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Risk Projection: Predicting Spread Volatility
The capability to measure risk precisely is probably the most crucial need for managing a credit portfolio ment. A vital advantage within the context of DTS of generating volatility forecasts is its utilization of existing spread levels to quickly in contrast, estimates realized spread volatility may take to adjust, with respect to the time the selected historical period of time is inherently subjective, and could not completely reflect the present state-of the marketplace.
The 2007–2009 credit crisis caught many investors off guard, with risk estimates calibrated to the sustained “volatility drought” of the previous few years severely underestimating the spread risk of corporate portfolios. It therefore provides an opportunity to compare forecasts based on DTS with those using realized spread volatilities over a trailing window.
The first forecast of volatility, based on DTS, is the product of the spread level at the beginning of the month and the (approximate) relative spread volatility of 10%/month from Chapter 1, that would have been available to investors at the beginning of the period. The plot also includes two estimates based on realized historical volatility, one over a trailing 36-month window and the other using the entire history (since September 1989) available at the start of each month.
In contrast, the “long-term” forecast was better prepared at the beginning of the crisis since it incorporated information from previous extreme market events such as the 1998 and 2002 crises. While its forecast of volatility for July 2007, for example, was higher than that of the “short-term” estimator, it generated grossly underestimated risk projections toward the end of 2008. Because the long-term volatility forecast adjusts to changing market conditions very gradually, the realized spread change in September 2008 would have corresponded to an 11.6 standard deviation event! Similarly, it underestimated the magnitude of the spread tightening beginning in early 2009 as market conditions started to improve.
Over the period, the DTS volatility estimator was consistently superior to both forecasts based on historical volatilities. The DTS-based forecasts quickly (albeit not perfectly) reflected both the increased level of risk once the crisis erupted and the reversal in market conditions in 2009, with most spread change realizations corresponding to less than two standard deviations. A notable exception was September 2008. Despite the already heightened level of spreads, the combined effect of the Lehman Brothers and Washington Mutual defaults and the bailout of AIG resulted in a 4.5 standard deviation event. However, as discussed previously, the forecasts using realized absolute spread volatility underestimated the risk by two to three times more than the DTS-based forecast.
Replication: Creating Index Tracking Portfolios
Portfolio managers often need to build portfolios that closely track the returns of a selected benchmark. Constructing a portfolio of cash instruments to replicate a target index can be accomplished using various methods, but a commonly used approach is stratified sampling. It relies on partitioning the index into “cells,” which represent the manager’s view of common risk factors affecting a given market (e.g., for credit these might be sector and rating). Bonds are then selected from each cell based on certain criteria and weighted such that they match various characteristics of the cell, such as the contribution to spread duration. The advantage of this approach is its simplicity and flexibility; its disadvantage is that it ignores the correlations among cells. We compare the results of replicating the U.S. Corporate Index using stratified sampling and matching only a single characteristic at a time: DTS or spread duration. Our intention is not to design the “optimal” replicating portfolio, but rather to focus on the relative efficacy of one characteristic relative to the other.
Five bonds are then selected from the high-spread duration-low DTS quadrant(HL), and from the low-spread duration-high DTS quadrant(LH). This set of 10 bonds is used in both variants of the replicating portfolio, to reduce noise from issuer selection and focus attention on the differences in systematic risk exposures. Within a quadrant, each bond is allocated a weight based on its relative market value. The weight of the two quadrants is determined such that the overall DTS (or spread duration) of the 10 bonds matches that of the cell.
The key difference is in how we weight the bonds within each cell: in the DTS-based portfolio, we match the DTS exposure of the index in each cell, while in the spread duration–based portfolio we match the index spread duration exposure. For example, Table 10.1 displays a market structure report of the U.S. Corporate Index along the sector/quality partition used in our replication exercise, at the beginning of the sample on December 29, 2006. Foreach cell of the partition, the report characterizes the exposure of the index to that market segment in three different ways: market weight, contribution to option-adjusted spread duration (OASD), and contribution to DTS. The spread duration–based replicating portfolio is constructed suchthat it matches the contributions to OASD in each of the index sectors (the second column from the right), whereas the DTS-based replication matches the DTS contributions in the rightmost column.
The last stage in our replication exercise is selecting the bonds that form the replicating portfolio. In a real-life portfolio management, security selection plays an important role in determining performance and several different criteria can be employed in the security selection process, depending on the portfolio setting. If minimizing tracking error is the primary goal, then the security weights within each cell should focus on the primary issuer exposures of the benchmark. Alternatively, managers may aim to maximize liquidity or add value by choosing securities that they believe will outper form. Ideally, however, as long as the portfolio has matched the benchmark allocations on the macro level, it should track well in the event of any major industry rally or decline. The key is to match the right set of macro exposures.
Our interest is not in the issuer selection mechanism, but in evaluating which set of macro exposures is most important to match. So, we test our replication methods using several different issuer selection mechanisms, to ensure that differences between the two replicating portfolios (DTS matched and spread duration matched) are independent of the specific bonds that were selected. One approach is simulation, where bonds in each cell are randomly selected, the replication results recorded and the analysis repeated multiple times. Another approach, which we use, is to specify explicit selection criteria based on bond characteristics.