The long-run behavior of the S&P Composite Price Index and its risk premium

We lay out here the basis for a long-term equity index model, with intent to extract the risk premium. This is done by first observing the behaviours of the S&P Composite price index, earnings and dividends over roughly 130 years of history, from 1871 to 1998, and then assessing whether they fit within an equilibrium and efficient-market framework. The notions of equilibrium and efficiency shall be defined and formalised here, as they relate to this work, using classical finance theory. The conclusions derived so far are twofold. First, there is a transition in the market’s behaviour at around 1945. It appears that prior to this, the dividend payment policy was, on aggregate, one of constant dividend yield. After this, the policy’s focus seems to have shifted towards achieving market equilibrium and efficiency. Second, the backward-looking risk premium during the post-transition period is found, in theory, to be simply the negative percent rate of change in dividend yield. Moreover, under the special-case scenario where the equity price is discounted at a constant “infinitehorizon” discount rate, the forward-looking risk premium becomes identically the dividend yield.