Optimising credit limit increases for profit, with Cristian Bravo
“Causality is the new explainability.”
We all know credit limit increases are one of the most, if not the most, important levers in the card profit model. And we all know the reality of managing credit limits is far more complicated than the theory - every action has a reaction and all of that. So we focus on pulling back and releasing the spring of the pinball machine and then just get ready to react as best we can.
But as data analytic techniques become more advanced, we can plan more and leave less to chance. So in this episode, I sit down with Dr Cristian Bravo, from Ontario's Western University, to talk about Sherly Alfonso-Sánchez's research into "Causal Learning for Credit Limit Adjustment in Revolving Lending Under Adversarial Goals"
Western University has data science programs at https://uwo.ca/sci/datascience/index.html
The Banking Analytics Lab is at https://thebal.ai/
If you'd like to speak to Cristian, or just stay up to date with the work he and the BAL are publishing, you can find him on LinkedIn https://www.linkedin.com/in/cristianbravor/
In our chat, Cristian mentions an early version of this research - that paper can be found and downloaded here: https://arxiv.org/abs/2306.15585
Or go read Sheryl's blog on this same topic at https://thebal.ai/2023/07/11/optimizing-credit-limit-adjustments-under-adversarial-goals-using-reinforcement-learning/
Then come and find me on LinkedIn, and while you're there, send me a connection request: https://www.linkedin.com/in/brendanlegrange
As mentioned far too many times last week, my action-adventure novels are on Amazon, some versions even for free, and my work with ConfirmU and our gamified psychometric scores is at https://confirmu.com/ and on episode 24 of this very show https://www.howtolendmoneytostrangers.show/episodes/episode-24
If you have any feedback or questions, or if you would like to participate in the show, please feel free to reach out to me via the contact page on this site.
Keep well, Brendan
The full written transcript, with timestamps, is below:
Cristian Bravo 0:00
There is an adversarial goal here: if you increase the limit, you have a potential profit from the person using the credit limit but you have a very real immediate hit to your provisions.
So now we needed some sort of modelling that didn't just give us whether to increase or not, but which would also give us the optimal value of that increase. We don't just give you a limit increase, we give you the one that minimises the value at risk and also the one that has, in terms of expected value, a profitable margin.
Ante la duda, abstente.
if you're in doubt, don't do it. We were giving increases to more people than before, surprisingly, but we were giving much more conservative and reasonable increases than what other competing policies would offer.
Brendan Le Grange 0:58
My career started in credit cards, so the quest to find the ideal credit limit strategy is one that I know well. And it's one that I've enjoyed.
And then, when I moved into the credit bureau space, I had the chance to take a bird's eye view of the landscape and the challenge became even more fascinating. If Lender A gives a customer of theirs a credit limit increase, sure they can see on their side if marginal spend increases, but what happens to the spend that same customer has at Lender B in that month? And the next month and the month after? And what happens when Lender B reacts, who is left better off and was it all worth it.
More importantly, asks our frined Werner Heisenberg, at what point do our attempts to measure the customer's behaviour impact that behaviour too much? Or at what point does the customer become so tempted with high limits, that they start on a spending path that they can't come back from?
I've referenced one scientific concept I barely understand already, so why not another? It's like fractals. The closer we look at this, the more complex it all becomes. Welcome to How to Lend Money to Strangers with Brendan le Grange.
Dr. Christiane Bravo, welcome to the show. You are the Associate Professor and Canada Research Chair in Banking and Insurance Analytics at Western University in Ontario, Canada.
You've come from Chile, you've worked in Belgium and Canada, around the world experience in banking topics. So talk to me about your experience, your background, the path that brought you to where you are today.
Cristian Bravo 2:44
I am an industrial engineer. I have a master's in operational research, and after I finished my master's, I work at the marketing area of a bank for a couple of years. Before deciding that actually, I liked a lot more research than I liked being in an office in meetings - so I decided to take a PhD, co-supervised between the University of Chile and the University of Southampton in the UK, with Professor Lyn Thomas, who is one of the grandfathers of modern credit risk, who sadly passed away many years ago.
I finished that I went to take a postdoc, as you said in Belgium with Professor Bart Baesens. I worked there for years if I recall correctly, then I took a first position by coming Tilly, and very soon Southampton University itself offered me a position. So I was a professor there for four years before the Canadian government, with Western University, offered me the Canada Research Chair.
So I feel very fortunate because I've been able to see the banking reality across the world. So from a highly sophisticated regulatory environment such as Europe, to the Canadian system that exists halfway between the American and the European and really trying to see how they balance both out to our developing country that was back then only Basel 1.7 they called it. And the cast allow me to have the Rankin Analytics Lab. If I may have a blog, their website is the V al.ai. Where we have now a large group we have six presentations here at the great scoring conference.
Brendan Le Grange 4:16
I always thought that credit analytics or banking analytics was a very niche topic, but more and more I'm seeing there's actually lots of good schools doing good work. As you said Christian you've got was six papers being delivered by your team here. In fact, one of the hardest things to do was get the time with you because there's always something happening.
But I'm going to focus just on "optimising credit limit adjustment and adversarial goals using causal learning"
Now, I've done a number of consulting projects where we've looked at credit limit management and what is the right approach and when do we need to do credit limit increases can we do credit limit decreases but your paper includes terms like causal learning and umbrella of supervised learning Taylor like expansion procedures, all big words that I don't understand myself. So let's start with some basic building blocks. You looked at data from a super app in Latin America for your credit limit data. What were you looking at? What sort of limits are we talking about? And then we can dive into what you learned,
Cristian Bravo 5:16
The specific technical details of the company, I can't really tell that much due to due to the confidentiality, but what I can tell you is that the way it works, you get a credit card with a low limit, very low limit and then if you really want to become profitable, you have to very aggressively start increasing the credit limits. Very aggressively.
Brendan Le Grange 5:16
Low and grow.
Cristian Bravo 5:17
Exactly that the what's called the high volume, low amounts for the right, spearheaded by Capital One that became the largest credit card provider in the US following that strategy. The thing is, how do you actually increase the credit limit in a way that makes sense?
So we first did it in a more supervised way, let's say, and that's a paper that's already pre-printed out there that you can look for, but we realise that that one was easy, because we use a fixed limit increase. So we were saying, Cristian, I'm going to increase 20%, every time they increase you under the session becomes binary, yes or no, that's the EC from a supervisor point of view. But really doesn't work like that, especially in this high growth strategies, we can increase the limit by as much as we want, right? All the way up to 300%, we have people in the database.
So the question is, how do you decide the optimal amount. So we needed some sort of modelling that didn't just gave us whether to increase or not, will also gave us the optimal value, that will increase you in percentage terms against your original balance, right.
And I'm going to start dissecting a little bit the title, because there is an adversarial goal here. If you increase the limit, what will happen is, you have a potential predict the expected profit from the person using the credit limit. But you have a very real immediate hit to your provisions, to your expected loss, right, just by increasing the limit, you're going to immediately take a provision hit.
And most papers we found out, only focus on the revenue side. So what we set out to do, we had this to adversarial goal, the profit and the provisions, the very real hit to provisions that pretty much had been neglected, given that limit was taking more as a marketing problem rather than a risk management problem.
So we mixed the two of those into this model
Brendan Le Grange 7:41
Talk about the provisions, you know, capital's expensive again and we do need to really think are we just giving limits that up doing no benefit, and of course, in the last terms, but in the human terms, as well, we know that for that person who's going into default, it's that extra runway that they can build up before they may be acknowledged the problem before they have to acknowledge the problem. And we know people don't want to phone a bank and then admit, if they're in trouble, and maybe they don't want to admit to themselves in trouble. That runway, they can then hit extra few £100 ponds that they owe, you know when they can't avoid it. But now they can't afford it.
So this is a real issues here. It's not just increase the limit and see what happens.
So I'm really happy to hear that you are looking at it carefully. And I think that underline that point you raise like before we would just as a saviour, increase the limit. And we say how much marginal utilisation goes up? And does it go up? Okay, great. And we carry on, and we left it at that. And so yeah, I'm interested to see what you picked up there as you started to get into into the details.
Cristian Bravo 8:40
There's also a second thing, an unintended consequence of these low value high growth strategies, and that's that utilisation is one of the major factors in people's credit risk scores, right. And if your limit is £200, you're gonna hit it every month.
So for a while, you're going to take a reasonable hit to your credit scores. So an increase is something that people should consider, even if they don't need it, because it will lower their utilisation, we want to keep them below 35%, give or take. So having a higher limit is something desirable in general, as long as you're not going to go over further.
So you have on the one side, the group of people that won the higher limit increase or they have a lower utilisation. And on the you're the ones that need the extra runway in the case of an emergency. So those two things come into account from the person's point of view.
In fact, the main thing that we saw is that there were three behaviours here that were pretty clear. You have the people that got the credit card and put it in a drawer, never use it and just accepted every potential credit limit increase. That came a huge provision costs for nonprofit. We have the group of people that use it, and paid it in full at the end of the month. Those are great, because the charges that their customers pay using a credit card, were enough to fund this violence between the two. So you normally want that, right. And you had the third group, that was the ones that any limit that you gave them, immediately they started using it. And those came, normally, with a pretty high provision cost.
So that was the balance of the modelling part, you needed to predict which group of customers you were in.
Now, the value of the increase. And I think that was our biggest innovation. Actually, causal learning for credit limits was proposed by Yurel Faner, whose outside somewhere here walking around, about 11 years 12 years ago. However, that was more of a position paper saying it may be cool. Yeah, our biggest innovation is that we probably brought it to real life right to something that was actionable. And the way that we did is that the causal model will give you a probability distribution of what will be the best value in traditional causal learning, you will just take the average of that distribution and just pick the biggest value.
That's not enough.
Because what really brings losses in credit limit increases is the fact that if someone defaults, that default is going to eat 10 profitable customers. So the extreme value, what we call in finance, the value at risk, was actually the key point here.
So we propose a way of studying and analysing the distribution of losses, given the distribution of properly data we get from causal learning, to give you the one that had the lowest value at risk, and that will give you the highest expected profit, even in the face of black swan events. And with that, we were able to create a system that beat the predictive system that we ourselves have built a year ago, beat the policy that the company had, by a significant margin - we were getting 20% 30% per customer increasing profit over their their own decisions. Yeah.
And that's why I showed yesterday in my talk, also, and this became fun, we were able to extract ever so slightly more of the more when we try to use a predictive model now, but to predict the future consumption of the limit increase. And with that, given the limit increase, are you going to be profitable or not?
So now, when we conditional three things, we don't just give you a limit increase, we give you the one that minimises the value at risk, and also the one that has unexpected value, a profitable margin, only then we gave you an increase. That makes sense. That meant that we were given increases to more people than before, surprisingly, but we were given much more conservative and reasonable increases than what all competing policies will probably be able to offer.
And that, to me was the biggest innovation of our work.
Brendan Le Grange 13:05
Whenever I do any talk on credit. The first thing I always mentioned is the risk is exponential, we often talk about averages but you know, like 80% of people are less risky than average, it doesn't work in an average way. And you do need to apply this underlying thing that the losses are not sort of evenly distributed through the population. One loss is 10 good people. And it's really great to hear that incorporated in and really interesting to hear that actually they're a little bit of who's marginal utilisation is going to increase is very secondary, actually to the actual profit calculation, you need to look at this value at risk.
And I think the other thing, before we get back to the actual, your actual studies, is I when I used to be in these conversations, we would look at credit limits in a lower and grow approach. And we didn't have the analytical tools that exist today. But I don't think we applied much more gut feel. And we said, well, maybe when the limits too low, people don't bother because they don't want to hit a limit in the shop. So they just don't use the cart. And we will be very round number approach. So is there like 50% increase or double the thing, do it every six months, whereas a smoother, more frequent smaller increase is maybe, well, it has been shown to be, the better approach.
The philosophy of low and grow is actually more what you're describing, right? Like each month, we get a little bit more data each month, we get a little bit more certain we get more exposure. And yeah, it's great to hear that that has been borne out and that then they're these causal learning approaches to help that so I'm going to take you a step back to causal learning because it's not, you know, I'm not familiar really with all the details of this.
So can you explain to me what causal learning is?
Cristian Bravo 14:43
Yeah, so as I said, that's really my talk: causality is the new explainability, right.
So is one step further for explainability. You can explain how the predictions are made. Well, that will give you whether there are correlations are meaningful. It will not really tell you where those current lesions imply our behaviour and underlying behaviour. Our personal learning model, first and foremost is about controlling the data that goes into the model.
There are many techniques, but honestly, you could do it with linear regression. The important part is that the data intersymbol allows you to contrast different people with the same underlying characteristics. But we're to whom different treatments have been made. Just like when you take a medicine, if, if a doctor or a pharmaceutical is testing a new medicine, what they will do is they will get a bunch of people with different characteristics. And they will give them different doses of the medicine. You take different people with different characteristics, and we give them different limit increases.
But how do we know whether the medicine affect more women, or people with a certain range of salary, in our case have great limits? Right, what we do is we take two people with similar income, and we give them different limits, and we see their behaviour later. We call that propensity matching.
And there are many other techniques that honestly are not really critical to the point. The important thing here is saying, when we are choosing the sample to train the model for some for most, we're going to choose a sample in which we can see all decisions being made, right across the full spectrum of decisions. And the model will be able to tell us, you know what, for these people with these characteristics, it is actually this decision, that was the most impactful,
Brendan Le Grange 16:43
Yeah, when when I started my career with Capital One, they were very big on test and learn. And then we did a lot of experiment design, the yellow envelope, the blue envelope, or the white envelope good, I opened more often. And then did the 10% or 15, or 20%, credit limit offer get responded to more often.
But we had to think upfront what our design of our thing would be. And we'd have to roll it out as a very, like a whole project to get the test out. But now, with the current techniques that sounds like I don't need to have thought of everything upfront, I don't need to do one test at a time and slowly build up knowledge. I can look at the data and look at the various decisions that have been made by chance, by design, whatever they've reason was behind them in the past, that data can be looked at all together and say, okay, that happened. Yeah, that happened. Yeah, that happened here. This person got that this person got that and identify that little nugget. That's the the interaction that that that made the uptick?
Cristian Bravo 17:40
Yes. First, the tests that you conducted are still the gold standard. That is the best way of identifying causality using a random control experiment. And that won't change, right.
However, when you either have a massive amount of data, where you know, this data has some randomness, I knew that I knew my data set, around half of the results have been given given pretty much at random, because the company had changed the policy across time. That's called a natural experiment, right? A semi randomly controlled experiment. So I did have some, very purposely the sign increases, and those I had to be very careful.
And that's what I mean about causal learning, right, is that you need to carefully control the data to create a quasi random experiment that will allow you to get better conclusions.
Okay, so still, if you have the ability to run control experiments, that he's going to be better, and that will give you more confident results. However, the scale usually is not possible unless you're a fintech. FinTech allows you through the app to run some possibly faster and more appropriate experiments. And probably this is something that banks can learn a lot from. And I certainly have been working with banks trying to do stuff like that, but in some cases it is not practical.
Brendan Le Grange 18:58
I'd imagine that for most organisations, unless you've had the culture of experimental design and knowledge management for the last 1020 years. And you've kept that discipline, a manager's been in the team, they've had an approach, they've thought of something, they've moved off somebody else's cam, they've changed things. Most of us are sitting with data that is somewhat randomised, because of the human nature of all our businesses.
And your limit increase strategy is one of the most important strategies within a revolving lending business, right? If you can get customers on board, but if they're not using the product, it's exposure to losses exposure to fraud, its cost to maintain it, if you get limit management, right? That's half the battle.
So what sort of uplift are we talking about?
Cristian Bravo 19:45
And I'm going to refer to the past study where we measure it a little bit better. So in this study, I measured it per customer and per customer, we are looking at on average, a profit increase per customer per quarter of around 20%.
Which sounds a lot what this actually when you see that the margin is 2.5%, we increase that to 3%, right? But it's still 20%. It's a 20% margin margin increase.
Suddenly our collaboration with the company finished by the time we were going to run the randomised experience. So my suggestion is always use this to build it. And once you have it always validated with a randomised experiment, that will be my way of being sure. What we're looking for 15% to 20%.
That was a surprise to us, you know, I was expecting it to be better, of course, right? Or was it we wouldn't have tried it. But we got such a big increase. And I think that the reason is the black swans.
We have a saying in Spanish, "ante la duda, abstente". If you're in doubt, don't do it. Our model is a mathematical formulation of that.
And what it does is it will say, I will increase maybe 60%. But you know what 40% gives me almost the same expected profit at an incredibly reduced risk is a no brainer. And this is your supporting these concepts are so natural in practice in a way that hadn't really been thought before any and, and that's really the sort of research I've always liked, right, trying to understand the system and taking the systemic view of what a financial institution is, and pulling it together in a way in which you get this overall view using these modern techniques that are out there now that we allows us to understand that one.
Brendan Le Grange 21:31
And I think that's just a fantastic illustration of what it's doing just we couldn't do that in the past, you said we would take an average, and we do it is 20%, better than 10%, we'll give everyone 20% the thinking was done once off. And it had to be done at scale for everybody was now when we talk about the broader concept of artificial intelligence, this is more about the machine thinking for us on a one by one basis,
Cristian Bravo 21:54
Subtleties in the data that animals are able to capture. And that's the important part, we use the same variables in the end, right, so we have the same thing. So you were describing plus a whole bunch more. And we let them all decide which ones are relevant. And that's what the three methods usually consult for us.
There are a whole bunch of techniques that are just extensions to this console world that control the data, control the loss functions in a way that makes sense. So how we actually train the model is slightly different. To take into account that we're looking at distributions.
Now. We're looking at probabilities, we're not looking at fixed points. Once you have all of that, and there have been several advances in the last two or three years on that what we really get is this decision making that make financial sense, right. And if we had the time, throughout the full files with an analyst, they can look at files one by one, they will probably make the same decision as we are. But what we don't have is cost, right that will be prohibitive, you will need an army of analysts.
So we defaulted to the techniques that you were describing. And it speeds it up in a way that then humans can take a look and say, yes, this makes sense.
Brendan Le Grange 23:04
Cristian, I think everybody listening who's got a revolving product needs to have a think about how they do limit strategies, because it is that driving things. So if anybody does want to speak to you want to see the work that you and the team are doing, remind us again, where they can go to get involved to to contact you or to see some of this research.
Cristian Bravo 23:23
Yes, perfect. So the first thing I have to say is that this has been the amazing work of my PhD student, Sherly Alfonso Sánchez, in co-supervision with Kristina Sendoval. So I'm just the face here because she's on maternity leave, so she couldn't be presenting or otherwise you will be interviewing her.
And you can find all the work that we do in our website, the banking analytics lab, so is the www.thebal.ai and there Shirly actually wrote a blog post about her paper, where you can see a little bit more detail and the preprint of the work with the good half. So you can play around with your own data, if you have it is going to come out in about a month or so I just am the one that hasn't finished reading it before it can be shown to the world.
Brendan Le Grange 24:09
I'll put all those links in there. I think, as I said, it's it's sort of mandatory reading for anybody to have a thing, even if they don't use the exact same approach is just to rethink, are we still doing what we were doing 20 years ago? And is there a better way to do it?
Cristian Bravo 24:24
Ultimately, research always and stop being you know what I should think about this differently. If you get those insights from my research, even if you don't implement them all that sometimes they are too academic, and that is true. Sometimes they are not. But just talking about these things differently are going to already bring you profitable solutions.
And that has been my experience so far.
Brendan Le Grange 24:45
Lovely. Thank you so much for joining me. It's been a pleasure.
Cristian Bravo 24:48
Thank you so much for the invitation.
Brendan Le Grange 24:50
And thank you all for listening.
Please do look for and follow the show on your favourite podcast platform and share the updates widely on LinkedIn where lending nerds are found in our largest concentration. Plus, send me a connection request while you're there.
This show is written and recorded by myself Brendan le Grange in Brighton, England and edited by Fina Charleson of FC Productions.
Show music is by Iam_wake, and you can find show notes and written transcripts at www.HowtoLendMoneytoStrangers.show and I'll see you again next Thursday.