costs. These forecasts are then used in the portfolio construction step described in the next main section.5 Forecasting Returns The process of building a quantitative return-forecasting model can be divided into four closely linked steps: (1) identifying a set of potential return forecasting variables, or signals; (2) testing the effectiveness of each signal, by itself and together with other signals; (3) determining the appropriate weight for each signal in the model; and (4) blending the model's views with market equilibrium to arrive at reasonable forecasts for expected returns. Identifying a list of potential signals might seem like an overwhelming task; the candidate pool can seem almost endless. To narrow the list, it is important to start with fundamental relationships and sound economics. Reports published by Wall Street analysts and books about financial statement analysis are both good sources for ideas. Another valuable resource is academic research in finance and accounting. Academics have the incentive and expertise to identify and carefully analyze new and innovative information sources. Academics have studied a large number of stock price anomalies, and Table 23.2 lists several that have been adopted by investment managers. For portfolio managers intent on building a successful investment strategy, it is not enough to simply take the best ideas identified by others and add them to the return-forecasting model. Instead, each potential signal must be thoroughly tested to ensure it works in the context of the manager's strategy across many stocks and during a variety of economic environments. The real challenge is winnowing the list of potential signals to a parsimonious set of reliable forecasting variables. When selecting a set of signals, it is a good idea to include a variety of variables to capture distinct investment themes, including valuation, momentum, and earnings quality. By diversifying over information sources and variables, the portfolio manager has a good chance that if one signal fails to add value another will be there to carry the load. When evaluating a signal, it is important to make sure the underlying data used to compute the signal are available and largely error free. Checking selected observations by hand and screening for outliers or other influential observations is a useful way to identify data problems. It is also sometimes necessary to transform a signal-for instance, by subtracting the industry mean or taking the natural loga- 5Some portfolio managers do not develop explicit forecasts of returns, risks, and transaction costs. Instead, they map a variety of individual stock characteristics directly into portfolio holdings. However, there are limitations with this abbreviated approach. Because the returns and risks corresponding to the various characteristics are not clearly identified, it is difficult to ensure the weights placed on the characteristics are appropriate. Further, measuring risk at the portfolio level is awkward without reliable estimates of the risks of each stock, especially the correlations between stocks. Similarly, controlling turnover is hard when returns and transaction costs are not expressed in consistent units. And, of course, it is difficult to explain a process that occurs in one magical step.