  One approach is to adjust each asset class proportionally to the ratio of current (valuation based) expected return and long-term expected return.  Let’s use a simple example of a portfolio with a long-term allocation of 32% LCDS, 23% LCFS, 16% SCDS, and 29% STDB (short-term domestic bonds).

Using the data collected from the portfolio tool, the second row of Table 1 shows the portfolio’s long-term allocation.  The third row shows the expected long-term real rate of return for each asset class, the fourth row the expected returns generated using the portfolio tool, and the fifth row the ratio of valuation model based expected returns and long-term historical expected returns.  In row 6, we adjust the allocation based off of this ratio, which sometimes results in the sum of the portfolio’s weights exceeding 1.0, so in the last row we scale the allocation using the reciprocal of the sum of weights found in the last column of row 5. Since the short-duration bond market is pretty efficient, in this example I set the STDB expected return equal to the long-term historical average.

Table 1:

 Asset Class LCDS LCFS SCDS STDB Sum Weights LT Allocation 32% 23% 16% 29% 1.0 LT average ER 6.7% 6.7% 10.6% 2.2% Valuation-Based average ER 6.8% 7.9% 8.5% 2.2% Ratio 1.01 1.18 0.80 1.0 Adj. Allocation 32.3% 27.1% 12.8% 29% 1.012 Tactical Allocation 31.8% 26.7% 12.5% 29% 1.0

An alternative approach, assuming that you generated your original allocation using a mean variance optimizer (NYSE:MVO), is to use the valuation model based expected returns and rate of return volatility as an input to the MVO and run a new optimization, after which you would run a sample of portfolios along the efficient frontier through the Monte Carlo simulator configured in optimization mode, and choose the allocation of the portfolio with maximal utility within the context of your financial goal as the tactical asset class allocation. Running these new returns through the MVO (using super-class mode) resulted in the SCDS asset class completely disappearing from the new portfolio.  This is because this MVO optimizes based off of geometric return, which fell to 3.8% (subtract the variance divided by two divided by (1 plus the arithmetic rate of return), which give it a very poor return / risk profile.

The efficient frontiers generated using the long-term asset class returns and the valuation-based expected returns are shown below, where the original portfolio (with long-term historical asset class statistics input to the MVO) is shown in red, the new allocation (with valuation-based asset class statistics input to the MVO) in blue, and the slider set to display the original portfolio’s asset class weights and expected return statistics. The reason the new efficient frontier does not extend as far to the right is that the SCDS asset class is absent from any of the efficient frontier portfolios, and the reason the new efficient frontier extends farther to the northwest is due to the higher expected return on LCFS, which allowed a more “efficient” frontier to be generated.

Which approach you should use depends on how far you are willing to diverge from your long-term asset class allocation, obviously the first method diverges quite a bit less.

Regardless of the tactical asset allocation approach used, the current valuations of the index's analyzed indicates that it would make sense to underweight small cap domestic stocks (which using ETFs could be implemented with iShare's IJR), and overweight large cap foreign stocks (which could be implemented with iShare's ACWX).

If you would like to try out the software I used in writing this article, you can download it from my website for a free trial:

Disclosure:  I have no position in any of the index funds mentioned in this article.