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The sources of stock market fluctuations

Author(s): John Cochrane

How much do dividend-growth vs. discount-rate shocks account for stock price variations?

From the Grumpy Economist:

An under-appreciated point occurred to me while preparing for my Coursera class and to comment on Daniel Greewald, Martin Lettau and Sydney Ludvigsson's nice paper "Origin of Stock Market Fluctuations" at the last NBER EFG meeting

The answer is, it depends the horizon and the measure. 100% of the variance of price dividend ratioscorresponds to expected return (discount rate) shocks, and none to dividend growth (cash flow) shocks.  50% of the variance of one-year returns corresponds to cashflow shocks. And 100% of long-run price variation corresponds to from cashflow shocks, not expected return shocks. These facts all coexist

I think there is some confusion on the point. If nothing else, this makes for a good problem set question.

The last point is easiest to see just with a plot. Prices and dividends are cointegrated. Prices correspond to dividends and expected returns. Dividends have a unit root, but expected returns are stationary. Over the long run prices will not deviate far from dividends. So 100% of long-enough run price variation must come from dividend variation, not expected returns. 

Ok, a little more carefully, with equations.

A quick review: 

The most basic VAR for asset returns is 

Δdt+1=bd×dpt+εdt+1
dpt+1=ϕ×dpt+εdpt+1

Using only dividend yields dp, dividend growth is basically unforecastable bd0 and ϕ0.94 and the shocks are conveniently uncorrelated. The behavior of returns follows from the identity, that you need more dividends or a higher price to get a return, 

rt+1ρdpt+1+dpt+Δdt+1

(This is the Campbell-Shiller return approximation, with ρ0.96.) Thus, the implied regression of returns on dividend yields,

rt+1=br×dpt+εrt+1

has br=(1ρϕ)+0=10.96×0.94=0.1 and a shock negatively correlated with dividend yield shocks and positively correlated with dividend growth shocks. 

 

The impulse response function for this VAR naturally suggests "cashflow" (dividend) and "expected return" shocks, (d/p). (Sorry for recycling old points, but not everyone may know this.)

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