The Nature of Market Growth, Risk, and Return

In the model of asset appreciation advanced here, the market economy and the market of asset claims on the economy are modeled as organic (or exponential growth) processes, similar to those commonly seen in nature and the biological sciences. In this model, investors have a log-wealth utility function. Within the framework, the market risk premium is derived as the premium that balances supply and demand among risky and risk-free assets. The model indicates that the premium is less than is indicated by ex post returns observed on U.S. stock markets. The model is consistent, however, with empirical observations that idiosyncratic risk and small company size are rewarded by the markets. In terms of the model, investors choose to allocate their portfolios long in both the risky market and the riskfree asset. Furthermore, their portfolios are independent of the investment time horizon.