Seeking diversification in credit

With policy headwinds rising as the Fed turns hawkish, an increasingly inverted yield curve, on top of conflict between Russia and the West, risks to credit returns appear to be mounting. Strategies that could insulate credit returns against a reversion in spreads may prove particularly timely, as credit spreads are still close to cyclical lows, especially in Asia. In particular, we seek returns that are less correlated with aggregate credit spread levels, and can thus offer diversification from cyclical swings in spreads.

Exploring ways to analyse the credit curve

A systematic analysis of drivers of the credit curve could help to derive such diverisifed strategies. In rates, a seminal work by Litterman and Scheinkman (1991) had shown how the variation in Treasury bond returns could be mostly attributed to three uncorrelated factors, namely 1/ level, 2/ slope, and 3/ curvature. Like rates, credit has a series of contractual cash flows, and it is trivial to model a credit curve for any single issuer. But could we aggregate credit curves and decompose their moves into similar level and slope factors? Also, are such level and slope factors uncorrelated enough to provide diversification?

Term structure analysis in aggregated credit is inherently tricky due to the heterogeneity of issuers with a wide range of credit quality in the market, unlike homogeneous Treasury bonds. Furthermore, corporate credit curves are often incomplete. A single issuer may issue only a few bonds over a small number of maturity dates. Erroneously matching credit to risk-free bonds of dissimilar duration, or not factoring in changes in risk-free yields, are also common analytical pitfalls highlighted by Hallerbach and Houweling (2013). With these issues in mind, we devise an approach to analysing systematic factors driving the credit term structure.

Credit Curves: Theory and Practice

Similar to how the yield curve implies an evolution of the spot rate over time, the credit curve also implies an evolution of the spot credit spread across time. Theoretical research by Merton (1974) and by Fons (1994) using a risk-neutral pricing model based on historical default data, suggest that credit spreads could be expected to widen or narrow over time, and so credit slopes may be upward-sloping, downward-sloping or even hump-shaped.

In contrast to theory, empirical studies by Helwege and Turner (1999) as well as Huang and Zhang (2008) found that the slopes of US credit spread curves are mostly upward sloping. What gives rise to a generally positive slope in the credit term structure? Collin-Dufresne, Goldstein, and Martin (2001) found that changes in US credit spreads are not too influenced by default risk, while uncovering a strong systematic component in the unexplained return residuals. Given such a finding, it could be that credit spreads across the term structure only partially reflect idiosyncratic default risks, while systematic factors dominate to produce a commonly observed upward slope. Such factors may arise due to forward expectations of policy, term premiums, liquidity premiums, or supply and demand shocks. For instance, a systematic shock is evident during the early phase of the pandemic, driving large co-movements in credit across geographies and sectors. We shall now seek to establish the presence of systematic factors that drive the level and slope of credit curves.

Modelling a credit curve with Asian USD bonds

We focus our analysis on the set of noncallable, straight USD bonds from 5 Asian economies (China, Hong Kong, Korea, India, Indonesia) which are quoted from Jan 2017 till Mar 2022. Focussing on Asian credit is for reason of expediency, as we can draw on our curated DBS Asian USD credit spread database. This gives us full confidence that all our credit spreads data had been derived consistently across countries and across time. Also, considering that the existing literature on credit is overwhelmingly US-centric, our research will be a contribution that broadens credit analysis to different economies, beyond typical cross-sector and cross-rating analysis on credit for a single country.

Methodology and caveats

We begin by outlining our methodology for credit curves, followed by highlighting peculiarities in credit compared to riskless bonds. All rates are expressed under continuous compounding for simplicity, but with no loss of generality.

Consider a coupon-paying straight bond with cashflows CF_i at time t_i from today, where i ∈{1,2,..T} and T represents maturity. The sum of its discounted cashflows gives a net present value (NPV) equivalent to:



The cashflows are discounted by a rate that is the sum of the risk-free spot rate r_i and a credit spread (or Z-spread) s_i for time t_i of each cashflow. Our risk-free rates are interpolated from publicly available zero curves, and the credit spread is then obtained by setting s_i to equalize the sum of discounted cash flows with the bond price. The credit spread is often interpreted as an additional rate of return from investing in a risky bond compared to a riskless bond.

Equivalently, a bond’s cashflows can be viewed as being discounted twice in our formula, first by the discount factor for the risk-free rate Z_i (r_i), and then by a discount factor for the credit spread Z_i (s_i). This separation makes clear the existence of two distinct discount curves, (i) the risk-free discount curve, and (ii) the credit discount curve. They correspond, respectively, to a riskless spot rate curve r_i and a credit spread curve s_i across the time interval [t₁,t_T]. Our analysis focuses on the latter.

If an issuer has only a single bond, it is natural to assume a constant Z-spread s_i across all cashflows. Given a set of bonds from an issuer that differ only in maturity and cashflows and have identical risk characteristics, it is then possible to derive a Z-spread or credit spread curve across different maturity dates based on the set of bond prices.

To derive this spread curve, we implement a piecewise-constant spot Z-spread model. Given a set of N bonds, they are sorted in order of maturity T_i for i ∈ {1...N}, such that T_i < T_j for i < j. Z-spread s_i is then assumed to be constant across the interval (T_i-1,T_i] for all i. Bootstrapping from the Z-spread for the first bond, the other Z-spreads can be recursively found. Despite the non-continuity of these credit curves, it detracts little from our analysis since we shall utilize available bonds of specified maturities, not interpolated spreads.

Last but not least, we highlight an important edge case in credit where default risks will completely determine the Z-spread curve, rather than the systematic factors that we are keen to extract. It occurs when an issuer is viewed to be critically distressed. Not only will credit spreads surge to atypically high levels, the credit spread curve will also turn sharply inverted, with spreads of short maturities being far higher compared to those of long maturities. The peculiar phenomenon of distress-induced curve inversion arises due to two unique features of credit.

First, credit usually has accelerated repayment or cross-default clauses, so all bonds from an issuer are presumed to enter default at the same time when any bond defaults, regardless of their maturities.

Second, in a default, there are no more cashflows and instead, the markets prices in a recovery value that is typically a proportion of par for all bonds regardless of their maturities. Hence, distressed bond prices will be similar across maturities, resulting in a highly inverted Z-spread curve. Such curve inversion has no economic implication for prospective returns, and does not reflect systematic factors.

Hence, to correctly extract systematic factors in credit curves, we must control and exclude distortions arising from such distressed bonds. But what criteria should we use to judge whether distress is critical or not for exclusion? We found no methods in the literature to determine such critical levels of distress. We thus venture to derive our own decision rule for exclusion, using a simple model that relates Z-spreads to default probabilities.

Exploring the distressed pricing boundary

In our model, we first define the marginal default rate of a risky bond, pd_t, as the probability of default in year t. For simplicity, we also assume that pd_t = pd, a constant over time. The cumulative default rate of a bond with T years of maturity is thus:



Under regular credit conditions, given an approximately similar marginal default rate over time, the cumulative default rate will increase as maturity T increases. Default risk of a longer-tenor credit will always be higher than that of a shorter-tenor credit.

Under the condition of critical distress however, prices will be such that the cumulative probability of default is almost equal across all maturities. We can model this by constraining cd_T as a constant across all T_i where i ∈ {1...N}. This allows us to tabulate how the breakeven Z-spreads for zero-coupon bonds change as our fixed cd_T increases from 0% to 40% across 1Y, 3Y, and 5Y maturities.

Our breakeven calculations assumed a fixed recovery value that is consistent with market prices of defaulted Chinese bonds from 2019-2021. Beyond default risk, there is no inclusion of other market factors that may explain credit spreads. In practice, our model will thus underestimate actual market spreads, which should be higher than breakeven spreads given risk aversion. Despite such shortcomings, we can still draw useful insights on the behaviour of spreads under critical distress.



First, note that the model’s credit spread curves are always inverted if the cumulative default rate (cd_T) is fixed across maturities. The degree of inversion also varies significantly across maturities and cumulative default rates. We make two observations:

1/ Modelled curve inversion is particularly sharp at the front end, even at low default rates. 2/ Inversion is also more pronounced across the 3Y and 5Y maturities when the cumulative default rate rises above 20%.

Combining both observations, our decision rule is thus to exclude all issuers with any bond that has a cumulative default rate of more than 20%, and bonds with 1Y or less to maturity. Our rule will automatically exclude bonds generating large and unmeaningful inversion when pricing approaches critical distress.

Factor analysis in Asian USD credit

For the five Asian USD credit markets in our analysis, the number of issuers with different maturities and with credit curves are few compared to the US. Nevertheless, numbers have increased over the last five years from 86 to 148 in Jan 2022. With a greater number of issuer curves and increased data availability today, it strikes as an opportune time to embark on a data-driven analysis in Asian credit.

For our first cut, we separate bonds into 9 bins (or portfolios) based on their remaining maturity, ranging from 2Y to 10Y. (A bin of tY contains bonds with remaining maturity of [t − 0.5, t + 0.5] years.) The available pool of bonds is updated at the start of every month, and then sorted based on their remaining maturity on the first day of the month. We list the number of issuers having bonds in each maturity bin on a semi-annual basis from 2017.



Weekly average Z-spreads are then calculated for the bonds in each of 9 maturity bins from Jan 2017 to Mar 2022. A naïve principal component (PC) analysis shows that the first PC has positive weights for all maturities, indicative of a systematic level factor. However, the second PC (and others) shows no relationship to maturities, and thus there is no prominent slope factor.

One problem is that the aggregate slope may have been distorted by averaging spreads within each maturity bin without explicitly controlling for differences in credit quality. Helwege and Turner (1999) reasoned that since higher quality firms are more likely to issue at longer tenors, spreads at longer maturities will become downwardly biased.

We thus propose a strategy to control for credit quality by matching short-maturity bonds to long-maturity bonds of the same issuer. It entails a portfolio position that is short short-maturity bonds and long long-maturity bonds of similar issuers, with a view towards the spread differential between the long and short positions. Such spread differentials give rise to an unbiased credit “slope”, as credit risks on both longs and shorts are matched.

Specifically, we focus on credit differentials relative to 2Y credit along the term structure. For N_T number of issuers with a bond in maturity bin T having spread s^Ti and also a 2y bond with spread s²_i, where i ∈ {1...N_T}, the average 2yTy spread differential is calculated as . We calculate the spread differentials on a weekly basis over time, with refreshes of the available bond pool and maturity binning done at the start of every month.

Given the high number of bonds with short maturities and low number of bonds with long maturities, binning bonds using annual maturities will result in unevenly sized bins. This is non-ideal. Each bin should represent a similar proportion of market variance for our PC analysis. Hence, we set four separate bins for 3Y, 4Y and a range of maturities instead, as shown in the table below. Bonds with 10Y or more of remaining maturity are excluded due to limited data availability.



Plotting the histograms of 2Y credit spreads (N = 60) against our matched 2Y3Y credit spread differentials (N = 29) for the first week of March 2022, it is easy to see that the variance of the spread differentials is far smaller than that of the credit spreads alone. Using spread differentials can thus substantially mitigate the issue of credit heterogeneity.



By pooling issuers with bonds of a particular pair of long-short maturities, we need not worry about the issuers that lack the specified bonds in their credit curve. Furthermore, our analysis on credit spreads, instead of bond yields, eliminates any impact from the risk-free curve. It also ensures stationarity in the data and avoids spurious PC analysis, a problem raised by Onatski and Wang (2021).

Distilling the slope factor in Asian credit

We conduct a PC analysis on the average spread differentials across our four maturity bins, using data from Jan 2017 to Mar 2022. Our first PC shows factor loadings that increase across the maturity bins, before declining at the last bin.






The slightly smaller loading at the 7Y-9Y bin may reflect smaller co-movement for bonds at such maturities, due to lesser liquidity and smaller transaction volumes. Nevertheless, it is still higher compared to loadings at the 3Y and 4Y maturity bins. With the PC loadings mostly increasing with maturity, the first PC can be interpreted as the common slope factor driving Asian credit curves.

Interestingly, the first PC can explain 69% of the variance in our four spread differentials. Thus, the systematic slope factor potentially has a large influence on returns for portfolios that are short and long credit of different duration.

Limited correlation between level and slope

To extract the level factor that impacts credit spreads across all maturities, we use a subset of bonds consistent with those used in the calculation of spread differentials. These bonds are binned in a similar way as before, but with an additional bin for bonds of 2Y maturity. The average credit spread is simply  for the T-year maturity bin. The first PC of the binned credit spreads show fairly even weights across all maturities, indicative of a level factor.



We use the normalized weights of the first principal component and the average spreads for each maturity bin to generate a level factor across time. Similarly, the slope factor can be generated from the normalized weights of our earlier PC analysis and average spread differentials across time.

Weekly differences in the level and slope factors can then represent changes in the level and changes in the slope of aggregate credit curves. We plot the time series of these two factors in the following chart.



We found a small correlation of 0.14 between differences in the level and the slope factors. As such, the two systematic factors of Asian credit show limited correlation. The implication is that strategies may utilize the slopes of Asian credit curves as an avenue for credit return diversification, given the small correlations to shifts in the levels of credit spreads.

Another way to interpret the slope of credit curves is the premium required for a forward credit position starting in the future. From this perspective, a higher slope suggests that markets are more wary of credit risks in the future than in the present. The steepening credit slope today may indicate an increased pricing of recessionary risks, with higher risk premiums for forward credit spreads.

We found that both the level and slope factors can drive significant variation across Asian credit spreads. We shall explore how a slope-based strategy can be implemented, and whether our factor analysis can be generalized to other markets, in future research.


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