A simple return attribution model is used to parse market returns over various time frames.

Did you know that from the US equity market low at the end of February 2009 to December 31, 2013, the S&P 500 (in US dollars) has generated a total return of 178.9% or 23.6% annuallized? While 2.3% annually has come from dividends, and 5.1% has come from nominal dividend growth, dividend revaluation has generated returns of 15.1% annualized, or 64% of the total, as yields have fallen from 3.8% to 1.9%.

Background information is here, and further analysis is here.

the premise

What drives equity market returns? The **total return to an equity index (TR)** over any period is a function of its **dividend yield (DY)**, its **dividend growth (DG)**, and **the return due to any change in dividend yield (rΔDY), ** that is, the change in the market valuation of dividends. A good approximation of this relationship is that total return is the **sum** of the three components:

TR(equities) ≈ DY + DG + rΔDY(1)

If the equity index is denominated in a foreign currency, then you must ad a fourth component, the return due to the foreign currency exposure, **rΔFX**.

Here is a quick example. Using monthend data, the S&P 500 bottomed in February 2009. From then to the end of 2012, it returned 110.66% or 21.45% annualized. Over that period the annualized value of each of the three components was

- DY: 2.04%
- DG: 3.26%
- rΔDY: 15.12%, as DY fell from 3.76% to 2.19%.

The sum of the three components is 20.43%, close to the actual total return of 21.45%.(2) This shows that most of the strong returns over this period have been due to the market confidently revaluing dividends — not to the sub-2% levels seen from 1997 to 2007, but still very low relative to long-term history.

Many other interesting examples are given on the equity analysis page. Similar kinds of analysis can also be extended to apply to nominal and real bonds and other asset classes.(3)

While the historical analysis is interesting in its own right, the analysis becomes very useful if it can help us generate some insight into what might happen in the future. For example, in the case of the US market, we can't expect ongoing large returns due to falling dividends, and future returns will have to be driven more by dividend growth if they are to match historical levels of return. You can see how this works by examining the attribution for 2013 here.

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(1) The precise form of this relationship is the slightly more complicated equation:

1+TR = (1+DY) * (1+DG) * (1+rΔDY)

I use this equation for most of the calculations on the website, although the first approximation gives a usefula rough and ready analysis.

When the components are properly defined, this last euation gives a complete explanation of equity return over any period. These relationships are explained in our book How do you get THEE from HERE? (Chapter 7 and appendices), as well as in other sources referenced there, and are fairly well known if not well understood. (Return to text)

(2) Using the equation in footnote (1) above, TR is calculated to be 21.31%, just 0.14% lower then the total return of 21.45%. With the a more precise definition of the return to dividend yield, the attribution can be made exact.(Return to text)

(3) For example, see Chapters 21, 23 and 24 of How do you get THERE from HERE?. (Return to text)

Structured Capital presents a book by Tim Appelt:

Learning and Playing the Long-term Investment Game

Historical analysis of long-term global equity and bond returns is used to develop an analytical framework for a historical attribution of returns. In turn this attribution approach is used to develop expectations of future returns that acknowledge the past but take into account current market conditions.

Further information: