A rise in the conditional volatility of fundamentals affects the price-dividend ratio
: it decreases the real risk-free rate through the precautionary savings effect, and it increases the expected excess returns that investors require in order to be compensated for the additional risk that they bear when holding an asset whose payoffs are uncertain.
Bansal, Khatchatrian, and Yaron (2005) show that consumption volatility is time varying and that its current level predicts future asset valuations (price-dividend ratio
) with a significantly negative projection coefficient; this implies that asset markets dislike economic uncertainty.
They employed a log-linear approximation of stock returns and derived a linear relationship between the log price-dividend ratio
and expectations of future dividends and stock returns.
If price-dividend ratios
vary at all, then, then either (1) price-dividend ratios
forecast dividend growth (2) price-dividend ratios
forecast returns or (3) prices must follow a "bubble" in which the price-dividend ratio
is expected to rise without bound.
However, since there is a lag between the moment when saving occurs and the time when output and dividends are generated, the price-dividend ratio
is as sensitive to demography as it was before.
In this case changes in log dividends are stationary, so from (10) the log price-dividend ratio
is stationary provided that the expected stock return is stationary.
The relative value price based on dividends for, say, the first quarter of 1985 is calculated by multiplying BellSouth's 1984 dividend by SBC Communications' 1985 price-dividend ratio
. (12) The relative value prices based on earnings and on sales were calculated similarly.
If we impose a unit slope coefficient and test the stationarity of the log price-dividend ratio
, the ADF test statistic is -3.47 (see Table 1).
In their study, Campbell and Shiller also investigate the relation between the price-dividend ratio
and stock price growth, which exhibits similar patterns.
Here, Ps, is the log price-dividend ratio
for country s, G[sub st] is defined as [delta (difference)!
Putting the argument a little more formally, we can separate the achieved average stock return into: (1) the initial dividend yield (dividend payment/initial price), (2) increases in the price-dividend ratio
, and (3) growth in dividends, giving growth in prices at the same price-dividend ratio
Table 4 also shows the price-dividend ratio
for each state, which we have divided by 2 to make it comparable with the more familiar PE ratio, commonly used for evaluating the level of prices on the stock market.