# Implied Probability of Bail-In

## An immediate, fundamental change in thinking is required to take the panic out of the Contingent Convertible/AT1 Bond market, Philippe Henrotte tells Wilmott

CoCo (Contingent Convertible) or AT1 (Additional Tier 1) Bonds have been receiving some attention recently due to a confluence of factors. In no particular order these include the fact that $40bn worth of contracts are up for call in 2020, that until very recently investors were piling into a market that has around$200bn outstanding and the capital markets are now reeling from the sudden impact of Post-Covid-19 crisis uncertainty.

This picture has been colored by events such as Deutsche Bank not calling a 2014 issued $1.25bn AT1 Bond earlier this year and Yes Bank in India writing off a$1.14bn AT1 Bond.

“It has not been a banking crisis so far compared to 2008.” Philippe Henrotte, Head of Research at ITO33, says of recent developments. “It could morph into one very soon as, of course, bad loans deteriorate, but so far banks have been OK.  As a result, they are all trying to send a signal to the markets that they are absolutely fine and one way to do that is to call their CoCos. A few banks have recently called their CoCos. But some of them can’t. Some of them are in real trouble, so of course they cannot. We don’t have an avalanche so far of CoCos being postponed, right? It could come …”

Henrotte has been working on the peculiarities of these structures in earnest for the past three years and suggests that it is a failure to recognise the appropriate narrative for these products and a lack of modelling expertise that leads to the current wailing and gnashing of teeth. Furthermore, what players need to get into their heads as soon as possible is that the foundational concept that is needed to make these products viable for investors is not fair weather friendship based on ideas of Yield to Call, but the concept of the Implied Probability of Bail-in.

“Who Looks Stupid at the End of the Year?”

From the Deutsche Bundesbank Monthly Report of March 2018, ‘Contingent convertible bonds: design, regulation, usefulness’ provides adequate definition of the structure in question:

“CoCo bonds are subordinated bonds that pay a coupon and are either converted into common equity tier 1 (CET1) capital or written down when contractually specified trigger events occur. In this manner, they may contribute to a quantitative increase in banks’ regulatory capital in a way that  pure debt capital cannot. After the write-down or conversion into common equity tier 1 capital, banks’ capital base will even be strengthened in qualitative terms. CoCos differ from traditional convertible debentures in that conversion cannot be triggered by the bondholder; it must take place automatically and immediately, ie without delay, when the conditions specified in the contract are met.”

First issued in 2009, what was initially a EU-centric structure has increasingly grown in popularity elsewhere, particularly Asia, since the bonds became eligible as regulatory capital under Basel III in 2013.

“When it all started people were laughing at the structure; ‘it’s just way too risky, thank you; not for me!’” Henrotte recalls, “As a result, the initial spread was very large. You could get 7 percent, 7.5 percent coupons. As you can imagine, a year later, you are the investment manager who got his seven percent return and the other guy was investing at more or less zero percent. So, who looks stupid at the end of the year?”

CoCos were, in fact, one of the best performing fixed income assets in 2019 posting total returns of near to 18 per cent.

“Sure enough there was a flood of money coming in that market, and by the way, it’s a market for big volumes because we are talking Santander, Credit Agricole, Barclays, Lloyds, all the banks around the world. It’s a market;  If I count the whole Tier 1 plus Tier 2 – all the regulatory instruments – it’s probably one trillion dollars already right around the world.”

Nevertheless, for all investors in this market the threat of bail-in was ever present.

The structures are simple. They’re perpetual, with an option for the issuer to call after 5 years, there’s no upside except your coupon payment, that coupon could be taken away by the issuer at any time, and furthermore, Henrotte reminds “not only can you lose the coupon, you can basically lose the entire structure and that is the ‘bail-in’. And that’s the point.”

The point is that instead of having taxpayers having to pay for anything bad happening to the bank, after the 2008 crisis it was decided that this class of instruments would suffer first or would be ready to be ‘bailed in’. This was defined by Basel III as being when a bank’s core equity (CET1) falls to less than 5.125 per cent, or if the regulatory authorities decide that it’s time to bail-in”

“It’s a bit of a nightmare for quants because how do you know that regulators will intervene or not? It’s not particularly clear how you model that, right?” Henrotte laughs. “You could see more or less how you could model the equity of the bank, you could have a model for that. Difficult to see how you could have a model on the regulator’s intervention.”

Henrotte says the core of the issue is that  market participants need a way to assess the probability of a bail-in; and this can be done by extracting that information from market prices, provided you have a decent model.

Fair to ask then, how were market participants dealing with this structure without that concept?

From Yield to Call to Implied Probability of Bail-in

“Well, let me tell you a story. It’s interesting. It started with very high spreads. That was in 2014, 2013; the first issues. Then obviously the market tightened because what people felt was, ‘that’s okay, it’s an okay market and we make a lot of money here.’ Fear and greed, you know the story, the market was complacent and there’s a lot of money coming in; as a result the spread started to go down.”

“Now, why is that an issue when you have an initial spread of 7 percent? These things, these structures are perpetuals but callable by the issuer. Let’s make it simple; you issue at 7 percent spread and then five years later you have the initial call and you discover that the current market is way tighter, so obviously it makes a lot of sense for the bank to call because they’re going to reissue at five, four something percent. Right?”

It was a no-brainer that for all the initial structures, banks would call their AT1s.

“As a result, life for quants was easy because you could more or less assume that although they think of this as a perpetual callable – risky and so on – in effect, it’s a five-year bond!”

“The market developed a concept which is yield-to-call; there’s no yield to maturity because there’s no maturity. But since first it’s very clear that people are going to call and second there is a gentlemen’s agreement that good banks behave, and they do that call in time. It’s not so difficult to price because you just price a good fat coupon for five years and that’s it. Yield To Call.”

As the market improved CoCo bonds were issued at lower spreads. Some of them, around 20% of current outstanding contracts, were issued five years ago.

“So now we have these bonds which have been issued with tight spreads and the spreads are now moving in the other direction. Right now, the decision to call is absolutely not obvious.” Henrotte explains.

‘You’ve got this game of ‘See? I can call because I’m a good bank!’ ING just did a call. There are a few banks that just gave a strong signal, by saying ‘You see it as a crisis, but we still do call and repay’, right? In February 2019 There was a big shock by Santander. Everyone was expecting Santander to play by the gentleman’s agreement. It was before the crisis. And they didn’t …

Henrotte points out that banks still need approval from the regulators before they can call as they must prove that the capital can be replaced with an equivalent.

“It was not optimal for them to call. The price of the CoCo was below 100. Why would they call at 100 when they can get away with a lower value? So, they didn’t call. And it was a big shock for the market and also for quants; because now you have to develop a model where there is at least a non zero possibility of a call.”

Credit Story

So that brings an end to the era of Yield to Call. A decent model is needed to capture the call now. What would that be?

“If you think about it these instruments are really credit instruments, not equity derivatives. Because what makes a decision to call or not is the value of the bond at the call time. Is it above par or below par?”

“If it’s below par, you’re not going to call, if it’s above par, you’re going to call. You call when the situation of the bank is good. The price is above 100. When you don’t call and extend it’s because the bank is in a bad situation. So, you see, for the investor, it’s precisely when the bank is in trouble that you get extended.”

“It’s a clear risk. Suddenly you have a long duration bond on a credit which is deteriorating. So, you see that it’s essential to have a stochastic credit story.”

“You need to have a model where you have stochastic credit, and that’s complex; it’s not your plain vanilla equity derivative model. The quants started by modelling these things with a barrier like an equity derivative – let’s say that it’s a bond, and if the stock price falls below some level which we are going to calibrate, then the bond will be bailed in. It works very poorly. It is really a shortcut for a real credit derivative, which it should be right?”

What you’re basically looking at is people pricing with the idea of yield to call, with the idea of a trigger at a down price and that’s essentially it? Are there any other triggers taken into account, the regulatory part not taken into account at all?

“So, let’s review. That’s difficult to take into account; the dual play between the regulatory and contractual bail-in. Right?  It’s difficult to capture the smile of vanilla options because if you have a simple model with a barrier, it’s going to be difficult to reconcile this model with the smile you see on say, the Santander vanilla options.”

“Good news/bad news. Good news: we have a lot of liquid information on Santander, right? It is not an obscure issuer. Bad news for the quants because you now have to calibrate on these data right now, of course, and people can’t because a simple model with a barrier won’t get you there.”

“Most importantly, Credit Default Swaps. Let me explain a bit; CDSs, of course, you would have to calibrate and as I told you, it is a credit story.”

“It’s difficult to calibrate CDSs with a barrier; again, you have one barrier and you have the term structure of CDSs. On top of that, we’ve got senior and sub CDSs.”

“We’ve got two ISDA definitions of CDSs, 2014 and 2003. There was a change in the definition of CDS default for banks by ISDA in 2014.”

“… post 2014, a bail-in by the government is considered default, not just the contractual bail-in. You do see that, of course, the 2014 CDS has a higher spread to take into account that extra possibility of default, which is regulatory bail-in.”

“Because we have data both on 2003 and 2014 CDSs we can calibrate on those the actual regulatory bail-in.”

How do you do that with a model with one barrier which doesn’t differentiate between the two?

“It’s impossible. But now you see the point. If you have a good model the CDS market is in fact more important that the vanilla’s. We can jointly calibrate the 2003 CDS the 2014 CDS and the smile; and then you get a nice picture. But as you can imagine, it’s a complex thing. And there are very few people today doing that, sadly.”

“The simplest model would be unique credit, stochastic credit. So, the simplest story would be a story where you’ve got a good regime, a bad regime.”

“Typically, the good regime would be the current one. Then you would have a tiny probability of a serious downgrade of the bank. In each regime you would have a different probability of bail-in. So typically in the good regime you would have zero probability of bail-in and everything’s fine. But if you start going into the bad regime, that’s when you could have a much, much worse credit of course and a high, not zero, probability of bail-in.”

“Because you do a kind of Markov of transition between good and bad regime you see how the model can play up to infinity. Each call decision time, depending on the regime where you stand, you may or may not decide to call -you can see the  complexity, because, of course, the decision to call impacts the value and the value of calls, decides whether you call or not.”

“As always in finance where there’s a kind of fixed point between your call decision and the value of the AT1 CoCo, it’s a complex thing because it’s up to infinity. You need to solve for that. You can infer from that the probability of being called or not.”

“It’s a simple story where you’ve got these two regimes, which, of course, drives also the CDS curves. So, yes, you infer the probability of this regime switching story. You infer the parameters of this story from basically the CDS markets and, also, to some extent the vanillas.”

“Although we are not yet in a banking crisis, it’s getting very important for managers and regulators to track this probability of bail-in as seen by the market. As always, with derivatives we are not guessing what will happen, we are just backing out from current prices.”

It’s an exceedingly interesting exercise to try to back out the probability of bail-in from current market prices of CDS’, vanillas and, of course, the CoCo bonds themselves.

“Implied Probability of bail-in; I think that’s the important concept. The important concept for options is implied volatility. The important concept for CoCos is the implied probability of bail-in. We should standardize that.”

“Now, how you get to it and with what model is a bit complex, of course.”

“I think that’s an important one because in summary, (the concept of the implied probability of bail-in) is more important than the actual model you use. Of course, you should have a good model, but the point is that risk managers need to have a notion of what is the probability of my bond being bailed in and how does this change through time? That is what they should monitor.”

Philippe Henrotte will publish a technical article on this topic in a forthcoming issue of Wilmott Magazine