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.
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.