On Tuesday (Feb 12, 2019), right at the deadline for the decision to be made, Banco Santander announced that it had decided not to repay its outstanding €1.5bn CoCo bonds. CoCo bonds are hybrid securities mostly belonging to Additional Tier 1 capital, introduced by regulators in the wake of the 2008 financial crisis, as they tackled the problem of banks’ resolutions by stressing the importance of capital adequacy. Basel III grouped different forms of bank’s securities in Tier 1 and Tier 2 capital, with the former showing the greatest loss absorption capacity and the highest subordination. Tier 1 capital is split between Core Equity Tier 1 and Additional Tier 1 capital. CET1 capital comprises common shares and retained earnings, i.e. the residual claims on bank’s assets. After CET1, Additional Tier 1 capital is made up by the riskiest and most junior securities issued by a bank, among which we find most CoCo bonds. CoCo bonds belonging to Additional Tier 1 capital are also known as AT1 bonds.

CoCo bonds are designed in such a way that, if the issuer balance sheet position drastically deteriorates, these securities are converted into common shares. The event triggering the conversion of CoCos in common equity (the so-called trigger event) is the fall of the bank’s CET1 capital below a specific level of Risk Weighted Assets (RWA). Under Basel III, the minimum trigger level required for a CoCo to qualify as Additional Tier 1 capital expressed in terms of CET1 ratio (CET1/RWA) capital is 5.125%. Such threshold is higher for the so-called “G-SIBs”, globally systematically important banks, on which, according to the Financial Stability Board, depends the stability of the global financial system.

Many banks issue CoCos with a trigger set exactly at that level. In so doing, banks manage to comply with the strict regulation (under Basel III, TIER1/RWA> 6%), raising precious capital qualifying as AT1 while simultaneously minimizing CoCos cost. In fact, the higher the trigger level, the most likely the conversion of CoCos to common equity, the higher their loss-absorption capacity and so the riskier the security from the investors’ standpoint. Additionally, if the regulator determines that the issuer has reached the point-of-non-viability, CoCos are converted to common equity, as well as any other AT1 and Tier 2 instrument.

The rationale behind CoCos is that, when the bank capital position weakens and its CET1 ratio falls below the trigger threshold, the conversion of CoCos reduces leverage and automatically re-strengthen the bank’s balance sheet. Therefore, CoCo bonds are designed to absorb losses and ensure an orderly re-capitalization (or eventual liquidation) anticipating its insolvency, thus avoiding systematic crisis and the highly criticized government bail-outs of financial institutions with tax payers’ money. From this perspective, AT1 bonds are usually referred to as “going concern” capital, securities which can be converted into equity while the bank is still alive. The other forms of debt (including the riskiest tranches of subordinated debt), only take losses when the institution is in resolution.

CoCos are by design perpetual and callable not earlier than 5 years from issuance. Nevertheless, investors in this market have long relied on a gentleman’s agreement that lenders will repay the bonds at the first opportunity, typically five years after they are sold. Therefore, it is easy to understand that Santander decision shocked bond market players.

Market Description

Globally, outstanding AT1 bonds account to $200bn. About $13.5bn worth of CoCos are redeemable this year, of which $8.4bn are from European banks (source Reuters). AT1 bonds became very popular among yield-starved investors. In the first stages of the CoCo market, private banks and retailers have been big buyers of these instruments. They were banned from this market by the FSA in 2014 and nowadays the main buyers of AT1 instruments are asset management companies, hedge funds and banks.

According to Bloomberg Barclays index data, over the past year, euro investors in CoCos gained 3.9%, compared with a meagre 0.5% generated by senior euro bank notes. This attractive return in an environment of interest rates at all-time lows compensates AT1 investors for their super-junior position. However, after Santander shocking decision not to redeem the bonds, investors now have to factor in another risk they have overlooked so far: extension risk, i.e. the possibility that the borrower may leave the callable security outstanding. In fact, investors have traditionally treated CoCos as fixed maturity (in most cases, 5-year) bonds. Now, AT1 holders discover they are in a tough spot as they are de facto shorting a put and a call. In fact, as bondholders, they are shorting a put on bank’s assets and, as holders of a perpetual callable security, they are shorting a call.

Security Description

AT1 bonds are hybrid securities, which share characteristics of bonds and equity. In the following bullet points, we list the key characteristics of CoCos and in particular Santander’s issue.

  1. AT1 bonds accrue non-cumulative cash distributions. Distributions are computed with a fixed rate up to the First Reset Date, which is the first date in which the bond is callable. In case of Santander’s EUR 1.5bn AT1 bond, the First Reset Date is March 12, 2019. The issuer has to notice its intention to call the security one month before the repayment and that is why February 12 was the key date of Santander’s shocking decision. In the first period, Santander’s AT1 bonds pay distributions quarterly at a fixed rate of 6.25%. After the First Reset Date, the interest rate on the distribution is reset periodically. In case of Santander’s AT1 bond, the rate reset is made every 5 years (starting from the First Reset Date) and the reset rate is computed as the EUR 5-year Mid-Swap Rate plus 5.41%.
  2. Distributions look like bond coupons but they are not. In fact, the bank may cancel the payment of any distribution in whole or in part. The cancellation of the distribution happens either when the bank has insufficient resources to pay the distributions or when the regulator, in its sole discretion, cancels the distribution to protect the bank’s solvency situation. Here we notice the key difference between AT1 bonds and traditional debt: paying bonds coupons is an obligation and failure to do so triggers default. This is not the case for AT1 bonds distributions.
  3. AT1 bonds have a perpetual maturity, though investors have long relied on a gentleman’s agreement that lenders will repay the bonds at the first opportunity. From this perspective, AT1 bonds are exposed to redemption risk. It is important to point out that redemption of AT1 bonds cannot be partial and has to be voluntary. In designing AT1 notes, regulators did not include a guaranteed coupon step-up. In fact, there is no guarantee that after the reset the distribution interest rate will be higher, since the new rate depends on the stochastic swap rate. As there is no guaranteed coupon step-up, the regulator gives bank no incentive to call the notes other than economic (and maybe reputational) reasons. When the bank decides to redeem AT1 bonds, it has to receive the regulator’s nulla hosta. Article 78(1) of the CRR provides that the Regulator will give its consent to a redemption of the bonds provided that either of the following conditions is met: “(a) on or before such redemption of the Preferred Securities [aka AT1 bonds], the Bank replaces the Preferred Securities with instruments qualifying as Tier 1 Capital of an equal or higher quality”, “(b) the Bank has demonstrated to the satisfaction of the Regulator that its Tier 1 Capital and Tier 2 capital would, following such redemption, exceed the minimum capital requirements”. Santander AT1 bonds are callable on a quarterly basis after the First Reset Date.
  4. Conversion to common equity. At conversion, the number of common shares received by each AT1 bondholder is determined by dividing the liquidation preference (€100,000 for each bond) by the conversion price. The conversion price is the higher of the market price of common shares in the market at conversion date, the floor price (set at €4.34 but adjusted periodically to take into account extraordinary dividends and newly issued shares) and the nominal value of a common share at the time of conversion (being €0.50 at the moment). In case of liquidation of the bank occurring after the conversion of AT1 bonds, the bondholder has become a shareholder and would receive the residual assets once all debtors have been repaid. If the trigger event occurs before such liquidation but the conversion has not occurred yet (due to technicalities), the AT1 holder is treated as a common shareholder, i.e. as if the conversion had actually taken place.

Decision and Potential Consequences

The decision of the Spanish lender not to call its AT1 bonds is backed by economic reasons. As central banks leave the QE and start withdrawing liquidity, funding costs are rising across the banking sector. As we saw earlier, regulators require the bank to raise new funds qualifying as Tier 1 capital before calling the bond. Given higher funding costs, skipping the call may work out cheaper for Santander because the new interest rate after the reset of the existing bond (5-year Euro Mid-Swap rate + 5.41%) is lower than current market-funding costs.

Against pure economic reasons, the bank has to weigh potential reputational damage that could drive up borrowing costs across its future subordinated issuance. Santander is a global systemically important bank, well above its capital requirements (current TIER 1 ratio 13.12% as of Dec 31, 2018, source Bloomberg), highly reliant on the wholesale debt market (it had €162.6bn of debt securities outstanding as of June 2018, according FT). Many analysts believe Santander did not call the bond just due to temporary regulatory problems but will do it at the next repayment date (June 2019). In fact, Santander has just completed the sale of a new dollar denominated AT1 bond, raising $1.2bn and offering a 7.5% rate.

Santander would be the first bank not to exercise the call at the First Reset Date and other banks may follow its path. Clearly, this will make it more expensive for banks to issue AT1 bonds as investors will demand a higher premium for bearing extension risk. Moreover, a question arises on call structures, i.e. the timespan between two dates in which the bond is callable. Long call intervals are negative for investors as AT1 bonds could be extended at below-market rates for longer periods. To give a simple example of long and short call structures, consider two AT1 bonds of Santander: Santander EUR 1.5bn 6.25% AT1 bond issued on March 2014 (the bond Santander refused to call) is callable on a quarterly basis after the First Reset Date, while Santander USD 1.5 bn 6.375% AT1 bond issued on May 2014 is callable every five years.

Testing the “gentleman agreement”

As mentioned before, there is, or at least, there used to be, an implicit “gentleman agreement” between the issuer of the AT1 instrument and the market concerning the habit of the issuer to call back the AT1 instrument at the first available date. If this is the case, and indeed it was for many instruments of this kind, it would be natural to assume that the market would have priced as plain vanilla 5-year note.

We decided to test whether this is true or not and, in order to do so, we adopted two approaches. The first one, which is discussed in this section, is based on a spot-rates discounting approach in 5 different dates. The second one, which is explained in the next section, involves the pricing of the embedded bermudan option via the Hull-White one-factor model.

However, before introducing in details the “discounting” approach, we would like to highlight all the issues that make pricing this type of instruments such an hard task and, actually, ends up to something closer to art than science.

The first and rather obvious consideration when it comes to estimate a “fair price” for an AT1 bond is that no close form solution exist – this is due to several reasons. Just to name two of them, consider the possibility for the issuer of skipping a “quasi coupon” payment without triggering a credit event as well as the presence of a bermudan option (which gives the issuer the possibility of redeeming the bond at face value at every payment date after the first 5 years).

And even stochastic models provide nothing but a big approximation: in fact, even with this more complex statistical models, in no way it will be ever possible to exactly model all the features of this security and the perpetual maturity of both the bond and the option make everything even more “messy”, to say the least.

In order to better explain the challenge associated with the pricing of AT1 instrument we would like to breakdown the “key features” of the security:

  1. The coupon is fixed only up until year 5. After that, every five years, it is reset following the formula: EUR 5y swap (if positive, otherwise 0) plus a fixed “margin” of 541 bps.
  2. It is perpetual therefore it (theoretically) calls for modelling the risk free rate structure and the credit spread structure up to infinity.
  3. “Coupons” are not guaranteed and, therefore, there is a non-zero probability (that can be either assumed to be deterministic or stochastic) that any n-th “coupon” payment will be skipped.
  4. There is no classic event of default, in the sense that, as outlined above, even in the case of an instantaneous default of Santander, during the bankruptcy process, these securities would be treated as if they were immediately converted into common equity the very moment before the default of the entity.
  5. In the event of a “precautionary conversion” into common equity shares not followed by the default of the issuer, the value of the common share received by the AT1 holder would depend on the price of Santander stock.
  6. Modelling the probability of the instrument to be converted into common equity requires modelling the evolution of the issuer balance sheet, more specifically, of the CET1 ratio, which is an accounting measure whose value is affected by all the items on the books of the bank.
  7. The probability of the embedded bermudan option to be exercise depends on the possibility for the bank to issue new AT1 instruments at lower yield and thus depends on the evolution of the credit spread structure.

To add some more complexity, as if it was not enough, it should be noted that a number of factors that determine the “fair price” of this security enters the valuation model through more than one “channel”: take for instance the structure of the short term interest rate. It enters the valuation model in at least four channels: the risk-free component of discount factors, the “rho” of the bermudan option but also it affects the interest margin of the bank and thus its profitability and, in this way it has an impact on both the term structure of credit premia as well as on the on the probability of conversion (lower interest margin implies lower profitability and thus on the balance sheet of the bank: a weaker balance sheet implies a higher probability of conversion, as it becomes more likely that the 5.125% CET1 threshold will be hit. Obviously when modelling these three components (interest rate, credit premium and probability of conversion), they should not be considered orthogonal one to the other.

After listing some of the challenges associated with establishing a fair price for the Santander 6.25% AT1 perpetuity, we would like to present in detail the simple “discounting” approach that we used to test whether the market priced the security according on the gentleman agreement of the bond being recalled at the first possible date, that is, the 12th March 2019.

In order to do so, we took data for the EUR swap curve and the Santander subordinated CDS in 5 dates: at issuance and then every year on March the 12th. Where spot rates were not directly available, we used linear interpolation from the two closest swap tenors.

We therefore computed the discount factor as the sum of the risk free spot rate, the premium paid on the subordinated CDS for the credit risk. However, we also needed to add an additional 100bps premium for the following reason: Santander subordinated CDS has senior subordinated debt as reference obligation. The senior subordinated debt issued by Santander has an average credit rating of Baa2 according to Moody’s. Instead, our AT1 security is a junior subordinated debt security. Since its features are very close to the ones of a preferred shares, we took Moody’s score of Santander preferred shares, that is, Ba1 as a proxy for the credit rating on our AT1 instrument.

Since the difference in average yield between Baa2 and Ba1 instruments is 100bps, we decided to add this amount of additional premium to our discount factors in order to take into account the higher risk of a junior subordinated debt compared to the senior subordinated one.

We discounted each remaining quarterly payment, equal to 1.5625 (6.25% yearly divided by 4) and the par value of 100 paid back on the first redeemable date using the discount factor relevant for each tenor obtained in the way outlined above. In this way, we arrived at the present value of all the bond cash flows on all the 5 “evaluation dates”.

Comparing this “theoretical price” on these dates and the actual price the bond was trading at on those days, it is possible to see the considerable difference between the two. In particular, according to this approach, the bond should have been trading very much above par for almost all its life.


We would like to remind the reader that this approach is not intended as a pricing tool but rather as a comparison tool between our AT1 security and a 5-year plain vanilla coupon bond paying an yearly coupon equal to the one of the Santander instrument, 6.25%.

The reader should however note that the theoretical price at issuance found with the discounting approach (113,94) is at odds with the price found with the above mentioned Hull-White one-factor model, described in the next section (98,4).

Among the several reasons that may explain this divergence, we would like to remind that in the “discounting approach” we assumed the market to attach a zero probability for any coupon payment to be skipped – an unrealistic assumption needed to evaluate the security without entering into stochastic models.

Pricing of the embedded option

The CoCo bond we are considering is callable, which means that it can be bought back at face value by the issuer at certain specified dates. So, the convertible bond can be considered as the union of a not-callable bond and a short position in a call option on the bond itself. As the CoCo bond is perpetual and the issuer can exercise the option only at predetermined dates, the embedded option is a Bermudan call option.

To price the Bermudan option, we employ the Hull-White one-factor model, in which the process driving the evolution of the short-rate is given by

 dr = \left( \theta \left( t \right) - ar \right) dt + \sigma \left( t \right) dW

under the risk-neutral probability. The model is implemented through a discrete time trinomial tree. We estimate the time-varying parameters \theta (t) and \sigma (t) so that the prices of standard securities computed with the tree match their market price. In particular, we want it to match the 3M EURIBOR swap curve and the Implied Volatility curve of 1Y EURIBOR swaptions.

We take into account the default risk of the security with an intensity model, where the risk-neutral probability of default between time t and t+ \Delta t is given by

Q^{D} \left( t, t + \Delta t \right) = 1 - e^{- \lambda_{t} \Delta t}

To estimate the default intensity \lambda_t, we calibrate the model to match the market price of CDS on Santander, adjusted by 100 bps as described before.

The most difficult characteristic of the bond to model is that fact that it is perpetual. The reason is that the procedure used to price securities with trinomial tree is backwards moving: you start by computing the final payoff of the security, then you discount its expected value in the previous time step until you reach the present value. So, we decided to price this perpetual bond as a callable bond with finite maturity and iteratively increase the maturity until the price reaches a stable value.


As we increase the maturity of the bond, its price decreases significantly from 98.4 with 5-yr maturity to 72.0 with 30-yr maturity. Our intuition of approximating the perpetual bond with a long-term maturity one seems correct, as the price flattens after the 15-yr maturity at around 72.

We would like to remind that our pricing model is based on a number of simplifying assumptions which allow it to be easily tractable. Thus, the prices we obtain as to be considered indicative of what the fair value could be, but not an exact measure of it (this is why we report them with one decimal figure). However, we think we can draw two conclusions from them:

  1. when it was issued, the bond was considered equivalent to one with 5-yr maturity. Even though the price we computed for a 5-yr bond is below par, it is the closest to the market price at issuance (slightly above par at 100.394);
  2. the fair value of a truly perpetual bond is sensibly below par, at around 72. So, at issuance the bond was trading at about 39% premium over its fair value. As the coupon rate is determined so that the bonds as issued at par, we tried increasing its coupon rate to meet this requirement. We estimated that the coupon rate must be about 400bps higher (which corresponds to an initial coupon rate of 10.25%) for the perpetual bond to be at par.

As a concluding remark, we would like to add some thoughts on why this mispricing may appear. In our model, this security is considered individually from the balance sheet of the bank. As a result, the payoff of the embedded call option is the market price of the underlying bond minus its face value because, if this quantity is positive, the bank can buy back the bonds at face value and issue new bonds at par which pay lower coupons. However, the financing policy of the bank is the outcome of the joint analysis of all the sources of capital and cannot ignore the signaling effect of missing the redemption of one instrument. Thus, our model lacks a “hidden derivative” whose payoff is the increase in cost of financing/loss in value of the bank contingent on the decision of calling or not the CoCo bond. The value of this “hidden derivative” is what could counterbalance that of the embedded call option and explain the apparent mispricing.

1 Comment

Banks Do Not Live on Grandma Savings Alone - BSIC | Bocconi Students Investment Club · 15 November 2020 at 16:00

[…] not contractual-, first was the Santander non-call event (more details on our article on the event:😉 and the second was Deutsche Bank not calling one of its CoCo bonds which had a first call date of […]

Leave a Reply

Avatar placeholder

Your email address will not be published. Required fields are marked *