A Systematic Distressed Investing StrategyTom YuzBlockedUnblockFollowFollowingMay 9IntroductionFinancial distress and bankruptcy exert significant pressure on corporate management, operations, and suppliers.
The cost of bankruptcy to the liquidating value of a business is estimated to be 7.
5% on average, with the largest bankruptcies extracting fees of over $1 billion dollars.
Understandably, the academic community has nurtured a rich literature on prediction of Chapter 11 and Chapter 7 filings.
Prior research is split between using market-based (option pricing, credit default swaps) versus accounting-based (earnings yield, debt to equity) methodologies.
Hillegeist et al.
(2004) recommends researchers use the Black-Scholes-Merton model over traditional measures such as Altman’s Z-Score or the Ohlson O-score.
Coelho and Taffler (2008), on the other hand, find little difference in the predictive accuracy of either of the two approaches.
We create a dynamic long/short, beta-neutral distressed investing algorithm capable of outperforming the market.
If researchers only use financial ratios in their probability of default (PD) models, they implicitly assume that all relevant information regarding a firm’s future trajectory is reflected in the annual accounts.
With the recent proliferation of big-data and the increased sophistication of market pricing algorithms, it is unlikely that the first and final stop for evaluating financial distress should be the 10-K.
Fortunately, recent work has championed a combination of both market-based and accounting approaches.
Chava and Jarrow (2004) find that accounting variables such as net income to total assets and market-based variables such as the idiosyncratic standard deviation of firm stock market returns are both statistically significant predictors of bankruptcy filing.
More recently, Tinoco and Wilson (2013) employ cutting-edge machine learning tools to raise the prediction accuracy generated by ordinary least squares regression.
Taking a holistic view of prior progress offers a meaningful mechanism for further building on current bankruptcy models.
Plan of ActionWe explore three promising avenues for crafting practical distress-prediction models.
Firstly, we incorporate macroeconomic predictors in conjunction with tried-and-true market and accounting variables.
Secondly, we evaluate whether our bankruptcy prediction models can be used to create systematic investment algorithms.
Thirdly, we explore whether various statistical “tricks” such as Z-scoring predictors and winsorizing values improve upon model outcomes.
Our results are impactful to a variety of stakeholders in the bankruptcy process, including:1.
Restructuring advisors and lawyers: Our model is unique in its focus on publicly-listed companies.
As a result, restructuring advisors and lawyers can use the model’s suggestions to be proactive in sourcing potential clients or attempting to preempt bankruptcy by offering liability-management assistance.
The model can also be used to assess the feasibility of a proposed plan by predicting a firm’s likelihood of refiling post restructuring.
Distressed and quant investors: Our model offers a mechanism for screening potential distress candidates and surveying the macroeconomic landscape.
With respect to quant firms, we also construct a successful systematic “distressed investing” algorithm aimed at generating beta-neutral returns.
Investment banks and insurance companies: Our model can serve as a “sanity-check” on internal prediction systems, ensuring that bank loans and insurance credit default swaps are priced appropriately.
Part 1: A Comprehensive Distressed Prediction ModelWe replicate the market, accounting, and macroeconomic-based models expressed in Tinoco and Wilson.
The data covers over 3,000 publicly quoted companies over the 1980 to 2011 period, of which 379 file for bankruptcy protection.
It is important to highlight our definition of financial distress.
As in traditional descriptions, a firm is in default if its shares are suspended for over three years, in voluntary liquidation, delisted upon bankruptcy filing, or under receivership.
More importantly, we also follow Pinado et al.
(2008) to categorize a firm as financially distressed if EBITDA is lower than interest expenses and market value is declining for two consecutive years.
This distinction is important considering the date of a legal motion does not always correspond to the date markets begin to expect financial insolvency.
In fact, firms stop reporting financial statements 1.
17 years on average before legally filing for bankruptcy.
Five percent of our sample (1,254 firms) are classified as distressed.
All subsequent data analysis is completed in Python.
The 5-variable Altman Z-model (1968) and the 7-variable Ohlson logit model (1980) demonstrate that only a few variables are needed to reach a high level of accuracy in financial distress prediction.
Our first step is using recursive feature elimination (RFE) to select only the most important predictors from over 130 total variables.
RFE (1) trains a logistic regression on a large set of initial variables, (2) obtains the point estimates of each variable, (3) prunes variables with the least significant coefficients, and (4) repeats the process until only the most important features remain.
The sample is divided into financially distressed and healthy firms.
The outcome is a binary dependent variable, and we use the panel logit framework to allow for time varying covariates.
Firms classified as financially distressed are given a value of 1 and healthy firms are given a value of 0.
RFE estimates the model with the greatest discriminatory accuracy taking the form of:Regression 1Where F(x) represents the probability of a firm being distressed Pr(Y = 1|x), and our predictors represent the accounting, macro, and market-based independent variables respectively.
Our recursive estimator identifies four accounting ratios, two macroeconomic variables, and four market variables which improve our model’s prediction accuracy over traditional calibrations.
Exhibit 1 offers a correlation matrix of the chosen predictors; low collinearity implies a high level of complementarity between our variables, with each explaining a unique amount of variance in the response.
We now consider the intuition behind the model’s selected predictors.
1 Accounting VariablesOur final four accounting ratios include Funds from Operations to Total Liabilities, Total Liabilities to Total Assets, Interest Coverage, and the No Credit Interval.
All four variables have substantial recognition in prior research papers.
Funds from Operations to Total Liabilities compares the cash flow of the firm to all short and long-term liabilities acquired by the company.
The ratio is praised in Marais (1979) for its discriminatory ability to contrast internal cash generation over financial obligations.
Total Liabilities to Total Assets estimates the proportion of a company’s assets financed by debt.
If a firm experiences a downward shock to total asset value, unchanging interest payments from fixed liabilities typically force technical defaults.
Interest coverage is one of the most common variables used to predict bankruptcy, measuring a firm’s ability to meet immediate interest obligations.
A notable result is the significance of the No Credit Interval variable.
Formulaically, the No Credit Interval is calculated as (Quick Assets — Current Liabilities) / ((Sales — EBITDA) / 365).
From a practical perspective, the No Credit Interval estimates how long a company can finance operating expenses without drawing down on liquid resources.
While the other three accounting variables focus on asset efficiency and credit coverage, the No Credit Interval highlights working capital stability.
Together, the accounting ratios zero in on a firm’s idiosyncratic business operations and its unique mixture of debt, equity, and assets.
2 Market VariablesShare Price, Abnormal Returns, Market Cap relative to the Market Index (Size), and Market Cap to Total Debt all prove significant in predicting default.
The number of market-based variables clearly suggests incorporating real-time data as a supplement to accounting variables offers meaningful discriminatory power in the model.
Variables such as Abnormal Returns and Size highlight the firm’s performance relative to peers.
Price offers an indication of supply and demand for shares from investors, while Market Cap to Total Debt relates market dynamics for equity to existing claims from creditors.
While the accounting variables focused on the relationship between a firm’s asset and cash coverage of financial obligations, the market-based variables stress investor’s evaluations of a firm’s future growth and cash generation opportunities.
3 Macroeconomic VariablesRepresenting a critical break from prior literature, we demonstrate the utility of incorporating macroeconomic variables into prediction of financial distress.
Among a list of eleven macroeconomic indicators, two are included in the final model: the Retail Price Index (RPI) and the 3-month Treasury rate.
The RPI measures the change in prices of goods and services for households.
As detailed by economists since Adam Smith, rising nominal prices are associated with rising revenues for firms given lagging wage growth, reducing the risk of bankruptcy.
The 3-month Treasury bill rate complement’s the RPI’s impact on lending rates.
For a constant level of inflation, higher rates imply rising real growth in an economy.
Improvements in the trend of real GDP growth are associated with greater firm productivity and ROI, leading to a reduced risk of default.
Overall, the use of macroeconomic variables fills in the gap left by accounting and market-based metrics by considering systematic risk to a firm’s finances.
The distressed community’s deemphasis of macro variables in favor of a focus on idiosyncratic risks has come at the expense of a lower accuracy in understanding probability of default.
4 Analysis of ResultsRFE only identifies which combination of variables offers the most predictive power.
We now evaluate each variable’s individual contribution to predicting changes in the response.
In Exhibit 2, we display three models for estimating probability of default: accounting variables only, accounting-and-macro, and a fully comprehensive model.
We estimate default likelihood both one and two years prior to corporate financial distress to offer greater prediction flexibility.
We highlight three key findings from the discriminatory analysis.
Firstly, macroeconomic variables are statistically significant in both one- and two-year time periods even when controlling for accounting and market-based covariates in Model 3.
Secondly, our most comprehensive model (Model 3) handily outperforms the industry-standard Altman Z-score based on Tinoco and Wilson’s estimates (Exhibit 3).
We demonstrate the robustness of the model’s results through Area Under Curve, Gini rank coefficient, and Kolmogor-Smirnov performance measures.
Thirdly, the simple logit model performs in line with more complicated structures such as a neural network analysis.
A neural network is a typical “black-box” algorithm which uses a collection of connected nodes interacting the model’s predictors to obtain a single output.
Logit models, meanwhile, offer simple significance estimates for individual predictors and are thus more practical for industry experts.
In summary, we have utilized recursive feature elimination to obtain a mixture of accounting, market, and macroeconomic variables useful for predicting financial distress.
Our model outperforms current industry methodologies and offers a simple tool that can be easily used by restructuring and distressed investing practitioners.
Part 2: Extending the Model to Distressed InvestingIn Part 1, we obtained a comprehensive model for predicting financial distress for publicly listed companies.
While we “trained” our model on a response corresponding to probability of financial default, it is natural to question whether our identified predictors can be used in a systematic “distressed investing” algorithm.
On one hand, traditional (fundamental) credit-managers belittle the idea of employing algorithms to invest in firms expected to undergo bankruptcy.
On the other, quantitative firms such as AQR and Citadel are investing heavily in building systems that short shares of financially distressed firms and go long the top quartile of healthy companies.
We thus offer our perspective on the lively debate captivating the distressed community.
Using the Quantopian Python module, we reconstruct our above-found predictors.
We set the Wilshire 5000 index as our investment universe and define our response as a firm’s forward monthly returns.
We assign a value of 1 to firm’s with positive forward returns and a value of 0 to firm’s with negative forward returns.
As above, we fit a logit regression taking the form of:Regression 2Where R(X) represents the binary probability of a firm’s returns being positive Pr(Y = 1|x), and our predictors represent accounting, macro, and market-based predictors respectively.
We discuss three key findings from our foray into systematic investing.
Firstly, a simple logit model using our predictors from Part 1 registers a precision and recall of 49% (Exhibit 4).
In other words, our logit model is worse than flipping a coin and betting that a stock will rise if we land on heads.
Secondly, even if we use machine learning to capture high-order interactions in the data, our gradient boosting algorithm only registers a 51% precision and recall in predicting returns — just slightly above random guessing.
Thirdly, our machine learning algorithm does not identify any macro factors as statistically significant predictors of a firm’s monthly returns.
However, as we extend our prediction horizon to quarterly and yearly returns, both the 3-month Treasury rate and the retail price index become important features of our model.
Overall, the slim success in predicting market returns is humbling, and emphasizes the importance of looking beyond easily available quant data.
As a final step in our analysis, we evaluate whether we can turn gradient boosting’s slight predictive edge into consistent profits.
We first create a baseline long/short portfolio of 300 stocks, split equally between long positions in firms with the lowest predicted probability of default and short positions in firms with the highest predicted probability of default.
A snippet of our back-tested results is included in Exhibit 5, with techniques such as winsorizing and z-scoring insignificantly changing our findings.
In 2008, our algorithm outperforms the market by nearly 50%, with a 5% positive y/y return.
However, every subsequent year after the financial crisis, the algorithm significantly underperforms the S&P 500, with an average return of 2.
The reason behind the algorithm’s middling performance is the frequency of distress within the sample.
While 2008 saw a 31% surge in bankruptcies, the average default rate is typically in the realm of 5% for publicly listed companies.
A beta-neutral long/short equity algorithm requires a proportionate number of healthy and unhealthy companies, or risks overexposure to particular sectors or firms.
We address the baseline algorithms shortcomings in two key ways.
Firstly, we evaluate the benefit of varying how many long and short positions the algorithm can initiate.
Secondly, we dynamically adjust our concentration of short positions based on market volatility.
For instance, if the VIX index is two standard deviations above its long-term average, our portfolio moves to 30% long and 70% short across all positions.
We thus capitalize on periods of rising systemic distress versus remaining an equal proportion long/short.
As shown in Exhibit 6, a dynamic distressed investing algorithm with 140 long and 40 short positions registers a sharp double the S&P500.
Our algorithm outperforms the S&P500 over the entire back tested period while limiting our 2008 drawdown to -5%.
By addressing the weaknesses inherent in simple implementations of our probability of default model, we successfully create an algorithm capable of generating alpha in a highly competitive market environment.
ConclusionWe advance the construction of bankruptcy prediction models for industry practitioners through three meaningful mechanisms.
Firstly, we have reemphasized the benefit of combining accounting, market-based, and macroeconomic variables in bankruptcy-prediction model.
The Tinoco and Wilson model registers an AUC score of 86% and outperforms the industry-standard Altman Z-score.
Secondly, we have demonstrated the difficulties associated with using our identified variables to accurately predict market returns even with cutting-edge statistical manipulations.
Finally, we have provided a capstone on our investment research by highlighting the efficacy of a dynamic long/short, beta-neutral distressed investing algorithm.
Our model can provide practical guidance to restructuring advisors, lawyers, insurance companies, and distressed investors interested in evaluating the probability of default of current and potential clients or investments respectively.
From bankers to quants, the restructuring arena continues to provide opportunities for innovation in the world of big-data.
Appendix: Ang, James S.
, et al.
“The Administrative Costs of Corporate Bankruptcy: A Note.
” The Journal of Finance, vol.
1, 1982, pp.
offer a useful summary of research progress.
 Black, Fischer, and Myron Scholes.
“From Theory to a New Financial Product.
” The Journal of Finance, vol.
2, 1974, p.
provide the first forays into market-based pricing models.
 Altman, Edward I.
“The Prediction of Corporate Bankruptcy: A Discriminant Analysis.
” The Journal of Finance, vol.
1, 1968, p.
is the seminal work.
 Brown, Stephen, et al.
“Management Forecasts, Litigation Risk, and Regulation FD.
” SSRN Electronic Journal, 2004.
 Coelho, Luis M.
, and Richard J.
“Anomalous Market Reaction to Bankruptcy Filings.
” SSRN Electronic Journal, 2008.
 Hernandez Tinoco, Mario, and Nick Wilson.
“Financial distress and bankruptcy prediction among listed companies using accounting, market and macroeconomic variables.
” International Review of Financial Analysis, 2013, pp.
 Tinoco and Wilson do not specify their variable selection process, though we obtain quantitively the same results.
 Note, TFOTL and Interest Coverage register a correlation of 0.
726, the highest among all the variables.
The reason is evident, as FFO/TL is extremely similar to EBITDA/Interest Expense.
However, FFO captures capex and working capital changes not covered by EBITDA, and TL covers financial obligations not directly captured by interest expenses.
 Zmijewski, Mark E.
“Methodological Issues Related to the Estimation of Financial Distress Prediction Models.
” Journal of Accounting Research, vol.
22, 1984, p.
 Important note: Rising inflation can spur rate hikes from the Federal Reserve.
Higher rates typically constrain credit and increase risk of default.
As a result, it is important to stress that higher inflation improves firm outcomes when controlling for constant rates, which our model does by virtue of regressing both RPI and Treasury rates at once.
 If interested, please email tomyuz@wharton.
edu for Python code (9 pages long, and hence not in exhibits).
 See Howard Marks’ investor letters.
 The precision is the ratio tp / (tp + fp) where tp is the number of true positives and fp the number of false positives.
The precision is intuitively the ability of the classifier to not label a sample as positive if it is negative.
The recall is the ratio tp / (tp + fn) where tp is the number of true positives and fn the number of false negatives.
The recall is intuitively the ability of the classifier to find all the positive samples.
 We are diversified on the long-book and concentrated in our short-book, taking advantage of our higher prediction accuracy for negative returns.