Home » Research Blog » Tracking systematic default risk

Tracking systematic default risk

Systematic default risk is the probability of a critical share of the corporate sector defaulting simultaneously. It can be analyzed through a corporate default model that accounts for both firm-level and communal macro shocks. Point-in-time estimation of such a risk metric requires accounting data and market returns. Systematic default risk arises from the capital structure’s vulnerability and firms’ recent performance, as reflected in equity prices. The metric is both an indicator and predictor of macroeconomic conditions, particularly financial distress. Also, systematic default risk has helped forecast medium-term equity and lower-grade bond returns. This predictive power seems to arise mostly from the price of risk. When systematic default risk is high, investors require greater compensation for taking on exposure to corporate finances.

Bao, Jack and Kewei Hou and Shaojun Zhang, “Systematic Default and Return Predictability in the Stock and Bond Markets” Fisher College of Business Working Paper No. 2023-03-013

Below are quotes from the paper. Emphasis, cursive text, and text in brackets have been added for clarity.

This post ties in with this site’s summary of macro trends, particularly the section on credit returns.

A model for tracking systematic default

“We construct a structural model-based measure of systematic default, which measures the joint probability of many firms defaulting at the same time…Our main contribution is to estimate a new economically motivated variable [of systematic macro default] and to show that this variable predicts both equity and corporate bond returns in- and out-of-sample.”

“We generalize the CAPM-style Merton model [assuming that] firms have a value process where the shocks to firm value have both a common term and an idiosyncratic term. The common term leads to correlated defaults, which can have significant effects on joint default probabilities as compared to assuming independent firm value processes…[This] allows us to calculate the probability of at least x% of heterogeneous firms defaulting at the same time, over a long sample period.”

“We develop an important extension to [the original model] that allows us to use firm-level data and incorporate heterogeneity across firms. To calculate firm-level parameters, we…calculate distance-to-default at the individual firm level.
When measuring systematic default, it is important to recognize that the average default probability across firms does not measure the same thing as the probability of many firms defaulting at the same time. As illustrated vividly by subprime mortgages during the Global Financial Crisis, the probability of many correlated defaults can be higher in reality than under the assumption of uncorrelated defaults.”

“Focusing on…nonfinancial firms excluding microcaps, our main measure of systematic default is the probability that at least 2% of these firms will default in the next year.”

Data and calculation

“We require both market returns and firm-level data. We calculate market returns as the weighted average of the CRSP value-weighted index (equities) and the Dow Jones Corporate Bond Return Index from Global Financial Data (bonds)… For firm-level data, we use equity returns from CRSP and balance sheet information from Compustat. All Compustat data are lagged by three months to allow for reporting delays.”

“The main inputs into our estimates of systematic default are firm-level balance sheet information and equity returns. Thus…systematic default is related to both changes in capital structure and the recent performance of firms, with the latter reflected in equity prices…We start with a dataset that contains the last 120 monthly log equity returns for the firm along with the start-of-month market value of equity [and] the face value of debt…One of the main features of our modeling framework is that market declines only significantly drive up systematic default if they bring already vulnerable firms, rather than safe firms, closer to their default boundaries.”

“We model the correlations as exposures to market-wide common shocks while allowing for firm heterogeneity. We devise a numerical procedure that avoids enumerating all possible combinations of defaults and survivals. This makes an estimation of the joint default probability over a large set of firms feasible.”

How systematic default relates to the macroeconomic environment

“Results suggest that systematic default is an important measure of macroeconomic conditions and, in particular, the aggregate vulnerability of firms to financial distress…Our systematic default measure is high during recessions, exhibits a positive correlation with contemporaneous default spreads and future realized default rates, and is associated with poorer economic conditions and greater macroeconomic uncertainty.”

“We plot the baseline series in Figure 1 along with NBER recession periods. A striking feature of our systematic default series is that it usually spikes during recessions. During the Global Financial Crisis, the estimated systematic default increased to over 20%. More recently, it again surpassed 20% in March 2020, at the height of the COVID-driven crisis. We also see large spikes in the mid-1970s, and similar, though smaller, spikes during recessions in the early 1980s and early 1990s.”

“Interestingly, systematic default spiked in 2002, rather than during the Tech crash in 2000…Firms that were particularly vulnerable to default (defined as the 10% of firms in the sample that are most likely to default based on our structural model estimates) did not have significant declines in equity values in 2000…Thus, while market declines tend to cause increases in systematic default, it is also important to take into account the overall vulnerability of firms prior to market declines. A key feature of our approach is that it distinguishes between market declines that bring many risky firms near their default boundaries and declines that do not.”

“We find a statistically significant correlation of 0.26 between systematic default and the failure rate… comprising of bankruptcies, distressed de-listings, and D ratings…over the next year. This correlation is driven by smaller firms…As an alternative to failure rates, we also consider realized default rates over the next year from Moody’s Analytics. The correlation between systematic default and the issuer-weighted default rate over the next year is a highly significant 0.47.”

“We also consider how our measure is related to the default spread, a traditional measure of aggregate default expectations. The default spread is defined as the difference between the yields on BAA bonds and AAA bonds. We find a positive and significant contemporaneous relation between systematic default and the default spread, with a 0.40 (0.41) correlation coefficient.”

Output gap and systematic default are negatively correlated while the unemployment rate and systematic default are positively correlated, regardless of whether we look at contemporaneous or forward-looking correlations. This is consistent with periods of high systematic default being relatively poor economic periods…[Also] sentiment tends to be low when systematic default is high.”

“We also find strong correlations between systematic default and measures of aggregate volatility and uncertainty: Systematic default is positively and significantly correlated with contemporaneous values of all seven volatility and uncertainty measures.”

Predicting equity and bond returns

“[The systematic default measure] predicts future aggregate returns for both equities and corporate bonds…The predictability results are robust to out-of-sample tests. In addition, stocks with higher systematic default betas earn lower average returns, consistent with these stocks being a hedge against increases in systematic default risk.”

Systematic default significantly predicts equity index excess returns, particularly at horizons of one month to one year. For example, a one standard deviation increase in the systematic default measure predicts an increase in the one-year excess returns of 10.79% for the CRSP equal-weighted index…
Default risk is particularly relevant for smaller firms…[However] systematic default does [also] predict future defaults of S&P 500 firms, especially those with speculative-grade ratings. The return predictability for the S&P 500 index, though weaker than for the CRSP equal-weighted index, is consistent with default risk also being important for some S&P 500 firms.”

For bonds, we find significant predictability for the BAA index at horizons of one month to three years, but much weaker predictability for the AAA index (only significant at the one-month horizon)… Because BAA bonds are subject to higher default risk than AAA or Treasury bonds, it is natural that our measure of systematic default should predict a greater increase in the required rate of return for them. Moreover, flight-to-safety may further increase the difference in expected returns between risky and safe bonds.”

“We test for return predictability for the Barclays speculative-grade bond index, finding stronger results than for the BAA index, consistent with systematic default being even more important for lower credit quality bonds.”

“To evaluate the out-of-sample performance of our systematic default measure, we use only the data available up to time t and estimate a univariate predictive regression of index excess returns. Then we construct an out-of-sample forecast of the index return for the next n-month holding period. To allow for enough observations in forming the initial estimate, we use the first half of the sample as the minimum burn-in period… We find positive and statistically significant OOS R2’s for equity indices at most horizons… For bond indices, we find positive and significant OOS R2’s for the BAA index up to the three-year horizon.”

“[The] evidence… suggests that the bulk of the return predictability arises from the price of risk. In bad times, as measured by high systematic default, investors require greater compensation for taking on risk in equilibrium…Our empirical results on the sources of return predictability suggest that risk premia increase exactly when there is an elevated threat of correlated defaults.”

“Even when predicting sector returns, it is the aggregate systematic default probability, not sector-level joint default probabilities, that drives the results.”


Related articles