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Decomposing Shareholder Returns into Valuation, Growth, Margins, Shares, and Dividends

Article Quant Q&A · Author: zsljulius
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Summary

The document derives a framework for breaking total shareholder return into changes in valuation multiples, sales, operating margins, shares outstanding, and dividend yield. It starts with price appreciation plus dividends, then rewrites the price ratio using earnings per share, sales, and EBIT margin. Taking logarithms motivates treating the multiplicative components as additive contributions.

The author asks how net debt growth enters the decomposition and notes important limitations. Their formulation does not handle negative earnings because logarithms of negative values are undefined, and their calculated returns do not always match the cited paper’s results using their data. The decomposition may still help interpret historical return drivers when earnings are positive, but the document does not resolve the net debt term or establish that the approximation reliably reconciles to observed returns.

Key ideas

  • Shareholder return can be expressed using price change and dividends.
  • Rewriting price through earnings per share, sales, and margins yields several candidate return drivers.
  • Logarithms motivate adding contributions from components that multiply together.
  • Negative earnings break the logarithmic decomposition.
  • The author reports a mismatch between their calculated returns and the cited paper’s results.

Tags

EquitiesStatisticsFactor investing
Full text
# How does this return decomposition work?


# How does this return decomposition work?












http://image-src.bcg.com/Images/BCG-Value-Creators-2017-Appendix-July-2017_tcm9-166061.pdf

The paper here decomposes total shareholder return into different components. Here is my derivation of the decomposition, price $P$ and dividend $D$ are in per share basis, other variables ($S$ for shares outstanding) are on firm level:

$$ \begin{eqnarray} TSR_t &=& \frac{P_t + D_t}{P_{t-1}} \\ &=& (\frac{P_t}{P_{t-1}} + \frac{D_t}{P_{t-1}})\\ &=& (\frac{P_t/(EBIT_t/S_t)}{P_{t-1}/(EBIT_{t-1}/S_{t-1})}\frac{EBIT_t/S_t}{EBIT_{t-1}/S_{t-1}} + \frac{D_t}{P_{t-1}})\\ &=& (\frac{P_t/EPS_t}{P_{t-1}/EPS_{t-1}}\frac{EBIT_t}{EBIT_{t-1}} \frac{S_{t-1}}{S_t} + \frac{D_t}{P_{t-1}})\\ &=& (\frac{P_t/EPS_t}{P_{t-1}/EPS_{t-1}}\frac{Sales_t}{Sales_{t-1}} \frac{S_{t-1}}{S_t}\frac{EBITMargin_t}{EBITMargin_{t-1}} + \frac{D_t}{P_{t-1}})\\ &\approx& g_{multiple} + g_{sales} + g_{EBITMargin} + g_{shares} + DivYield \\ \end{eqnarray} $$ The last step comes from taking log on both sides of the equation.

However, where does that net debt growth part come from?

Update

I have done a similar simple decomposition with Amazon, and quickly find that the definition just doesn't work when Earning is negative. One simply cannot take log of a negative number, One can only multiply those terms instead of adding. BCG paper always use sum which doesn' seem like possible. The decomposition that I do as listed above works well when Earning is not negative. As @DavidAddison mentioned, the TRS doesn't match up with my calculation based on my data (Also CaptalIQ).

I think there is still some merits to this decomposition, because you can see what factors drive the return more clearly, at least historically.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.