of exposures Standardized exposure = - The resulting standardized exposures from this approach are measured in units of standard deviation. In practice, there are some variations to this methodology. For example, the universe used to standardize investment style exposures may be based on the individual assets industry classification. Suppose we were going to standardize the size factor according to this approach. In this case, we would first group all size exposures (measured by market capitalization) according to their respective companies' industry designations. So, the market caps of stocks belonging to the automotive industry would make up one group, all financial stocks would make up another group, and so on. Next, within each group we would compute the mean market capitalization (mean exposure) and the standard deviation of the market capitalizations (standard deviation of exposures). Third, we would standardize each asset's exposure by its group (i.e., industry) mean and group standard deviation. Chan, Karecski, and Lakonishok (1998) suggest an alternative approach for standardization. Their methodology consists of three steps. Step 1 Define the universe of assets over which a particular group of exposures is to be standardized. Step 2 Rank exposures. Step 3 Rescale the ranked exposures so that their values lie between 0 and 1. , ,. , Rank of raw exposure-1 Standardized exposure = Maximum (Rank of raw exposure-1) How Asset Exposures Are Used in a Linear Factor Model In the case of the linear factor model, asset exposures measure the sensitivity between returns on factors (e.g., momentum) and the asset's return. To show this, let's consider a three-asset, two-factor example: One of the factors is market size, while the other is an industry-computer hardware. Moreover, assume that we use the first method when it comes to standardizing exposures. We assume that asset 1 has an exposure of 1.0 standard deviation to market size and is in the computer hardware industry. Assets 2 and 3 have exposures of -1.0 and 0.5 standard deviations to market size and both are not in the computer hardware (HW) industry. The linear factor model posits the following relationship: Asset 1 's total return = 1.0 X Return to market size + 1 X Return to computer HW + Asset l's specific return (20.28) Asset 2's total return = -1.0 X Return to market size + Asset 2's specific return Asset 3's total return = 0.5 X Return to market size + Asset 3's specific return