LO 4.1: Explain the principles underlying VaR m apping, and describe the m apping

LO 4.1: Explain the principles underlying VaR m apping, and describe the m apping process.
Value at risk (VaR) mapping involves replacing the current values of a portfolio with risk factor exposures. The first step in the process is to measure all current positions within a portfolio. These positions are then mapped to risk factors by means of factor exposures. Mapping involves finding common risk factors among positions in a given portfolio. If we have a portfolio consisting of a large number of positions, it may be difficult and time consuming to manage the risk of each individual position. Instead, we can evaluate the value of these positions by mapping them onto common risk factors (e.g., changes in interest rates or equity prices). By reducing the number of variables under consideration, we greatly simplify the risk management process.
Mapping can assist a risk manager in evaluating positions whose characteristics may change over time, such as fixed-income securities. Mapping can also provide an effective way to manage risk when there is not sufficient historical data for an investment, such as an initial public offering (IPO). In both cases, evaluating historical prices may not be relevant, so the manager must evaluate those risk factors that are likely to impact the portfolios risk profile.
The principles for VaR risk mapping are summarized as follows:
VaR mapping aggregates risk exposure when it is impractical to consider each position
separately. For example, there may be too many computations needed to measure the risk for each individual position.
VaR mapping simplifies risk exposures into primitive risk factors. For example, a
portfolio may have thousands of positions linked to a specific exchange rate that could be summarized with one aggregate risk factor.
VaR risk measurements can differ from pricing methods where prices cannot be
aggregated. The aggregation of a number of positions to one risk factor is acceptable for risk measurement purposes.
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2018 Kaplan, Inc.
Topic 4 Cross Reference to GARP Assigned Reading – Jorion, Chapter 11
VaR mapping is useful for measuring changes over time, as with bonds or options. For example, as bonds mature, risk exposure can be mapped to spot yields that reflect the current position.
VaR mapping is useful when historical data is not available.
The first step in the VaR mapping process is to identify common risk factors for different investment positions. Figure 1 illustrates how the market values (MVs) of each position or investment are matched to the common risk factors identified by a risk manager.
Figure 1: Mapping Positions to Risk Factors
Figure 2 illustrates the next step, where the risk manager constructs risk factor distributions and inputs all data into the risk model. In this case, the market value of the first position, MVp is allocated to the risk exposures in the first row, x^ , x12, and x^y The other market value positions are linked to the risk exposures in a similar way. Summing the risk factors in each column then creates a vector consisting of three risk exposures.
Figure 2: Mapping Risk Exposures
Investment Market Value
Risk Factor 1 Risk Factor 2 Risk Factor 3
1 2 3 4 5
MVX m v 2 MV, m v 4 m v 5
*n
*21
*31
*41
*51
*12
*22
*32
*42
*52
*13
*23
*33
*43
*53

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