as abstract concepts. In this section we define factors and provide some examples of their practical application. We begin with a definition. A factor is a random variable that, at a particular point in time, can explain or account for the variation among a set of security returns/ Put another way, a factor is a variable that is common to a set of security returns, influencing each return through its factor loading. There are five key points to remember about equity factors: 1.    Their values take the form of factor returns. For example, if the market is a factor, then its value is the market return. 2.    A factor is common to all stocks at a particular point in time. 3.    Estimates of factor return covariance matrices are based on time series of factor returns. 4.    Factor loadings individualize factor returns. Loadings measure the sensitivity of a stock's return to a factor return. Alternatively, we can say that a factor return measures the sensitivity of a stock's return over a period for a given change in the factor's exposure. 5.    Stock-specific returns, u(t), measure the difference between the ?zth stock's excess return and the factor return contribution (loadings times factor returns), u(t) = R(t) - B(t- l)F(t). Factors can be defined in a variety of ways. The definition of different factors leads us to consider different types of factor models. Some examples of factors include: II Macroeconomic factors (e.g., gross domestic product and the default premium). II Market factors (e.g., the capital-weighted market portfolio). II Fundamental factors (e.g., price/earnings and price/book value). Regardless of the type of factor, managers require a time series of their values (i.e., factor returns) so that we can estimate a factor return covariance matrix. For example, returns to macroeconomic factors, such as the U.S. default premium (measured as the difference between the return on a high-yield bond index and the return on long-term government bonds), are observed time series. And, at each point in time, one value of the default premium corresponds to all values of stock returns. While we know the value of the factor, we do not know its sensitivity (factor loading) to each stock return. Hence, we have to use time series information on stock returns and the default premium to estimate factor loadings. The loading on the default premium factor may appear as the coefficient in a regression of stock returns on the return to the default premium factor. Alternatively expressed, we estimate the loading from the time series model 'This set contains one or more security returns.