Analytical cyclical price-dividend ratios

How non-linear are (log) price-dividend ratios in the fundamental state variables? The accuracy of log-linear approximations lies at the heart of much contemporary asset pricing. We analytically solve a parsimonious partial-equilibrium valuation model and uncover preliminary evidence suggesting that some caution be in order only if the fundamentals are extremely persistent. We work out the stock price's exact exposure to discount rate risk to shed more light on the "good" nature of discount rate risk relative to cashflow risk. Persistence in the price of risk not only inflates such exposure but also renders it markedly dependent on the level of the price of risk.