Transactional and Revolving credit
I highly recommend this post by interfluidity, where he slices a credit card into the transactional and revolving portions, and makes this finance blogging thing look easy. He write about how we should focus on bringing back the transactional side – the kind where credit is a substitute for cash and you pay back your balance every month, and the disadvantages of relying too heavily on the revolving side, where the revolver is the line of credit you spend now and pay back over time. A renewed focus to this split is a good move for the debate. I remember asking why businesses don’t ask for cash more, and I got a universal “because cash is a pain-in-the-ass to manage” response. Transaction cards would be a nice balance for both businesses and consumers.
But I want to talk about the other side, the revolver credit card side. I want to ask a question that has been bugging me: Is the idea that the interest rate on credit cards reflects credit risk complete bullshit?
Credit Risk and the Credit Card Quants
The interest rate increases that Congress calls “arbitrary” are anything but. Credit card companies have complex models that include dozens of variables consisting of different customer characteristics. After everything is taken into account, a rigorous, highly tested credit recommendation pops out of their risk management engine. They literally have math and statistics PhDs who are in charge of this stuff. Congress seeks to prevent such complex analysis….
I could tell you stories about some card companies I visited when I was a banker and consultant that would make your skin crawl….
Because of that high risk involved, it’s important for credit card companies to be able to dynamically alter their terms and conditions, or else their risk models won’t be able to accurately protect the money they lend. Without that dynamic nature, they will have to treat the credit line as a loan for the full value of the line, just in case. That will result in higher rates and more fees in general, since they need greater protection. Is that preferable? Maybe to some, but probably not to people who pay their bill every month.
Literally. There is always something wonderful about watching the consultants sell quant models they don’t understand. (Maybe that is unfair, but when I hear MBAs start repeating the word ‘dynamic’ over and over, I reach for my revolver.) It’s a pretty sweet job, being a financial engineer – even after we’ve blown up the world, the free-market front-liners will hit the trenches arguing that everything must be fine just by our very presence, because both their paycheck and their ideology hangs on it being so. Those doing green energy research are held to a much higher standard.
Anyway, he brings up a good point, one I’ve been kicking around in my head: do credit card interest rates actually reflect credit quality? I have never worked on the consumer end, or for a bank, so I have no inside knowledge. The thing that bugs me about it is the complete lack of granularity in the rates. I can price a CDS or a CDO to within a hundredth of a percent (a basis point, bp). You may think I’m just making it up, or concentrating tail risk, or performing a market and thereby creating the market, but at least I can get very specific with rates and prices. I can also tell you the specific movements that move it 10 basis points this way or that way. I never have seen that with credit cards.
But I was only two days late!
Let’s discuss a general credit event you may have encountered. Something in life happens, and you mail your credit card payment two days late, so it arrives two days after the balance is due. Your interest rate goes from 8% to 28%. That something might be a brief medical deal, it may be a big vacation, it may be stress from the office distracting you, it may be that you were waiting for someone to pay you back. This is a credit event, and your rate has more than tripled.
The thing that is important is how large the jump is, and that the numbers seem to be the same for everyone. When I was dirt broke in graduate school, and paying just above the minimum payment, and was three days late during Winter finals, it made that jump. It also made the same jump for this guy: David C Nelson, CEO of DC Nelson Asset Mgmt. LLC and former Lehman Portfolio Manager. He’s late one payment on his AmEx card and his rates go to 27.99%, just like mine did while I was not making CEO wages. This has happened to any number of people I know.
So I ask you the reader: how much more likely do you think it is that you will go bankrupt as a result of being a few days late?
Let’s break out some basic finance. Given interest rates and a risk-free rate, we can back out an implied probability of default. (Here’s a good refresher paper on the topic.) I’m going to use that paper’s argument:
R is recovery rate. I’m going to use ideas and numbers that are most generous to the credit card industry to justify their high rates, so we’ll make R zero – if I default, the money they get from me equals the cost of the lawyers and collection agents. Little r is the interest rate. Since we are just looking at credit risk, it’ll be the rate at which the bank can borrow and process the bills, plus the spread related to complicated bond stuff – convexity, timing, liquidity. We aren’t going to worry about that – we’ll assume that all adds up to 6%. S is the difference between what you pay and that 6%, so 2% in this case. d is the default rate, with (1 – e^(-d)) being the probability you’ll default.
So when I pay 8% as I start my credit card term, the bank thinks I am about 1.8% likely to default over the year. That’s pretty high, but I compensate them for it.
So now I am two days late paying my interest. How likely is it I’m going to default? r and R stay the same – LIBOR is the same, and the cost of mailing me my bill is the same – but now the total rate is 27%, so S has gone from .02 to .21. So the bank now thinks I am 20% likely to default.
So as the result of being two days late, in a perfect market the bank believes I am over 1,100% more likely to default than I was before. That is insane. Note the lack of granularity here. I never hear about interest rates moving from 8% to 10% (representing a doubling of the interest rate risk), or from 15 to 17%. I always hear the 8% to 27% movement. That immediately makes me think something is fishy.
But Mike, what does this look like as a transition Matrix?
Now we do have such a thing for bond finance. From the excellent a credit trader, here is an S&P transition matrix for corporate bonds.
This is the probability of movement from one credit state to another credit state during one time period. Time t is now, time t+1 is a year from now. The columns represent the liklihood that I move from one credit state, say BB to another state, better or worse. State D is default – I’ve gone bankrupt.
Now here is where all those statisticians should kick in and have a variety of credit states I can wander in and out of based on my fundamentals, but instead it looks like I go from BB (the initial 1.4% I started with) to something near junk status (the 34% there). It looks like the credit card industry really just does a flip switch between the two. We can train a monkey to do this kind of modeling, and that is fine. But there’s no reason to believe all those PhDs are adding any value, or that the credit industry has really gotten this thing down, or that what you pay reflects specific information about you. It’s just pretending there are two types of people: the good and the bad.
That’s True! There are two kinds of people: The good kind like me who pay their bills, and the leeches, the “losers” CNBC tells me about.
Often when we emphasize borders and oppositions we are letting the outside construct the inside and then hide…wait. No critical theory today. Only finance. Fair enough. But if there’s only two kinds of people, we can do a linear interpolation to get the interest rate. 42% of Americans are the good kind, and only represent that 2% default risk. 58% are CNBC’s “loser” class, and they have X% default risk. In general, a rule of thumb I have heard from many banksters is that losses trail the unemployment rate. I’m going to give losses an average of 7%. (Nerd alert! [it's a little late for that] That is high, but I’m compensating for the covariance between the two, regardless what the ‘good people’ think of themselves, they risk losing their jobs and being a bad day away from being a loser).
7% = 42% * 2% + 58% * X ; X = 10.6%
If that’s the case, we should see a credit spread of around 11%, for a total of 17% in the bad state. But we see more like 28%. So even in this Mad Max Credit Risk model, credit card companies are gouging their customers to the turn of 11%.
This is all finance 101. And I’ve been generous. Recovery is going to be higher. Also I’m modeling this as the entire bond, which Daniel said was extreme, instead of a revolver, where the losses in default wouldn’t necessarily be the maximum. I have a lot of financial engineering tricks to drill down into the risk on the basis point level, with stochastic interest rates and correlated recovery etc. etc. But those will adjust the value on the order of 50 or 150 basis points – we are off by 1,100bp! 11%! What am I missing?
One model is that the credit card companies are lying to you – they think of you less as an individual to have a dynamic risk factor dynamically assigned to you, and instead as part of a portfolio to have a specific rate of return extracted from. So they have statisticians and psychologists not to create a credit risk, but instead to figure out who is likely to pay what when, and use that to keep their returns very high. Quants to study how much they can squeeze from someone – not too much, but not too little. So it is less about the awesome part of markets, the price information and the convergence and feedback, and something more feudal.
I could be wrong. In fact I’m probably wrong on a lot, but the back-of-the-envelope (front-of-the-blog?) estimates are on the order of 10% off. Crowd-sourcing request: What is wrong? What glaring things am I missing?
Update: So after discussing with some people, I think the big problem, as was a problem with subprime mortgages, in invoking the market is that the inital rate is competitive, but the refinancing later is not. Companies bid up and down your initial rate plus rewards package. However once you are locked in, and get a balance going, nobody is bidding against your rate.
There’s a huge conceptual difference between saying “this is a market price” versus “this is a price someone in the back office came up with.” You essentially have to bid yourself, trying to shop your balance around to different cards; but suddenly collusion makes sense (”don’t mess with my drowning customers, and I won’t with yours”) and the informational and transactional costs are huge.
I have posted follow-up thoughts.