- the market portfolio should be the portfolio with the highest Sharpe ratio of all possible portfolios and should include all investible assets (since the true market portfolio includes all investible assets worldwide it is often said to be unobservable)

- expected excess returns for the market are assumed to be known - this is based on 2 assumptions (1) investors have access to the same information and agree on the risks/returns for all assets (2) distribution probability beliefs of investors match the true distribution of returns.

The arbitrage pricing theory model assumes that returns can be modeled with a multifactor regression model of the following form:

R_N = R_F + X_n,1 x b₁ + ... + X_n,k x b_k + u_n

The qualified model's market portfolio will have the lowest risk of all possible portfolios given identical factor exposures

minimum amount of unexplained variation for the market portfolio - all important underlying risks are captured and all unsystematic risks diversified away.

Structural models: assume an underlying relationship between a factor and stock returns, relationships can be macroeconomc, fundamental, and/or market related.

Statistical models do not rely on underlying economc relationships - they rely instead on mathmatical relationships.

- Principal component analysis - attempts to explain all factor exposures using a small number of uncorrelated exposures which do an adequate job of capturing risk.

- Maximum likelihood factor analysis - fits a mathmatical model to data using estimation by maximum likelihood.

- Asymptotic Principal Components: constructs a T-by-T covariance matrix for T months across N stocks.