# The Market Model for a Security’s Returns

When a portfolio manager considers a security for addition to a portfolio within the construct of mean variance analysis, he/she must determine what return for the x-variable represents “market portfolio”.

The Market Model assumes that some security market index, such as the S&P 500, represents the market portfolio.

The Market Model & Quant: The Market Model is a single variable regression model, where alpha return is the constant and beta is the security’s return coefficient on the independent (x) variable of the market index’s.

The market model allows for a security’s expected return to be priced by linear regression.

Ri = αi + βi(RM) + εi

• Ri = Return of security i

• αi = The return from the asset that is not related to the market’s return. This is “alpha” return from the security

• βi = Beta or the return from the security explained by the market index’s return

• RM = The market index’s return

• εi = Error term for past returns not explained by the regression equation

There are three assumptions in the market model:

1. The expected value of the error term in zero.

2. The errors are not correlated with the market returns.

3. The firm specific evens are not correlated across the assets.

Using these assumptions, the procedure for mean-variance analysis becomes very simple.