A binomial model approach to modelling portfolio volatility in continuous time

The present article offers a binomial model replication of Merton's (1969, 1973) model of portfolio selection allowing volatility in continuous time. Interestingly, the investor risk premium is modelled as a consequence of the mathematics of risk itself (rather than that of investors setting prices at the start of each investment period). The model reveals the inherent circularity of the CAPM as an explanation of investor volatility-return preferences. In the model, the outcome return on a risky asset is identified as having an idiosyncratic risk component. The model thereby challenges the traditional interpretation of Markowitz portfolio theory, namely that idiosyncratic risk variations cancel