With f(1)in hand, we can calculate a new h=h(1)that solves equations (35)
and (36) for f=f(1). This h(1)gives us a new candidate f=f(2)from (37). We
continue this process until convergence occurs: f(i)→f, and h(i)→h.
C. Stock Prices in Economy IFigure 7.3 presents price/dividend ratios f(zt) that solve equation (24) for
three different values of b 0 : 0.7, 2, and 100, and with kfixed at 3. Note
that f(zt) is a decreasing function of ztin all cases. The intuition for this is
straightforward: a low value of ztmeans that recent returns on the asset have
been high, giving the investor a reserve of prior gains. These gains cushion
subsequent losses, making the investor less risk averse. He therefore dis-
counts future dividends at a lower rate, raising the price/dividend ratio.
Conversely, a high value of ztmeans that the investor has recently experi-
enced a spate of painful losses; he is now especially sensitive to further
losses, which makes him more risk averse and leads to lower price/dividend
ratios.
Figure 7.3 by itself does not tell us the range of price/dividend ratios we
are likely to see in equilibrium. For that, we need to know the equilibrium
distribution of the state variable zt. Figure 7.4 shows this distribution for
250 BARBERIS, HUANG, SANTOS
Figure 7.3. Price-dividend ratios in Economy I. The price-dividend ratios are plotted
against zt, which measures prior gains and losses: a low ztindicates prior gains. The
parameter b 0 controls how much the investor cares about financial wealth fluctua-
tions. We fix the parameter kat 3, bringing average loss aversion close to 2.25 in all
cases.