28 July 2013

Default Risk Modeling: Little Experiment (Part 1: Data)

As you might be aware of, assessing the borrowers’ default probabilities and the expected credit portfolio default rates belongs to the most crucial tasks for each creditor – no matter if that creditor is a bank or a private individual via increasingly popular debt crowdfunding platforms. After all, it is closely linked to correct credit pricing – and pricing of countless credit derivatives etc. Remember the basic risk-reward relationship? Higher risks ought to mean higher expected returns (and other way round: lower risks <-> lower returns).

Given sufficient data about borrowers, it’s not all that difficult to rank-order them from the safest to the riskiest pretty accurately (even I can do it :-)). Using rather robust statistical credit scoring models can easily be enough for this purpose. What remains much more of a trouble is predicting correctly the exact levels of default risk. In other words, the very information that a creditor needs the most is rarely precise enough. The reason is that default probabilities and default rates in a credit portfolio depend on the overall financial and economic conditions – and you may not want to bet on these…

I assume that I’m not the only one pondering about this issue time and time again; so I’ll discuss some of the interesting and not so interesting data relationships that might be helpful for those trying to forecast default rates. Hopefully I’ll end up with some sort of more or less reasonable model. And yeah I’m not pretending to academic correctness. It’s just a blog, not a research paper. 

First a few words about the data in general. Indeed: no data crunching exercise is possible without the input data except maybe some very theoretical Monte Carlo simulation or the like.

It’s about exploring the U.S. corporate annual default rates, as recorded by the Standard & Poor’s (S&P) in its 2012 Annual U.S. Corporate Default Study. I included both, investment grade and speculative grade companies. My little study covered only the years 1991-2012 as some of the other data that I wanted to look at was not available before 1991. The average default rate over this time frame was 1.88%, i.e. on average, 1.88% of the S&P rated companies defaulted each year (on average – of course the default rates varied a lot in different years).

Just for a quick comparison: Moody’s annual average corporate default rate since 1920 has been ca. 1.19% as U.S. corporate defaults were rare during the period from late 1940s to late 1960s when finance was boring; then U.S. President Richard Nixon changed the rules of the “Money Game” and financial people got creative… But that’s another story.

Anyways, during the considered time frame (1991-2012) there have been two major peaks in bad credits: in 2001 when the default rate reached 4.54%, and in 2009 when it was 5.76%. Needless to add that the first peak was preceded by the dot-com bubble of 1997-2000 and the second one was linked to the U.S. housing bubble which peaked in 2006 and triggered the global financial crisis of 2007-2009. Generally you’d assume that a credit crunch is preceded by a stock market crash and the economy starting to slow down, in that order.

What data could be used for forecasting the next year’s U.S. corporate default rate, i.e. what are the best explanatory variables? When choosing the potential risk indicators for exploration, I relied on the common industry practices combined with my own judgment. Access to data and time available for the analysis were limiting factors.

I dismissed inflation rate as systematically biased revisions in its definition are almost notorious. (For illustrative charts, see Shadow Stats, for example.) It did not seem to have any considerable predictive power either.

I also skipped consumer spending and business spending even though these might be good to look at if one has more time; instead, I assumed that GDP is adequately capturing both of them.

I did not look at the unemployment rate as this seems a rather suitable explanatory variable for private person credit portfolios – and it is a lagging indicator too. Furthermore, official unemployment data is yet another group of stats that is not quite reliable due to (at least partly) politically motivated revisions in the definitions.

Treasury yields I found rather insignificant on standalone basis; however, they are included in the calculation of corporate bond spreads.

Delinquency rates were good but only as far as it came to explaining the past – which is useless when future is to be forecasted; I wonder if certain specific business and/or data recording practices have something to do with it when it comes to large companies.

The data that I did look closer is in detail discussed below. To get a preliminary idea about how one or another indicator variable relates to the default rate, I simply depicted two time series on one graph: the variable under consideration (blue dashed line, left scale in the following figures), and the default rate (black continuous line, right scale in the following figures). Here it is important to remind that in modeling one should not forget the time lag: for trying to guess (or predict which might be considered as more informed guessing) future, we only can use the data of today. This time lag is not present on the graphs in this article.

One more note: I have made some calculations based on the source data on my own as I deemed appropriate (averages, annual growth rates etc.); thus my numbers may somewhat differ from those that you find elsewhere.

Let’s now go specific about the default risk indicators on macro level.

When it comes to the macro statistics, we ought to start from something that everyone is looking at for various reasons: economic growth as measured by the real GDP growth rate (see the graph below – GDP data are by the Bureau of Economic Analysis). As can be seen – surprise-surprise or not so much of a surprise – lower growth rates tend to correspond to higher default rates and vice versa. Though the relationship doesn’t seem all that strong and stable in time nor can we assume that the last year’s economic growth is a good predictor for the current year’s default rate. As for solving the second issue, we could try to make use of GDP forecasts instead of the past data. Why do we have macro economists and -forecasters after all? For my little modeling experiment, I’ll use the forecasts from the Federal Reserve Bank of Philadelphia’s Survey of Professional Forecasters. Concerning the first highlight, I’d just point out that over long run, annual economic growth rates in the U.S. (and probably also in the other advanced economies – haven’t just checked) are trending downward, even though with significant ups and downs meanwhile. It has been so at least since late 1940s. As this trending is slow, let’s leave it for now; however, this phenomenon is actually worth a study on its own. 
The next graph (here I used the figure from an S&P’s publication; I think that it’s good) is much more revealing when it comes to default rates. Indeed, I found it just amazing how much predictive power the indicator of changes in credit standards has over one year horizon or so. See: the default rates jumped just after the banks in the Fed’s Senior Loan Officer Opinion Survey on Bank Lending Practices – on net basis – had reported tightened credit standards over the past three months. Furthermore, it’s not just the direction, but also the extent of the impact that matches almost perfectly. Is there any rational reasoning behind? Absolutely! If you’d cut off credit lines of your borrowers and many other creditors would do the same, companies that significantly rely on short-term debt financing simply cannot refinance their existing debts and hence, default in a row as repayment dates of the outstanding credits arrive. The opposite is true as well: if credit is very loose and liquidity is ample, hardly any company (except what we might consider as a minimal rate of failures) would be unable to refinance. Of course, there are reasons why credit standards are tightened or relaxed over time. You might skip this indicator and try to forecast the default rates based on the second or third order effects, that is via trying to first figure out what makes creditors change their standards. I assume you’d lose a great deal of the model’s precision, however.

(I based my subsequent analysis on the answer to the survey question no. 1: “Over the past three months, how have your bank's credit standards for approving applications for C&I loans or credit lines – other than those to be used to finance mergers and acquisitions – to large and middle-market firms and to small firms changed?” I only looked at the large and middle-market firms this time.)

Another interesting explanatory variable in the credit risk context I found to be the so-called fear index VIX, the popular measure of the implied volatility of S&P 500 index options (the next graph – data is from the Yahoo! Finance website). Yeah, by definition VIX is representing the market's expectation of stock market volatility over the next 30 day period. Is it just a coincidence that when it goes up, soon the default rates will peak as well? Is it just a coincidence that the correlation between the December value of VIX and the next year’s default rate is 0.86 in my sample? Recalling the time in bank during the crisis of 2007-2009: the share price of my employer plummeted, yet we were assured that what’s going on in the stock market has not much to do with the real risks (explanations along the lines that prices are driven by emotions). Sure, financial markets are myopic and almost always wrong about the fair pricing of the underlying assets as calculated by the fair value models. However, changes in the stock prices do reflect the market’s perceptions of the risks (which most probably were wrong at the start, but this doesn’t matter here) and, among other self-reinforcing effects, feedback via tighter credit. As we just saw, in obvious reasons tighter credit relates to higher default risk for the debt-dependant companies (incl. banks with high loan-to-deposit ratios) and thus is a good predictor of the future default rate for a reason. I’m jumping ahead of myself, but in fact there is an empirical evidence of a very strong correlation between the VIX and the availability of credit. Yet to be remembered: low default rates deriving from the ample liquidity for re-financing rather than from the operational cash flows are clearly speculative. We ought to come back to this when interpreting the modeling results…
The natural next question is: what about credit spreads? What could be more suitable indicator of credit risk, after all? (Credit default swaps were introduced only too recently – according to Wikipedia in 1994 – and public data availability is way too limited for exploring CDS spreads instead or in addition to corporate bond data even if this might be rewarding.) As for the data, I did some approximate calculations of my own based on the selected interest rates from the website of the Federal Reserve Board: “Moody’s yield on seasoned corporate bonds – all industries, Baa” minus “Market yield on U.S. Treasury securities at 10-year constant maturity, quoted on investment basis” (annual data; the maturity of 10 years for the Treasury securities is somewhat arbitrary). The results are depicted on the chart below. A relationship between the bond spreads and the default rates is apparent. However, while lagging behind and more recently moving more or less in parallel with the default rates, spreads do not quite look like predictive indicators. This outcome is in a way expected: risk estimates ought to define spreads and not the other way round. Yet when it comes to finance and economics relationships are not one-directional but self-reinforcing. Thus, for forecasting purposes one might actually check the very recent spreads instead of the annual average figures. 
Out of the curiosity I among others considered the rating activity of the S&P to see how corporate rating changes relate to the default rates. One might assume that there are relatively more downgrades than upgrades (i.e. the downgrade/upgrade ratio depicted on the graph below is higher) before the default rates actually pick up. (Shouldn’t downgrades of credit ratings serve as signals of increased underlying risks?) The data are from S&P-s “2012 Annual U.S. Corporate Default Study And Rating Transitions”. I’m saying “out of the curiosity” because the default rates are also for the S&P rated companies meaning that using its rating downgrade/upgrade ratio for the modeling purposes could easily lead to over fitting the model for that particular sample. What we see in reality seems rather odd, however: there are proportionally more downgrades only when the default rates are already peaking, not even to mention that in the early 2000s recession, rating actions were lagging behind the events. So much about credit ratings being forward-looking… As an excuse or explanation, it might be said that these credit ratings are through-the-cycle and looking at them in this way is not quite appropriate. Yet again: if ratings are truly through-the-cycle risk estimates then movements in the downgrade/upgrade ratio should not reflect the ups and downs in the default rates this precisely.
The last potential early indicator of changing default risk that I’m looking at this time, is the Purchasing Managers’ Index (PMI) for the U.S. (the ISM Manufacturing: PMI Composite Index (NAPM)). The index is derived from the monthly surveys of private sector companies. It can take values from 0 to 100; a PMI reading above 50 percent indicates that the manufacturing economy is generally expanding; below 50 percent that it is generally declining. The historical data I took from the website of the Federal Reserve Bank of St. Louis. The following graph suggests that we might indeed have a forward-looking measure. That’s the good news. The bad news is that the relationship with the default rate is not very clear and uniform – but it seems strong enough to live with it. Just to point this out: as of mid-2013, the index value is hovering around 50 while having pointed to slightly dealing economy in May.  
We’ll continue our little experiment of modeling the U.S. corporate default rates in Part 2 of this series. In short, we’ll work on with the five out of the six data series discussed above:
1) (forecasted) real GDP growth rates,
2) reported changes in credit standards,
3) VIX,
4) corporate bond spreads, and
5) Purchasing Managers' Index.
Plus as the sixth explanatory variable, I’ll add the default rate itself with one year time lag.


Making otherwise proprietary financial expertise available to those who bother to pay attention – as best I can…

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