THE LOG-NORMAL ASSET PRICING MODEL (LAPM)

We derive a discrete Log-Normal Asset Pricing Model (LAPM) based on log-normal distributed risky asset returns. Providing an analytical description of the efficient frontier in E(Log(R))-STD(Log(R)) space, we than show that under the log-normality of returns' assumption a segmented market equilibrium is created. The LAPM overcomes some of the drawbacks of the CAPM, hence better conforms with empirical observation; it shows how different portfolios of risky assets may be optimal for different investors; it shows why optimal portfolios may contain only a small number of risky assets, as well as why even with homogeneous expectations optimal portfolios for some investors may include risky assets held in short positions.