A fresh approach to loss distribution

In reality, a company defaults because it runs out of cash. Unfortunately, modelling the change in a company’s cash balance is much more complicated than it may seem. This is because almost every financial item — inventory, fixed asset, investment, receivable, debt, payable, equity capital etc — interacts with the level of cash. In essence, modelling cash requires modelling a company’s entire balance sheet in its full dimensionality. Such a direct approach has not been explored to forecast default. However, my research has recently made breakthroughs along this direction.

We applied the method to eight actual companies provided by Creditflux and using data from Credit Rubric. All were downgraded to triple C during 2020, and are still held by European CLOs. We use eight years of historical company financials as model inputs and simulated the future paths of operating actions, such as capacity utilisation, sales ratio and sales margin as random variables based on calibrated historical values. For the future values of actions associated with company planning (corporate real options), such as the level of new debt, level of capital expenditure, and pay-down rate of payables, a child-simulation performs a five-year forward-scenario analysis (based on the realised operating values) at each time step. This selects the values that reduce most of the risk of default and achieve most of a given growth target.

Using 300 simulated paths, we derived the annual default probabilities and recovery rates (separately for senior secured debt and unsecured debt) over a 12-year forward horizon. The results imply fairly high 10-year cumulative default rates, ranging 75%-100%, among the eight companies. In comparison, the historical 10-year default rate for all Caa/C rated corporate bonds is 74%¹. The principal recovery rates of senior secured debt are mostly above 60% and as high as 100% (ignoring recovery delay), while unsecured debt gets zero recovery for all but one company². The expected principal loss over time approaches 37% for the majority of secured debt but 100% for most unsecured debt.

Figure 2 shows the default timing of the eight companies from 11 out of 300 simulated paths. To derive aggregate loss, we assume a portfolio of secured debt equally weighted in the eight companies. For the purpose of illustration, we assume the portfolio has a 10-year tenor with constant principal balance (ie, for a company not in default, always replace matured debt with new debt). Figure 3 shows the distribution function on aggregate principal loss over one, five and 10-year periods. The loss distribution for year one peaks at a relatively high 25% aggregate loss, with a small but positive likelihood of no loss. The most likely level of aggregate loss increases only slightly above 25% over the years, although the peak likelihood itself does increase significantly from year one to year five. At all times, the distribution falls quickly to zero for any aggregate loss greater than 30%.

To compare our results with a rating-based method, we assume for all eight companies an annual default probability curve of 21% in year one, 15% in year two and three, 13% in year four, 11% in year five, and 10% in year six and after, as suggested by the historical default rates of all Caa/C companies¹. We assume exogenously a 70% recovery rate on secured debt for six of the eight companies and 100% for two of the eight companies.

Directly modelling the cause of default through balance sheet dynamics can derive default risk, recovery rate and default correlation within a single consistent algorithm. The result can potentially lead to loss distribution functions more closely connected to company fundamentals and hence more accurate pricings of CLO tranches.