for a particular asset. In this case, the regression in step 3 becomes a multivariate regression. Within the context of the local model, we can estimate the return to the local market. In the case where the exposures matrix consists of a vector of ones-that is, a constant-the corresponding factor return may be interpreted as the return on the market after controlling for other local factors (such as industry and investment styles). Another way of deriving the return on the market is to use local market betas as each asset's exposure to the local market. In the case of the global model, if one of the columns of the exposures matrix is a vector of ones, then the corresponding factor return is the global factor return. Currency Exposures An asset's currency exposure attempts to capture how sensitive its returns are to the returns on a particular currency. Currency exposure may be computed in the same way as country exposure. For example, if you hold IBM stock that trades in Germany, your country exposure is to United States and the currency exposure is to the euro. Standardizing Exposures In practice, we standardize some asset exposures to investment style factors. A primary reason for doing so is to make exposures across different investment styles comparable. In other words, the values of different types of exposures can be very different, and, therefore, we need to rescale them in such a way as to make their comparisons useful. Take the example of comparing an asset's exposure to market size and volatility. One measure of an asset's market size exposure is the square root of its current market capitalization. A company may have a market capitalization of Si billion, which produces a market size exposure of $31,663. The same asset's exposure to volatility may be 24 percent (historical volatility annualized). Therefore, any such analysis comparing $31,663 and 24 percent would be more meaningful if these values were converted to some standardized units. After standardizing, we may find that the asset's market exposure and volatility exposure turn out to be 1.0 and 1.5 standard deviations, respectively. As explained in more detail later, we interpret these numbers as showing that this asset has a high exposure to the market size and volatility factors. We discuss two methodologies for standardizing asset exposures. The first approach works as follows. For a particular exposure (e.g., market size), carry out the following steps. Step 1 Define the universe of assets over which a particular group of exposures will be standardized. Step 2 Compute the average exposure of this universe where the average is based on the market capitalization weights of each asset. Step 3 Compute the simple standard deviation of exposures for this universe. Step 4 An asset's standardized exposure is defined as the raw (original) exposure, centered around the mean (computed in step 2), all divided by the standard deviation of exposures.