Market Clearing Conditions and the CAPM Equation

In the Capital Asset Pricing Model (CAPM), the market clearing is equivalent to the market portfolio's clearing, which is the union of the semi-clearing condition (the tangent portfolio equals the market portfolio) and the value clearing condition (the value of all investors' optimal holdings equals the market portfolio's value). We prove that the CAPM equation is equivalent to the semi-clearing condition. Only when the market portfolio's value is given, can we compute the prices of the primitive securities from the CAPM equation. Additionally, we present the analytic solution to the mimicking payoff that is equivalent to the semi-clearing condition.