Calculating Real Equity Returns with Dividends and Inflation
Summary
The document explains how to interpret long-run annual equity index returns reported by Dimson, Marsh, and Staunton. It gives a formula for converting price change plus dividends into a real total return by adjusting the nominal return for inflation. In this setup, the dividend is included in the period’s total equity value, and inflation is applied as a separate adjustment to express purchasing-power growth.
The answer points to an associated research paper as support, but does not provide a detailed derivation, data construction procedure, or a direct discussion of whether the published series uses arithmetic or logarithmic returns. Its formula and explanation therefore clarify the basic real-return calculation, while leaving open implementation details such as dividend timing and index conventions.
Key ideas
- Real total equity returns include dividends as well as changes in index prices.
- Inflation adjustment converts nominal total returns into purchasing-power returns.
- The document expresses the calculation as a simple return rather than a logarithmic return.
- It does not establish the full construction details of the historical return series.
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# How did Dimson, Marsh and Staunton (2002) computed the equity index annual real return?
# How did Dimson, Marsh and Staunton (2002) computed the equity index annual real return?
I was trying to read the triumph of the optimist, but it was almost impossible to see a well-written formula to show how the returns have been computed. In a simple sense, I do not know how the annual return index have been computed? I am also not sure whether natural logarithm has been applied to say (P(t)-P(t-1))/ln(p(t-1)). If anyone has encountered this argument please refer me to a page or help us understand whether the returns found in Ibbotson associate is natural logarithm or simply simple returns?
These data are commonly used for long-term investors such as in pension funds, They also seem to have been called low-frequency returns.
## Answer by Anonymous (score 1)
https://quant.stackexchange.com/a/33597
All of the DMS returns are adjusting for dividends. Hence dividends are accounted in the sample. Moreover, DMS have also accounted for inflation. Hence, the real total net equity index return, now and hereafter, $e_{t}$, may be mathematically defined as \begin{equation*} e_{t}=\frac{1+\frac{P_{t}+D_{t}}{P_{t-1}}}{1+\pi_{t}}-1 \end{equation*} where $P_{t}$, and $D_{t}$ refers to the price of the index and dividend. $\pi_{t}$ refers to the inflation between periods $t-1$ and $t$ `\cite[see,][]{dimson2000risk}`.
```
@article{dimson2000risk,
title={Risk and Return in the 20th and 21st Centuries},
author={Dimson, Elroy and Marsh, Paul and Staunton, Mike},
journal={Business Strategy Review},
volume={11},
number={2},
pages={1--18},
year={2000},
publisher={Wiley Online Library}
}
```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.