Extraction of a Mathematical Capital Asset Pricing Model within the Framework of Mental Accounting

Ordinary investors do not look to their portfolio as a whole. These investors consider their portfolio as a set of mental arithmetic. In mental accounting, the conventional issue of maximizing the expected return is faced with the constraint of maximum likelihood to fail in achieving the return threshold. The present study extracts the capital asset pricing model from Markowitz Mean-Variance Portfolio Model and risk-free asset entering the limitations of this model. Then, MA-CAPM model is extracted by creating a mathematical equivalence between the components of this model and the limitation of mental accounting. In this model, expected investment return for any purpose presented in the form of mental arithmetic is a function of the return on risk-free asset, beta and risk premium of mental arithmetic where the risk premium of mental arithmetic equals the difference between returns of each account and risk-free return on assets. Expected rate of return on assets in the MA-CAPM will be influenced by return threshold and likelihood to fail in reaching this threshold, i.e. mental arithmetic risk.