# LO 32.4: Calculate the stressed expected loss, the stress loss for the loan portfolio

LO 32.4: Calculate the stressed expected loss, the stress loss for the loan portfolio and the stress loss on a derivative portfolio.
Loan Portfolios
The expected loss (EL) for any counterparty in a loan portfolio is a function of the probability of default (PD^, exposure at default (EAEL), and loss given default (LGDj). The EL for a portfolio is the sum of the individual exposures:
EL =
N
i=l
2PD; x EADj x LGD; J
Stress testing the EL could involve stressing the PD, which is a function of several other variables, including the unemployment rate or a relevant exchange rate. The stressed expected loss (ELS) is, therefore, conditional on the impact of these variables on the PD. The ELS can be expressed as:
ELS =
N
i=l
x EAD; x LGD;
The stress loss for the loan portfolio is the difference between ELS and EL. The financial institution could create different stress scenarios by increasing the PDs or by stressing the various variables. Note that the variables tend to be macroeconomic or balance sheet values.
Derivatives Portfolios
The EL and ELS for a derivatives portfolio are derived similarly to the loan portfolio in that they both use the PD and LGD. However, exposure at default, which is stochastic and depends on market factors, is replaced with the expected positive exposure (EPE^ multiplied by an alpha factor (a). This allows CCR exposures to be used in a portfolio credit model. We can then measure EL and ELS for derivatives portfolios as:
PDi x (EPEi x a ) x LGD{
EL =
N
i=l
N
ELS = ^ pD? x(EPEf x a jx L G D i
i=l
Stress losses are done on a portfolio of derivatives counterparties. Similar to the loan portfolio, the financial institution could create different stress scenarios by increasing the PDs, or by stressing macroeconomic variables, balance sheet values, or values of financial instruments.
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Page 245
Topic 32 Cross Reference to GARP Assigned Reading – Siddique and Hasan, Chapter 4
In the context of EPE, institutions could also stress market variables including swap rates and equity prices. The stresses to these variables may either increase or decrease EL. Their overall impact will depend in part on the directional bias of the financial institutions portfolio, which counterparties are margined, and which have excess margin. This differs from stresses on the loan portfolio, which tend to be directionally the same and, therefore, have similar effects across counterparties. It is important to note that an institution that conducts EPE stresses does not need to separately consider aggregating them with its loan portfolio, since loans are not sensitive to market variables and will not change exposures due to changes in these variables.
Financial institutions typically shock a series of market variables instantaneously. During these instantaneous shocks, the institution shocks the initial value of a derivative prior to running the EPE simulation. How much this affects EPE will depend in part on the degree of collateralization and the portfolios moneyness. A series of shocks could also be performed over time; however, the common approach is to perform shocks to current exposure only.
Financial institutions could also consider joint stresses between credit quality and market variables. Although this is conceptually easy, it is challenging in practice since the variables are not tied by any meaningful connection. Equity-based approaches may be the closest to modeling joint stresses; however, the link between a shock to exposure and the equity-based default probability is unclear. It is also difficult to model the connection between exposure and PD in calculating wrong-way risk. Currently, the best way to identify wrong-way risk is to stress current exposure and identify the counterparties most exposed to wrong-way risk.
Treating CCR as a credit risk allows an institution to improve the management of its loan portfolio. Performing stress tests to CCR allows aggregating losses with loan portfolios and allows considering counterparty credit quality. On the other hand, treating CCR as a market risk allows for easier joint stresses of credit quality and exposure, and allows an institution to derive the PD from market variables.
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