fraction of price volatility to changes in consumption, stock returns are in-
evitably highly correlated with consumption growth.
We also report the mean and standard deviation of the simulated
price/dividend ratio. It is striking that while we aresuccessful at matching
the volatility of returns, we significantly underpredict the volatility of the
price/dividend ratio. To understand how this can be, it is helpful to con-
sider the following approximate relationship, derived by Campbell, Lo, and
MacKinlay (1997) with the help of a log-linear approximation:^26
rA ftttDt++^11 ≈+log −logf+σ +^1.PROSPECT THEORY AND ASSET PRICES 255Table 7.4
Asset Prices and Returns in Economy IIb 0 =0.7 b 0 = 2 b 0 = 100 Empirical
b 0 = 0 k= 3 k= 3 k= 3 ValueLog risk-free rate 3.79 3.79 3.79 3.79 0.58
Log excess stock return
Mean −0.65 1.3 2.62 3.68 6.03
Standard deviation 12.0 17.39 20.87 20.47 20.02
Sharpe ratio −0.05 0.07 0.13 0.18 0.3
Correlation w/consumption
growth 0.15 0.15 0.15 0.15 0.1
Price-dividend ratio
Mean 76.6 29.8 22.1 17.5 25.5
Standard deviation 0 2.9 2.7 2.4 7.1
Average loss aversion 2.25 2.25 2.25
b 0 =0.7 b 0 = 2 b 0 = 100
k= 20 k= 10 k= 8Log risk-free rate 3.79 3.79 3.79
Log excess stock return
Mean 5.17 5.02 5.88
Standard deviation 25.85 23.84 24.04
Sharpe ratio 0.2 0.21 0.24
Correlation w/consumption
growth 0.15 0.15 0.15
Price-dividend ratio
Mean 14.0 14.6 12.7
Standard deviation 2.6 2.5 2.2
Average loss aversion 5.8 3.5 3.2
Moments of asset returns are expressed as annual percentages. Empirical values are based
on Treasury Bill and NYSE data from 1926–1995. The parameter b 0 controls how much the
investor cares about financial wealth fluctuations, while kcontrols the increase in loss aversion
after a prior loss.
(^26) More specifically, this follows from equation 7.1.19 in chapter 7 of the book.