  # Economic Factor Model

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• Economic Factor Model

### Economic Factor Model

In factor model, the stock return is estimated by the product of factor premium (payoff to risk)  and factor exposure (exposure to risk). In economic factor model, we assume the factor premium is known value for the market which can be calculated from given data. And the factor exposure, which is stock’s sensitivity to factor premium, needs to be estimated by the regression of stock return on factor premium.

Unlike fundamental factor model, factor premium of economic factor model can not only be return of stock’s factors such as fundamental, momentum or quality factors, but also economic data, like inflation rate, interest rate, GDP and so on.

There are 3 steps to estimate stock future return by economic factor model:

For stock’s factors like fundamental or technical factors, we need to first identify the stock universe. After construct zero-investment portfolio for each factor, the portfolio return will be consider as the factor premium / return.
2. Estimate factor exposure:
Factor exposure in economic factor model will be determined by time series regression of stock returns on factor premiums. By repeating the regression for each stocks, we will able to get regression coefficients (factor exposures) for each factor of each stock.
3. Estimate stock return and covariance matrix:
Once we have factor premium and factor exposure, we can use them to estimate stock’s future return and covariance matrix.

### Stock Universe

We select the stock universe for zero-investment portfolios similar to Fama & French’s method:
1. Belong to NYSE, NASDAQ and AMEX
2. Common stocks
3. Stocks’ unadjusted prices are larger than \$1 to prevent them turn into OTC stocks in a short period

### Zero-investment portfolio

After selected the stock universe, we can construct zero-investment portfolio for each factor.:
1. At each end of June, we rank all stocks in stock universe in terms of the factor
2. We can create high-exposure(top 30%) and low-exposure(bottom 30%) stock portfolios by value‐weighting.
3. Calculate the difference of these two portfolio return as the zero-investment portfolio return.