The recent development in credit markets is characterized by a flood of innovative credit risky structures. State-of-the-art portfolios contain derivative instruments ranging from simple, nearly commoditized contracts such as credit default swap (CDS), to first- generation portfolio derivatives such as first-to-default (FTD) baskets and collateralized debt obligation (CDO) tranches, up to complex structures involving spread options and different asset classes (hybrids). These new structures allow portfolio managers to implement multidimensional investment strategies, which seamlessly conform to their market view. Moreover, the exploding liquidity in credit markets makes tactical (short-term) overlay management very cost efficient. While the outperformance potential of an active portfolio management will put old-school investment strategies (such as buy-and-hold) under enormous pressure, managing a highly complex credit portfolio requires the introduction of new optimization technologies.
New derivatives allow the decoupling of business processes in the risk management industry (in banking, as well as in asset management), since credit treasury units are now able to manage specific parts of credit risk actively and independently. The traditional feedback loop between risk management and sales, which was needed to structure the desired portfolio characteristics only by selective business acquisition, is now outdated. Strategic cross asset management will gain in importance, as a cost-efficient overlay management can now be implemented by combining liquid instruments from the credit universe.
In any case, all these developments force portfolio managers to adopt an integrated approach. All involved risk factors (spread term structures including curve effects, spread correlations, implied default correlations, and implied spread volatilities) have to be captured and integrated into appropriate risk figures. We have a look on constant proportion debt obligations (CPDOs) as a leveraged exposure on credit indices, constant proportion portfolio insurance (CPPI) as a capital guaranteed instrument, CDO tranches to tap the correlation market, and equity futures to include exposure to stock markets in the portfolio.
For an integrated credit portfolio management approach, it is of central importance to aggregate risks over various instruments with different payoff characteristics. In this chapter, we will see that a state-of-the-art credit portfolio contains not only linear risks (CDS and CDS index contracts) but also nonlinear risks (such as FTD baskets, CDO tranches, or credit default swaptions). From a practitioner’s point of view there is a simple solution for this risk aggregation problem, namely delta-gamma management. In such a framework, one approximates the risks of all instruments in a portfolio by its first- and second-order sensitivities and aggregates these sensitivities to the portfolio level. Apparently, for a proper aggregation of risk factors, one has to take the correlation of these risk factors into account. However, for credit risky portfolios, a simplistic sensitivity approach will be inappropriate, as can be seen by the characteristics of credit portfolio risks shows:
Credit risky portfolios usually involve a larger number of reference entities. Hence, one has to take a large number of sensitivities into account. However, this is a phenomenon that is already well known from the management of stock portfolios. The solution is to split the risk for each constituent into a systematic risk (e.g., a beta with a portfolio hedging tool) and an alpha component which reflects the idiosyncratic part of the risk.
- However, in contrast to equities, credit risk is not one dimensional (i.e., one risky security per issuer) but at least two dimensional (i.e., a set of instruments with different maturities). This is reflected in the fact that there is a whole term structure of credit spreads. Moreover, taking also different subordination levels (with different average recovery rates) into account, credit risk becomes a multidimensional object for each reference entity.
- While most market risks can be satisfactorily approximated by diffusion processes, for credit risk the consideration of events (i.e., jumps) is imperative. The most apparent reason for this is that the dominating element of credit risk is event risk. However, in a market perspective, there are more events than the ultimate default event that have to be captured. Since one of the main drivers of credit spreads is the structure of the underlying balance sheet, a change (or the risk of a change) in this structure usually triggers a large movement in credit spreads. The best-known example for such an event is a leveraged buyout (LBO).
For credit market players, correlation is a very special topic, as a central pricing parameter is named implied correlation. However, there are two kinds of correlation parameters that impact a credit portfolio: price correlation and event correlation. While the former simply deals with the dependency between two price (i.e., spread) time series under normal market conditions, the latter aims at describing the dependency between two price time series in case of an event. In its simplest form, event correlation can be seen as default correlation: what is the risk that company B defaults given that company A has defaulted? While it is already very difficult to model this default correlation, for practitioners event correlation is even more complex, since there are other events than just the default event, as already mentioned above. Hence, we can modify the question above: what is the risk that spreads of company B blow out given that spreads of company A have blown out? In addition, the notion of event correlation can also be used to capture the risk in capital structure arbitrage trades (i.e., trading stock versus bonds of one company). In this example, the question might be: what is the risk that the stock price of company A jumps given that its bond spreads have blown out? The complicated task in this respect is that we do not only have to model the joint event probability but also the direction of the jumps. A brief example highlights why this is important. In case of a default event, spreads will blow out accompanied by a significant drop in the stock price. This means that there is a negative correlation between spreads and stock prices. However, in case of an LBO event, spreads will blow out (reflecting the deteriorated credit quality because of the higher leverage), while stock prices rally (because of the fact that the acquirer usually pays a premium to buy a majority of outstanding shares).
These show that a simple sensitivity approach – e.g., calculate and tabulate all deltas and gammas and let a portfolio manager play with – is not appropriate. Further risk aggregation (e.g., beta management) and risk factors that capture the event risk are needed. For the latter, a quick solution is the so-called instantaneous default loss (IDL). The IDL expresses the loss incurred in a credit risk instrument in case of a credit event. For single-name CDS, this is simply the loss given default (LGD). However, for a portfolio derivative such as a mezzanine tranche, this figure does not directly refer to the LGD of the defaulted item, but to the changed subordination of the tranche because of the default. Hence, this figure allows one to aggregate various instruments with respect to credit events.