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Smart Credit Investing - Risk points and their applications

05-12-2013 | Research | Patrick Houweling, PhD, Paul Beekhuizen Introduction
Portfolio management within the fixed income credit markets consists of various, linked steps: from company analysis and relative value assessment, to constructing a well-diversified portfolio, measuring its risk, and finally attributing the realized performance to the decisions taken. All steps require an intricate knowledge of the behavior of credit markets. At Robeco we use the ‘risk point’ framework in an integrated manner in all these steps.

The elegance of this framework is that the product of a bond’s spread-duration and spread, succinctly referred to as its ‘risk points’, is sufficient to describe the volatility of that bond. As our risk estimates depend directly on the observed spread, they react instantaneously to market turmoil, and are therefore more accurate than traditional ‘moving window’ estimates that depend on a longer history.
By having an accurate prediction of a bond’s volatility, portfolio managers can construct a well-diversified portfolio in which all their high-conviction positions have equal risk contributions. Moreover, risk-adjusted returns can be calculated almost in real time, allowing timely relative value assessment.

Finally, portfolio positions can be evaluated periodically in the same framework as they have been implemented, yielding important insights and possibly giving rise to reevaluation of these positions. Robeco’s credit portfolio managers use sophisticated proprietary tools in every step of the investment process, which helps them make and implement superior beta and alpha decisions.

Spreads move in a relative fashion
The foundation of the risk point framework lies in the following key research finding 1,2: credit spreads move in a relative rather than an absolute fashion. We illustrate this in Table 1 by showing spread changes in an absolute and relative framework. We consider two bonds, X and Y, with spreads of 100 and 400 basis points (bps), respectively. In an absolute framework, spread changes are parallel, as is common in interest rates. That is, if the spread of bond X widens by 10 bps, so will the spread of bond Y, all else being equal.

In a relative framework, however, a spread change of 10 basis points for bond X corresponds to a spread change of 40 basis points for bond Y; both spread changes are 10% of the original spread. The insight of relative spread changes has an important implication for risk measurement, as we do not only need to take the spread-duration3 into account, but also the level of the credit spread.

In Figure 1 we display the spread change volatility of 10 spread portfolios, i.e. every month we assign the 10% of bonds with the highest spread to portfolio 1, the 10% below that to portfolio 2, and so on, and for each portfolio we calculate the spread change volatility. The figure shows that the volatility of these portfolios is indeed proportional to the spread level, i.e. bonds with higher spreads are more volatile. This strongly supports the notion of relative spread changes.

Figure 2 confirms the relationship between excess return volatility and relative spread volatility empirically. In this figure, we assign bonds to five spread x duration portfolios. We then subdivide every portfolio into six spread portfolios, resulting in 30 portfolios in total. For every portfolio, we calculate excess return volatility. The graph indeed shows that volatility is proportional to spread x duration, independently of the level of the spread. Therefore, only the product of spread and duration determines the risk of a bond, not how that product comes about: a lower spread with a longer duration, or vice versa, as long as the multiplication of spread and duration gives the same outcome, the expected volatility will be the same. For example, a bond with 1-year duration and 500 bps spread has the same expected volatility as a bond with 5-year duration and 100 bps spread.

Using relative volatility yields for more accurate risk estimations
Traditional risk models often use ‘moving windows’ to estimate risk, e.g. the past 36 months of historical returns. A considerable disadvantage of such models is that they react slowly to market events. For example, at the onset of the financial crisis of 2008, such models would still be based on the quiet periods of 2005 and 2006. This results in a severe underestimation of risk.

The persistence of relative volatility is illustrated in Figure 3, where we show the rolling window volatility of absolute and relative spread changes, of three different rating groups: BB, B, and CCC. Clearly the relative spread change volatility is much more persistent than absolute spread change volatility. In particular, relative spread change volatility remains remarkably stable during the burst of the IT bubble in 2001 – 2003 and the financial turmoil of 2008 – 2009. On the other hand, absolute spread change volatility dramatically rose in those periods.

A traditional credit risk model, based on absolute spread changes, will severely underestimate risk during such periods, because it takes into account the low-volatility period before that. Furthermore, after such volatile periods, a traditional model will overestimate risk, because it is still partly based on the crisis period with large absolute spread changes. Because the volatility of relative spread changes is more stable over time, it is more useful as the basis of a risk model. And because this volatility is multiplied by spread x duration, the risk estimates immediately react to the higher or lower market spread and are therefore more accurate. So, the combination of stable volatility estimates with the usage of spread x duration are the two ingredients of the accurate estimates of our credit risk model.

Risk points tell you where your risk is
In our risk model, the contribution of a bond to the systematic (beta) risk of the portfolio is calculated as weight x spread x duration. By adding up these contributions over all portfolio constituents we obtain the total amount of risk points of the portfolio. A similar calculation yields the amount of risk points of the benchmark. The beta can be conveniently approximated as the ratio of the portfolio’s risk points to the benchmark’s risk points.
The computation of beta risk using risk points is exemplified in Table 2. Here, the benchmark has 1,000 risk points and the portfolio 1,100, either by leveraging, by investing in bonds with a higher spread or a longer duration, or any combination. Hence, the beta of the portfolio is approximately equal to 1,100/1,000 = 1.1.
Furthermore, it is assumed that the volatility per risk point is estimated at 0.40 bps. Because the portfolio has 100 risk points more than the benchmark, it has 100 x 0.40 = 40 bps tracking error due to beta.

In a similar fashion, tracking error contributions of sectors and individual companies can be computed, as can be seen in Table 3. Here, we have a market value overweight in company A (1% vs. 0.5%). By multiplying the market value weight by spread and duration, we obtain the risk points in that individual company. As we have bonds of company A that have higher spread and duration than in the benchmark, we have an even higher position in terms of risk points (30 vs. 10).

A key difference between our risk model and traditional models that use market value, is that it is possible to be overweight in terms of market value, but underweight in terms of risk points. So, the portfolio weight in a particular company can be lower than in the benchmark, but the portfolio can still be more exposed to that company in terms of marktomarket volatility, e.g. by buying longer-dated bonds.

This can be observed for company B in Table 3. We have an underweight position in company B in terms of market value by 0.05%. However, because we have bonds with a higher spread and duration than the benchmark, we are overweight company B in terms of risk points (9 vs. 2.7). Company B thus actually has a higher contribution to risk than the benchmark; a fact hidden by its market value, but revealed by its risk points.

As part of our risk measurement process, we construct reports with beta, sector and issuer risk on a daily basis for all portfolios that contain credits. We have been generating these risk reports since the inception of the model in 2004.

Relative valuation using relative volatility
With relative valuation, the attractiveness of bonds, sectors, regions, ratings, etc. are compared to each other, for example by looking at historical returns. Here, it is important to consider risk-adjusted returns rather than the raw returns. Suppose that the Financials sector had a return of 2% last month, and the Utilities sector 1%. Although the higher return of Financials may look attractive, it can also be obtained by buying higher-spread or longer-duration bonds within the Utilities sector.

If Financials have exactly twice the risk as Utilities, then the risk-adjusted returns are identical, and investors should be indifferent between both sectors. However, if Financials have less than twice the risk, their risk-adjusted return is superior to that of Utilities.
Because we measure risk by risk points, we calculate the risk-adjusted returns as the excess return per risk point. This is our measure for relative value. The excess return per risk point can also be interpreted as (minus) the relative spread change, as follows from simple rewriting:

Using this interpretation, we can assess which issuers, sectors, regions, ratings, etc. have become cheap and which have become expensive. For example, in Figure 4, the excess return per risk point during a month is shown for different sectors, in EUR and USD. In this month, USD securitized bonds underperformed other sectors in the dollar market, but EUR securitized strongly outperformed on a risk-adjusted basis.


Figure 5 illustrates an alternative method for using excess returns per risk point to determine whether a particular bond has become expensive or cheap with respect to the benchmark. Here, the spread of Thames Water (ticker THAMES) is compared to the spread of the benchmark. However, rather than considering the spread difference, as might be the obvious choice, we consider the ratio of the two spreads and the change in that ratio.

If THAMES outperforms the index on a risk-adjusted basis, not only does its spread tighten relatively more than that of the index, but also the ratio of the THAMES spread to the index spread decreases.
Figure 5 indicates that the spread ratio is at a 12-month high, indicating that the bond has become cheaper. Further quantitative or fundamental analysis should indicate possible reasons why the risk has increased, and whether THAMES is a candidate for inclusion in the portfolio.

Steering risk using risk points
Suppose that, in the previous example, fundamental analysis confirms that THAMES is cheap and that it should get an overweight position in the portfolio. By measuring its relative position in risk points, it is assured that it becomes comparable in terms of risk contribution as other high-conviction positions in the portfolio. A position of, say, 40 risk points has the same contribution to risk regardless of whether it is a high-spread name, has long duration, or simply more market value weight.

Risk points have a similar advantage when it comes to steering the beta of the portfolio. A long position of 100 risk points has roughly the same tracking error through time. This is illustrated in more detail in Table 4, which compares various risk point positions in a volatile period (March 2009) and a more tranquil period (March 2013). A beta of 1.15 has a tracking error of 3.75% in March 2009, because of the high market volatility, but only 1.25% in March 2013. However, a position of 500 risk points leads to a tracking error of 2.5% in both periods. This is a consequence of the fact that relative spread change volatility is stable through time.

The impact of these observations on the actual implementation of positions is twofold. Firstly, when a portfolio beta position is taken, the size of the beta position should be measured in risk points. Secondly, for each portfolio there is a range that determines the maximum number of risk points the portfolio can be over- or underweight. This range is fixed and set in advance and determines the maximum tracking error available for the beta policy. Depending on the level of conviction of the portfolio manager, a beta position at the low or high end of this range is implemented.

Summarizing, by using risk points in the portfolio construction, portfolio managers make sure that risk contributions are comparable across names and across time.

Risk points tell you where your return comes from
The final step in the portfolio management process is performance attribution. The main goal of performance attribution is to measure the impact of portfolio decisions, such as beta positions and issuer under- and overweights, on the portfolio’s outperformance vs. the benchmark. Since positions are measured in risk points, and relative valuation is based on excess returns per risk points, our performance attribution methodology is also based on risk points.

A hypothetical example is displayed in Table 5. Here the portfolio has 1,100 risk points and the benchmark 1,000, so the portfolio has a beta of 1.1. Furthermore, in this example the portfolio has an excess return of 1.15%, while the benchmark has a return of 1%: an outperformance of 0.15%. Given that the portfolio is 100 risk points long, and that the benchmark’s excess return per risk point equals (1%/1,000) = 0.1 bps, the return contribution of the beta position is equal to 100 x 0.1 = 10 bps. Alternatively, given that the active beta position is 0.1, the return contribution of this beta exposure is 0.1 x 1% = 10 bps. The remaining 0.05% of outperformance is thus due to issuer selection.

The outperformance due to issuer selection can in turn be attributed to different issuers. For example, suppose we have a position of 40 risk points overweight in THAMES, and that THAMES has a relative spread tightening of 10%, whereas the benchmark tightened only 5% (see Table 6). The contribution of this position is calculated as the position in risk points (40) multiplied by outperformance per risk point (10%-5%), or equivalently, by the position in risk points times the relative spread change difference.

All individual performance contributions and the beta performance together add up to the total portfolio outperformance. We can thus attribute the entire outperformance to individual portfolio decisions.

Unlike interest rates, spreads move in a relative manner. That is, high spreads are more volatile than low spreads. As a consequence, the risk of a bond is best measured by its spread x duration, a.k.a. risk points, which is the foundation of our credit risk model.
Furthermore, as relative spread change volatility is more stable through time than absolute spread change volatility, the risk estimates of our risk model are more adaptive to changing market environments than traditional estimates, and are therefore more accurate.
The use of risk points has found its way into all aspects of credit portfolio management at Robeco: risk measurement, relative valuation, portfolio construction, and performance attribution:

  • Using risk points, we can correctly compute risk contributions of bonds. Without using risk points, the risk of high-spread bonds would be underestimated and the risk of low-spread bonds overestimated.
  • Risk points are used in relative valuation by comparing the excess return per risk point (or equivalently the relative spread change). In this way, the higher risk of high-spread bonds is properly accounted for by demanding a higher excess return.
  • Betas are not comparable over time, because the same beta leads to a higher tracking error in a volatile market than in a tranquil market. Risk point positions, however, are comparable over time: as relative spread change volatility is stable through time, the same risk point bet leads to the same tracking error, regardless of the market environment.
  • Finally, because positions are taken using risk points, performance attribution is also conducted using risk points and relative spread changes. In this way, the performance attribution shows the impact of the implementation decisions made on the relative performance of the funds.
In all aspects of the investment process, the credit portfolio managers can use proprietary tools to optimally balance risk and return, enabling them to make, implement and evaluate superior beta and alpha decisions.

  1. The research was originally conducted for High Yield and documented in the 2004 Robeco research
    note “The New Risk Model for High Yield Corporate Bonds”. Later, it was extended to Investment
  2. See the 2007 publication in The Journal of Portfolio Management, by Ben Dor, Dynkin, Hyman,
    Houweling, Penninga & van Leeuwen, entitled “Duration Times Spread: A New Measure of Spread
    Exposure in Credit Portfolios” for more details about the research. 
  3. changes, from now on we will use the shorter word ‘duration’ to improve readability.
    Although ‘spread-duration’ is the proper phrase to reflect a bond’s sensitivity to credit spread

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