portfolios based on the forecasts described in the preceding section. In particular, we compare ad hoc, rule-based approaches to more formal portfolio optimization. The first step in portfolio construction, however, is to specify the investment goals. While having good forecasts (as described in the previous section) is obviously important, the investor's goals define the portfolio management problem. These goals are usually specified by three major parameters: the benchmark, the risk/return target, and specific restrictions such as the maximum holdings in any single name, industry, or sector. The benchmark represents the starting point for any active portfolio; it is the client's neutral position-a low-cost alternative to active management in that asset class. For example, investors interested in holding large-cap U.S. stocks might select the S&P 500 or Russell 1000 as their benchmark, while investors interested in holding small-cap stocks might choose the Russell 2000 or the S&P 600. Investors interested in a portfolio of non-U.S. stocks could pick the FTSE 350 (U.K.), TOPIX (Japan), or MSCI EAFE (world minus North America) indexes. There are a large number of published benchmarks available, or an investor might develop a customized benchmark to represent the neutral position. In all cases, however, the benchmark should be a reasonably low-cost, investable alternative to active management. Although some investors are content to merely match the returns on their benchmarks, most investors allocate at least some of their assets to active managers (see Chapter 14 on how to allocate the active risk budget among active and passive strategies). In EPM, active management means overweighting attractive stocks and underweighting unattractive stocks relative to their weights in the benchmark.10 Of course, there is always a chance that these active weighting decisions will cause the portfolio to underperform the benchmark, but one of the basic dictums of modern finance is that to earn higher returns, investors must accept higher risk-which is true of active returns as well as total returns. A portfolio's tracking error measures its risk relative to a benchmark. Tracking error equals the time-series standard deviation of a portfolio's active return-which is the difference between the portfolio's return and that of the benchmark. A portfolio's information ratio equals its average active return divided by its tracking error. As a measure of return per unit of risk, the information ratio provides a convenient way to compare strategies with different active risk levels. An efficient portfolio is one with the highest expected return for a target level of risk-that is, it has the highest information ratio possible given the risk budget. In the absence of constraints, an efficient portfolio is one in which each stock's 10The difference between a stock's weight in the portfolio and its weight in the benchmark is called its "active weight," where a positive active weight corresponds to an overweight position and a negative active weight corresponds to an underweight position. For instance, if the weight of a stock is 3 percent in the portfolio but only 2 percent in the benchmark, then the active weight is 1 percent, an overweight. On the other hand, if the portfolio weight is zero (i.e., the stock is not held) and the benchmark weight is 1 percent, then the active weight is -1 percent, an underweight.