Fundamental factors can also be used in the cross-sectional risk factor model. In fact we’ll discuss two that we saw in the Fama-French time series model, the book to market value and market cap. This is an interesting example because we can see that there are two approaches to working with the same factor. There’s the method we saw using a time series risk factor model, and now we’ll see how to do this with the cross-sectional risk factor model. Just to revisit our goal, we’re going to fill in the values to calculate the portfolio variance. For starters, let’s see what data we already have to work with. For each stock, we have a book to market value, which may be updated once every three months if the company is based in the US. We also have a market cap, which may be updated daily. These values can be set as the factor exposures. Notice that in the Fama-French time series model, the book to market and market cap, were used in theoretical long-short portfolios to set the factor returns. However, for the cross-sectional model, these values are used directly as the factor exposures instead. We can also obtain the stock returns, and we want to estimate the factor returns using regression. So, we’ll take the following steps. For all the stocks in the selected stock universe, obtain each stock’s factor exposures, which are the book to market value and market cap. Also get each stock’s return for one time period. Next, request the stock return against the factor exposures. The regression estimates the factor return for each of the two factors. Since this factor return is estimated based on all the stocks in the stock universe, it is general enough to apply to all those stocks. Notice that in practice, even if the stock universe is 9,000 stocks, we may use a subset of those stocks to perform the regression. This subset is called the estimation universe because it’s the stock universe that is used for estimating these model parameters. To get a time series of factor returns, repeat this process of performing a multiple regression for each day. Once we obtain a time series of factor returns, we can calculate factor variances and covariances to fill in the covariance matrix of factors. To fill in the matrix of specific variances, we can calculate the specific return from the stock return minus the estimated stock return using the chosen factors. The variance of the specific return time series for each stock is what we’ll use to fill in the matrix of specific variances.