Business — Banking — Management — Marketing & Sales

Portfolio models generate a loss distribution at a future horizon selected by the end-user. This horizon applies to all facilities regardless of their maturity. Maturities of facilities serve to assign default probabilities as a function of time and to date the exposures.

Horizon

Portfolio management implies continuous restructuring of the risk-return profile of the portfolio through limits, syndications, securitizations, loan trading and usage of credit derivatives. These actions bring the banking portfolio closer to trading. The trend towards more active portfolio management makes the buy and hold philosophy less necessary and less relevant. Sticking to the hold to maturity philosophy creates a bias towards a higher capital charge and is not in line with the facility of restructuring the portfolio risk within a shorter period than maturity. From a portfolio management perspective, the relevant horizon is a period that allows:

• Restructuring the portfolio to bring its risk in line with bank goals.

• Raising capital, if the existing capital is less than required to ensure adequacy with the portfolio risk.

Both actions take time. Hence, an intermediate period between long maturities and the minimum time to adjust portfolio risk and/or capital seems adequate. Such a horizon might perhaps extend to 1, 2 or 3 years. From a practical standpoint, the 1-year horizon offers many benefits. It is in line with the budget process. It corresponds to the disclosure period of official financial statements. It offers a visibility making assumptions reliable, while longer horizons make them more questionable. Using 1-year or 2-year horizons makes sense, but dealing with amortization over several subperiods is also a desirable specification of portfolio models, even when deviating from the buy and hold principle.

All models require setting a fixed horizon, typically 1 year, and some offer the possibility of making calculations for long periods [CreditRisk+ and Credit Portfolio View (CPV)]. With a fixed horizon, calculations depend on facility maturity:

• If the facility matures before the horizon, the risk exposure goes up to the maturity but the value of the facility at the horizon is zero. In addition, the loss calculation should adjust the default probability to the actual maturity.

• If the facility matures after the horizon, its value at the horizon is random, in full valuation models, due to migration risk. The valuation at the horizon embeds any migration between current dates and the horizon. However, the maturity influences the risk measures and the credit risk VaR through the valuation of the facility at the horizon, which includes the value of all future cash flows up to the final maturity, revalued at the forward time point.

Measuring economic risk suggests differentiating the period of exposure to risk. The longer the exposure, the higher the risk because the default probability increases with the length of exposure. There is a case for capturing risk until the final maturity of all facilities. This is not what most models do when they measure a credit risk VaR. Note that, even with a short 1-year horizon, there is an effect of maturity since the forward valuation at the future date discounts all future cash flows to maturity. Short horizons ignore the migrations and default beyond the horizon, not the maturity. Hence, there is a case for extending the horizon. One reason for sticking to relatively short horizons is the portfolio management philosophy, which deviates from the buy and hold philosophy. Other drawbacks are technical. The drawback of extending the horizon over which we capture migrations and defaults is that calculations get more complex and less intuitive. The excess spread of facilities over market yields creates valuation effects interacting with maturity effects. Long horizons also require longer projections of exposures, whose relevance is questionable. The portfolio amortizes gradually. At the last date of the longer-life facility maturity, the loss distribution narrows down to zero. Hence, we end up with several distributions at various intermediate time points, with data for estimating such distributions less reliable as time passes. Moreover, extending the horizon to long periods would require us to deal with new business. Frequently updated views on the portfolio structure might be more useful than capturing the entire time profile of the portfolio up to the longest maturity. Finally, the longer-life facilities would increase the capital charge, thereby making long maturity deals less attractive. This makes sense, but there is a balance to strike between mechanical penalties assigned to long maturity and business policy.

The regulatory view on maturity is that the capital weights should increase with the maturity of exposures, subject to a cap. This captures the increased period of exposure to credit risk. Ignoring valuation effects, such an increase with maturity is less than proportional for high-risk facilities, and more than proportional for low-risk facilities.

Intermediate Periods before Horizon

When considering long periods, it is necessary to assign default probabilities varying for different periods of exposure and to match them with the time profile of exposures. Amortizing exposures are packages of bullet facilities, so that addressing the issue for bullet facilities is sufficient. In general, the default probabilities broken down by subperiod are the marginal default probabilities applying to each successive period for a given rating class. The first step is to define time points for breaking down the overall maturity into subperiods (Figure 50.1).

In practice, there are two cases to consider depending on whether a bullet facility matures before the horizon or not. If it does mature before the horizon, the default probability should be time-adjusted because it does not make sense to assign a full year default probability to a 3-month exposure. A proportional time adjustment is sufficient for short periods. For instance, with a horizon of H = 1 year and a maturity T< H, the time-adjusted default probability d(0,1) x T suffices. After the horizon, the default probabilities should differ according to subperiods and apply to amortizing balances. In practice, it is easier to assign a single forward default probability d(1, T) from the horizon to maturity.

Assigning default probabilities is not sufficient to date default. Default dates can be at any time between current date and any horizon. They serve for discounting to present future losses. Distinguishing between defaults occurring before and after the horizon, and selecting time points, are necessary. For short maturity facilities, dating default at maturity makes more sense than waiting until the horizon date 1 year ahead. For longer maturities, and a single horizon, the valuation occurs at the horizon. Therefore, both migrations and default are at the horizon. This is consistent with default as a European option exercised at maturity only.