The main advantages of ADRs are (1) there is no currency conversion in trading and receiving dividends, (2) they help in minimizing higher overseas transaction costs and custodial fees, and (3) there is uniformity in information available due to mandatory disclosures. Histories In order to generate a time series of returns to factors, histories of exposures are required. Often, it may be difficult to obtain/procure comprehensive historical exposures. In addition, the definition of exposures can change over time, making it necessary to link old and new classifications. For example, the Internet became a new industry classification according to some schemes in 1999. In order to estimate the risk associated with investing in Internet stocks, the volatility of the returns to the Internet industry is required. This volatility estimate requires a time series of returns to the Internet industry, which, in turn, requires a time series of Internet exposures. If we need three years of history to estimate Internet volatility, one question would be, what was the return to the Internet industry in 1996? In order to answer this question, we could find proxy industries that have similar price behavior to the Internet industry at a time when we have no exposures to the Internet. One example of such a proxy would be the commercial services industry. In this case, we would use the returns to this industry as a substitute for the unknown returns to the Internet industry. Estimating Factor Returns Equation (20.27) provides us with a mathematical description of a linear factor model. In this section we explain how we estimate the factor returns, Ff{t), which are required to estimate risk. Briefly, a time series of factor and specific returns are generated as follows: Step 1 Define a set of exposures to factors for each asset in the estimation universe. Step 2 At each point in time (e.g., each day) run a cross-sectional regression of asset returns [R*(?)] on a set of exposures [Bf(t - 1)]. This requires asset returns from period t-ltot (where t denotes one day) and exposures as of period t - 1. In some cases, however, exposures and asset returns are updated at different frequencies. Step 3 A time series of factor returns, Ff{t), and specific returns, w£(£), is generated by repeating these regressions over successive periods. Define Assets Used in Estimating Factor Returns The estimation universe mentioned earlier is a group of security returns that are used to estimate the factor returns. It comprises one of four universes that we define in the factor return estimation process. 1.    The asset universe is the set of all assets tracked. 2.    The estimation universe represents the set of all assets used to estimate factor returns. Estimation universes can be defined in a variety of ways. For example,