The Mapping of Macroscenarios to Balance Sheets: The Bottom-Up Approach

Translating a macroeconomic framework into the balance sheet of a financial institution requires mapping macrovariables into a set of common risk factors that can be applied to stress individual balance sheets. Applying a stress to an individual balance sheet under the bottom-up approach involves shocking the risk factors that determine the underly­ing value of a portfolio and then revaluing that portfolio. Because most portfolios have numerous instruments, each with a unique price, the process of revaluing a portfolio may require knowledge of hundreds or thousands of market prices. Financial institutions typically simplify this process by mapping each element of a portfolio into a smaller set of common risk factors. Thus, two mappings are required to implement a system-focused stress test: one mapping from the macroadjustment scenarios to the set of common risk factors and another mapping from the common risk factors into all of the instruments in a portfolio.

For a financial institution, implementing a stress test typically requires a range of spe­cific indicators. The indicators include interest rates (e. g., the term structure of the risk­free rate and credit quality spreads), exchange rates (e. g., spot and forward, bilateral, and trade-weighted), asset prices (e. g., market price indices), and credit exposures and quality. Thus, it may be necessary to supplement the output of the macromodel with additional estimates of what each scenario would imply in terms of the common risk factors.

Some financial institutions have their own internal models that link macroeconomic factors to the performance of their balance sheet, which can, in turn, be used to help calibrate this mapping to a set of common factors. Other potential sources of information to flesh out the details of this mapping could include either studies that are performed on the domestic economy and that address the term structure of interest rates, or models used to estimate the equilibrium real exchange rate. Two examples of this process may prove illustrative:

• Suppose the macro-model produces only two interest rates: an overnight cash rate and a 10-year bond rate. An empirical model of the term-structure of interest rates could be used to produce an estimated set of interest rates for a larger set of maturi­ties. In turn, those data could be used to derive credit spreads.

• Suppose the macromodel produces only a trade-weighted exchange rate or a single bilateral exchange rate. If one is to get a broader range of exchange rates, it may
be possible to use the weightings implicit in the trade-weighted index to produce a set of bilateral exchange rates. Producing a range of exchange rates from a single bilateral exchange rate forecast from a macromodel can be accomplished by assum­ing some pattern of cross rates.

Once the macro-scenarios have been mapped into a set of common risk factors, the next step is to map the risk factors into the portfolios of individual institutions. The party that is usually best placed to construct such a mapping is the individual institution involved in the stress-testing exercise because it typically has the best access to expertise and detailed information on the portfolio itself. It may also have a well-developed risk management model that is capable of performing many of the calculations. The range of techniques that are typically used to estimate sensitivities of a balance sheet or income statement to shocks in specified risk factors can vary according to the complexities of the portfolio and the scope of risk management framework used by banks. The techniques also differ according to the type of risk being assessed, as illustrated in section D.3 of this technical note. As mentioned earlier, some financial institutions have macroframeworks that can be used to link the larger macroeconomic picture (e. g., unemployment rate, GDP growth, sectoral growth rates) to portfolio performance and so can map the adjustment scenarios directly into their own balance sheets and income statements by using their internal models.

In many circumstances, individual institutions will not have internal models capable of translating broad macroeconomic developments but will have their own internal models or expertise that can be used to construct an appropriate mapping. For example, many banks have internal models that use credit scores or default probabilities as key parameters in understanding the evolution of credit risk in their portfolio. Banks can estimate the effect of macroeconomic changes on those internal risk model parameters or can use the most recent economic downturn as a guiding rod for assessing the effect of broad economic changes on their portfolio. In some cases, it may be necessary to rely on the expert judgment of risk managers in adjusting the key parameters, particularly if the systems have been in place for only a relatively short period of time and thus have not spanned an entire economic cycle.

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