Equity Returns as Dividend Yield, Valuation Change, and Dividend Growth
Summary
The document explains how equity returns can be decomposed into an initial dividend yield, a change in valuation, and growth in dividends. Starting from the one-period return that combines the next stock price and dividend relative to the current price, the answer takes logarithms and uses a first-order Taylor approximation. The resulting expression links return to the dividend yield, the change in the price-to-dividend ratio as a valuation proxy, and dividend growth. The price-to-dividend ratio plays a role similar to the more familiar price-to-earnings ratio.
The decomposition is presented as accounting rather than an economic theory of what causes returns. The approximation is an important qualification: the log-return expression uses a Taylor expansion, so the components are not an exact identity in that form. The answer also connects the idea to the Gordon growth relation, where expected return is expressed as yield plus growth. It does not provide empirical evidence or discuss how reliably the components predict future returns.
Key ideas
- A one-period equity return includes both the price change and the dividend received.
- A log-return approximation separates return into dividend yield, valuation-ratio change, and dividend growth.
- The change in the price-to-dividend ratio serves as a valuation-change component.
- The decomposition is accounting-based and relies on a first-order Taylor approximation.
- The Gordon growth relation similarly expresses return as yield plus growth.
Tags
Full text
# Drivers of equity returns: dividend yield, change in P/E and dividend (or earnings) growth
# Drivers of equity returns: dividend yield, change in P/E and dividend (or earnings) growth
In an NBIM paper I read the following:
> "... one can break down the total equity return into the dividend yield (the starting valuation), the change in the P/E ratio (the change in valuation) and the growth in dividends (or earnings) per share."
This breakdown is claimed to be an accounting exercise.
I do not see how these three components together form the equity return. In additon, how does this breakdown relates to this formula capturing equity return: $\frac{P_{1}-P_{0} + D}{P_0}$, with $P_1 - P_0$ the stock price increase and $D$ the dividend.
http://www.nbim.no/en/transparency/discussion-notes/2012/economic-growth-and-equity-returns/
## Answer by fni (score 2)
https://quant.stackexchange.com/a/22318
This is really the Campbell-Shiller (1988) decomposition: one of the key contributions leading to the 2013 Nobel Prize. The idea is very simple. By definition, the return between today and tomorrow is $$R_{t+1}=\frac{P_{t+1}+D_t}{P_t}$$ You can invert this: $$P_t = \frac{P_{t+1}+D_t}{R_{t+1}}$$ Take logs ($log P_t = p_t$ , $logR_{t+1}=r_{t+1}$ , $log D_t=d_t$, $\Delta d_{t+1}=d_{t+1}-d_t$ , $\rho$ is just a constant), take a first order Taylor expansion (details here): $$r_{t+1}= \rho(p_{t+1}-d_{t+1}) - (p_t - d_t) + \Delta d_{t+1}$$
So $-(p_t - d_t)=log \left(\frac{D_t}{P_t} \right)$ is related to the dividend yield, $\rho(p_{t+1}-d_{t+1}) - (p_t - d_t)= log \left(\frac{P_{t+1}}{D_{t+1}}\right)^{\rho} - log \left(\frac{P_{t}}{D_{t}}\right)$ is related to the change price-earnings (proxied by price-dividends ratios), and $\Delta d_{t+1}$ the growth in dividends. Notice that there is zero economic assumption here (just accounting) and that the only bit of math is the Taylor approximation.
By the way, this is very similar to Gordon’s growth model where $P_0 = \frac{D_1}{r-g}$ and therefore $$r=\frac{D_1}{P_0} + g $$ i.e. the return is dividend yield plus its growthShown 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.