are predictions of future movements and comovements of returns. Step 7 At this point we begin to construct our risk estimates that are a function of holdings, exposures, and variance and covariance statistics. Thus far we have loaded all the information we need except for holdings. In order to compute portfolio weights: 11 We take the number of shares held for that asset on a particular date (e.g., 100 shares held on November 15, 1999) and multiply this amount by the close-of-business price for the 15th (e.g., $10). It We compute the total market value of the portfolio by taking the sum of all individual assets' market values (computed in the previous step). ■1 Each asset's portfolio weight is given by the ratio of its market value to the market value of the entire portfolio. On each day we need to load portfolio files for all the accounts as well as benchmark portfolios. For each asset, we compute its managed weight (its weight in the managed portfolio), its benchmark weight (its weight in the benchmark portfolio), and its active weight (defined as the difference between the managed and benchmark weights). Note that in the case where an asset is not held in the benchmark, its benchmark weight is zero and the active weight is equal to the portfolio weight. Conversely, for assets that are in the benchmark but not in the portfolio, their active weight is equal to the negative of the benchmark weight. Given the portfolio weights, active weights, exposures, and covariance matrices, we compute forecasts of portfolio risk and tracking error. Step 8 In this example, the final step in the risk estimation process involves finding the sources of risk. For example, we can decompose tracking error and portfolio volatility into various sources including the local market, industries, and investment styles. SUMMARY This chapter presented an overview as well as a detailed look into the linear factor model. The overview was presented in the form of a taxonomy of equity factor models. We classified factor models into those with observed and unobserved factor returns. Next, we took an in-depth view of the linear cross-sectional factor model. We presented both local and global specifications. As part of this discussion we defined the various types of asset exposures used in linear factor equity models. The linear cross-sectional factor model forms the basis of risk calculations. We presented these risk calculations, introduced both relative and absolute contributions to risk, and showed how risk can be attributed to factors and assets. Finally, we summarized the practical implementation of the linear cross-sectional model. The eight-step process includes the data collection and the computations.