Market portfolio

In a one-period normal-return model with common beliefs and unrestricted exponential utility investors, their risky holdings are proportional to $V^{-1}b$, where $b$ is the expected excess-gain vector and $V$ its positive definite covariance matrix. The aggregate risky holding defines the common market portfolio.

The expected excess return obeys $\mathbb{E}(R_i-r)={\beta }_i\mathbb{E}(R_M-r)$ in the mean-variance market model. The beta of an asset is a covariance-to-market-variance ratio.

For a nondegenerate market return $R_M$, ${\beta }_i=\mathrm{Cov}(R_i,R_M)/\mathrm{Var}(R_M)$. It measures the asset's market-related exposure and enters the capital asset pricing model.