1. Supply

The bank chooses the size of an investment in assets and how to finance the assets. There are four ways to finance, deposits D, short-term debt S, (long-term) CoCo C, and equity E, though deposits and equity have limited roles in this model. Hahm, Shin, and Shin (2013) report that deposits and equity do not depend much on financial market conditions. This is presumably because depositors are usually protected by deposit insurance and depositor preference during insolvency proceedings. Moreover, depositors’ primary motive for holding deposits is to use payment and settlement services; hence, they are less likely to change the balances of their deposit accounts simply because financial market conditions change. In this regard, I assume that depositors invest in the bank a fixed amount D at a zero net interest rate. When banks increase their investments in assets, they usually finance these investments with debt rather than equity, as equity issuance is often deemed the most expensive means of financing due to the associated risks, tax disadvantage, and dilution. In this reason, I assume that equity E is fixed. Below, I assume that D = E = 0 without loss of generality.

The model is focused on CoCo and its relationship with short-term debt. Short-term debt is inexpensive given that it is demandable on short notice and collateral is posted against it, whereas CoCos are expensive due to their longer maturities, greater level of default risk, and the risk of bail-ins. However, the merit of a CoCo is that it is recognized as regulatory capital according to the Basel III accord and other international regulations on capital adequacy.

The bank succeeds with probability (1 − p) and fails with probability p. If it fails, the bank earns nothing. By the limited liability, in this case, the bank pays nothing to creditors. If it succeeds, the bank earns (1 + α)A from its investment in assets A. The return on investment α(A)A is assumed to be increasing and concave with regard to A. I also use the two regularity conditions and .

Below, I derive the CoCo supply function.

Discretion-based trigger: The bank (or its stockholders) solves the following problem.

where the first and second constraints are the accounting identity and capital adequacy requirement with the regulatory minimum capital ratio c, respectively. Note that the (net) interest rate on short-term debt is assumed to be zero. As CoCos are more expensive than short-term funding, it is optimal to issue a CoCo only when the capital requirement is binding, that is, when the minimum capital ratio c is high enough. Since the global financial crisis and subsequent European sovereign debt crisis, regulations on international capital have been greatly strengthened. In this sense, I assume that c is sufficiently high that the capital adequacy requirement is binding. Then, by substituting cA for C, the optimal choice of assets A^*(r) is determined by the following first-order condition.

The equation above implies that the optimal size of investment A^*(r) is decreasing in r because α(A)A is concave in A. Thus, the CoCo supply is equal to C^s(r)≡cA^*(r), which is also decreasing in r.

Rule-based trigger: Bank stockholders gain nothing if the CoCo trigger is activated.10 In this case, the bank as an entity enjoys a reduction in its liabilities but the existing stockholders’ value is assumed to be fully diluted. Therefore, they receive zero payoff regardless of whether the bank is solvent or not. If the loss-absorption mechanism of the CoCo is mandatory conversion, the existing stockholders’ value is greatly diluted as the current international regulation pertaining to CoCos requires the conversion ratio to be disadvantageous for existing stockholders. If the loss-absorption mechanism calls for the write-down of principal and interest, existing stockholders are, in principle, intact, but in reality, they are wiped out as the stock price plummets. If the trigger is not activated but the bank is insolvent, the bank as an entity has nothing and hence its stockholders receive a zero payoff. Finally, the stockholders face a positive payoff only when the trigger is not activated and the bank is solvent. Therefore, they solve the following problem:

Because the asset size and CoCo do not affect the probability of solvency or the probability of the trigger being activated, the CoCo supply is still equal to C^s(r) = cA^*(r).

2. Demand

There is a unit-measure of investors who choose whether to buy CoCos. These investors are risk-neutral. Each investor is endowed with one unit of money.11 Investors may use the money to purchase one unit of the CoCo or to invest in an alternative project. The reservation utility from this alternative project is u, which follows distribution G on the support [0,1].

Discretion-based trigger case: If the bank becomes insolvent, the government can choose whether to activate the trigger of the CoCo. If it chooses to activate it by declaring that the bank is at the point of non-viability, the CoCo holders’ claims are canceled and they absorb losses. If the government does not activate the trigger, it has to repay the CoCo holders on behalf of the insolvent bank. Note that one cannot think of a situation in which the bank is insolvent, the government does not activate the trigger, but neither the bank nor the government repay the CoCo holders as, in this case, the CoCo holders can legitimately require repayment as their claims are still valid. If these valid claims are not satisfied, the bond holders can force the bank to enter into a bankruptcy process, resulting in the exposure of the financial market to a systemic crisis. Let q^e ∈ {0, 1} denote the investors’ expectation of the probability that the government does not activate the trigger but uses taxpayers’ funds to repay CoCo holders. That is, q^e can also be interpreted as the expected probability of regulatory forbearance. I assume that investors form a common expectation because they are identical in every aspect except for the reservation payoff. Then, the probability that CoCo holders lose is equal to p(1− q^e); hence, the CoCo demand is given by

Note that the CoCo demand is increasing in r.

Rule-based trigger: Note that the probability that the trigger is activated is (1 − p)F₁ + pF₀, where F₁ = F₁(x) and F₀ = F₀(x). Recall that the government can observe and supervise the bank and is therefore able to detect whether the mechanical trigger is soon to be activated. If it realizes that the trigger condition is about to be satisfied, it may consider saving the CoCo holders for a reason to be explained momentarily. Thus, the investors form the belief q^e ∈ {0, 1} where q^e = 1 means that the government chooses to recapitalize the bank preemptively just before the trigger is activated, while q^e = 0 means that the government lets the bond holders take losses. Thus, CoCo holders lose with the probability of ((1 − p)F₁ + pF₀)(1 − q^e) and hence the CoCo demand is given by

Note that the CoCo demand is increasing in r.

If the unbiased threshold x′ is used, the probability of the trigger being activated is equal to the probability of insolvency. In this case, the CoCo demand is simplified to

3. Market-clearing Outcome

Discretion-based trigger: The CoCo demand G((1 − p(1 − q^e))(1 + r)) depends on the investors’ expectation on the likelihood of regulatory forbearance q^e in case the bank becomes insolvent. If investors believe that the government will activate the trigger (q^e = 0), the CoCo demand is G((1 − p)(1 + r)) and hence the market-clearing interest rate and quantity r⁰ and m⁰, respectively, are given by

m⁰ can be understood as the mass of CoCo holders as each investor buys only one unit of the CoCo. See Figure 1. In contrast, if they believe that the government will not activate the trigger but will save CoCo holders using taxpayers’ funds (q^e = 1), the demand increases to G(1 + r). In this case, the market-clearing interest rate and quantity are correspondingly r¹ and m¹ such that

FIGURE 1.

THE DEPENDENCE OF THE MARKET-CLEARING OUTCOME ON EXPECTATIONS

Note that r¹ is lower than r⁰ while m¹ is larger than m⁰.

Rule-based trigger: Suppose that the threshold x′ of the signal x is unbiased. In this case, the market-clearing outcome is identical to that under the discretion-based trigger. That is, the pair consisting of the market-clearing interest rate and quantity is (r⁰, m⁰) if q^e = 0, while it is (r¹, m¹) if q^e = 1.

Note that r¹ is the risk-free rate because it is the market-clearing interest rate when the probability that CoCo holders will lose is zero. Thus, the difference between the market-clearing interest rate and risk-free rate can be understood as the bail-in risk premium required by investors. If investors believe that the government will not save CoCo holders (i.e., q^e = 0), they require (r⁰ − r¹) as the bail-in risk premium. In contrast, if investors believe that the government will rescue CoCo holders (i.e., q^e = 1), they acknowledge that there is no bail-in risk. This result holds for both types of triggers.

Lemma 1. (i) r⁰, m⁰, r¹ and m¹ exist uniquely, and r⁰ > r¹ but m⁰ < m¹. (ii) If the trigger is discretion-based, the market-clearing interest rate and quantity are correspondingly r⁰ and m⁰ if q^e = 0, whereas they are r¹ and m¹ if q^e = 1. The same is true if the trigger is rule-based and the threshold is unbiased (i.e., x = x′).

Proof. (i) The existence and uniqueness follow from the fact that the CoCo demand is increasing while the CoCo supply is decreasing in r and the two regularity conditions and . Given that G(1 + r) > G(1 − p)(1 + r)) for all r ≥ 0 and A^*(r) is decreasing in r, equation (8) and (10) imply that r¹ < r⁰. Because r¹ < r⁰ and A^*(r) is decreasing in r, equation (9) and (11) imply that m¹ > m⁰. (ii) Equation (5), (8), (9), (10), (11), and the fact that the market-clearing outcome is invariant to the type of triggers immediately implies (ii). ■

The market-clearing outcome depends on the investors’ expectation of regulatory forbearance and thus constitutes a rational expectations equilibrium if and only if the expectation is consistent with the government’s actual choice. Below, I model the government’s behavior and derive rational expectations equilibria.

1. Discretion-based trigger

When the bank becomes insolvent, the government decides whether to activate the trigger of the CoCo. During this decision process, the government considers three types of associated costs: fiscal, political, and shock costs.

If the government activates the trigger and lets the CoCo holders take losses, it is a shock to the investors, who may then withdraw their confidence in the banking system. Related to this, it was reported in February of 2016 that Deutsche Bank may be unable to pay the interest on its CoCos. Immediately, the stock price and CDS spreads decreased sharply and worries about Deutsche Bank and the European banking system spread quickly.12,13 These worries could cause liquidity problems even when there are no insolvency issues. For instance, if a money market fund invests heavily in such a bank, not only the given fund but also other similar money market funds could suffer from fund runs. Let θ ≥ 0 denote the shock cost the government bears when it chooses not to save distressed CoCo holders.

If the government does not rescue the CoCo holders, certain political costs also arise. As the CoCo holders absorb losses, they withdraw their political support for the government and even protest against or sue it. Therefore, the government faces a political cost. This cost would be larger as more CoCo holders are forced to absorb losses. Similarly, during the 2016 banking turmoil, the Italian government was very reluctant to activate the trigger for bail-in debt, including senior and subordinated bonds, as most of the affected bond holders were ordinary citizens. It was reported that one third of senior bond holders and 46% of subordinated bond holders are retail investors.14 Let π_dc(m) denote such a political cost, where π_d > 0 is the intensity of the political cost and c(m) is a nonnegative and increasing function of the number m of CoCo holders.

In contrast, suppose that the government decides not to activate the trigger but to recapitalize the bank at the expense of taxpayers. In this case, the shock cost is not a concern, whereas a fiscal cost arises because taxpayers’ resources are used. The fiscal cost is δ(1+ r)m, where δ ∈ (0, 1) reflects the possibility that bailout funds are repaid at least partially in the future by the rescued bank and (1+ r)m is the amount of money used in the bailout.15

For the following analysis, I use the assumption below pertaining to the political cost and the fiscal cost in order to focus on interesting and reasonable cases.

Assumption 1.

The first part of Assumption 1 means that the political cost is lower than the fiscal cost if the shock cost is zero and, therefore, the government will never rescue the troubled CoCo holders. If CoCos are issued by small or medium-sized nonfinancial companies, the news that the government will not save troubled CoCo holders may not have any impact on the overall financial market. In this case, the shock cost is zero and hence the government never chooses a bailout. However, if the CoCos are issued by systemically important banks, the news will cause a panic in the financial market and will lead to financial instability. In this case, the shock cost is positive and large and the government therefore considers whether or not to save the bond holders.

The second part implies that the political cost rises more rapidly than the fiscal cost with the number of CoCo investors. A possible justification is as follows. The fiscal cost is a monetary cost and therefore increases linearly with the number of investors to be rescued. However, the political cost increases convexly with the number of investors because the cost is associated with the majority voting rule: if the number of troubled investors who are voters is smaller than a certain threshold number, the ruling party may not lose in forthcoming elections. However, if the number of troubled investors is only slightly larger than the threshold, the ruling party may lose in such elections. That is, the associated political cost of the ruling party increases suddenly as the number of investors who purchased CoCos rises.

In sum, the government should compare the total cost of a bail-in and the total cost of a bailout when determining whether to activate a discretion-based trigger. If it chooses to activate the trigger, the government should bear the total cost of the bail-in, which is the sum of the shock cost θ and political cost π_dc(m). Instead, if it decides not to activate the trigger but to help the failed bank repay the CoCo holders, the government should take the total cost of bailout, which is equal to the fiscal cost δ(1+ r)m.

Note that the political cost and fiscal cost depend on the expectations of investors regarding whether the government will rescue CoCo holders. If they believe this to be so (i.e., q^e = 1), the market-clearing number of CoCo holders and the interest rate are m¹ and r¹, respectively. Accordingly, the corresponding political cost and fiscal cost are π_dc(m¹) and δ(1+ r¹)(m¹). Similarly, if they do not believe a bailout will occur (i.e., q^e = 0), the political cost and fiscal cost change to π_dc(m⁰) and δ(1+ r⁰)(m⁰), respectively.

Let q∈{0,1} denote the government’s choice. q = 1 indicates that the government chooses a bailout for troubled CoCo holders, while q = 0 means that the government decides to activate the trigger. If the expectation q^e is consistent with the actual choice q, then q^* = q^e = q constitutes a rational expectations equilibrium.

The following proposition characterizes the rational expectations equilibria (see Figure 2).

FIGURE 2.

DISCRETION VS. RULE (IN CASE WHERE )

Proposition 1. (Discretion-based trigger case): Suppose that Assumption 1 holds. Then, there are and such that ,

(i) (q^* = 0, r⁰, m⁰) is the unique equilibrium if ,

(ii) both (q^* = 0, r⁰, m⁰) and (q^* = 1, r¹, m¹) are equilibria if , and

(iii) (q^* = 1, r¹, m¹) is the unique equilibrium if .

Proof. According to Assumption 1, there exists a unique and such that and . Because δ(1+ r⁰)m⁰ − π_dc(m⁰) > δ(1+ r¹)m¹ − π_dc(m¹), I have .

(i) If , Assumption 1 (ii) implies that

. It then follows that (A) δ(1+ r¹)m¹ ≥ θ + π_dc(m¹) and (B) δ(1+ r⁰)m⁰ ≥ θ + π_dc(m⁰). (A) indicates that when investors believe that the government will save distressed CoCo holders (i.e., q^e = 1), the government will not save them (i.e., q^e = 0), as the total cost of a bail-in θ + π_dc(m¹) is lower than the total cost of a bailout δ(1+ r¹)m¹. That is, the expectation is not consistent with the actual choice. (B) means that when investors believe that the government will not rescue troubled CoCo holders (i.e., q^e = 0), the government will do so (i.e., q = 0). Therefore, q^* = 0 is the unique rational expectations equilibrium.

(iii) This can be proven analogously.

(ii) As , it follows that (C) δ(1+ r¹)m¹ < θ + π_dc(m¹). Also, implies that (D) δ(1+ r⁰)m⁰ > θ + π_dc(m⁰). (C) and (D) mean that the government chooses a bailout (bail-in) if investors believe a bailout (bail-in) will occur. ■

The intuition of Proposition 1 is as follows. In one extreme case in which financial turmoil due to the government’s choice of a bail-in is sufficiently high (i.e., ), the government has no choice but to save distressed CoCo holders for the sake of financial stability. In the other extreme, in which investors are fully aware of the possibility that the government could let them take losses and hence the action of a bail-in causes only a negligible shock on the financial system (i.e., θ < θ^′ ), then regulatory forbearance does not arise regardless of how many investors have long positions in the CoCo. In an interesting case where the shock cost is moderate, the equilibrium depends on the expectation. If investors believe that the government will be lenient in treating troubled CoCo holders, then more investors choose to buy the CoCo and, hence, the government should bear a greater political burden when it chooses to activate the trigger. Consequently, it chooses to save the CoCo holders. However, if investors believe that the government will be tough on CoCo holders, the number of risk-exposed CoCo holders will be smaller, as will be the political pressure regarding a bail-in. Thus, the government chooses not to save the CoCo holders.

2. Rule-based Trigger

The type of trigger has an important implication with regard to the government’s political cost of letting creditors take losses. A rule-based trigger is activated mechanically. Therefore, the government has no authority over or responsibility for trigger activation. Thus, the government does not get ‘blood on its hands’, even if CoCo holders lose money. Nevertheless, the government may feel some degree of political pressure because investors may blame the government for its failure of supervising the bank. In this sense, I assume that the political cost parameter π_r under the rule-based trigger case is positive but smaller than π_d .

Suppose that the realized level of the signal x is higher than the threshold (i.e., x ≥ x ). In this case, the trigger is not activated. Even if the signal is good, the actual financial status of the bank could be poor. If the bank becomes insolvent (i.e., X = 0 ), the bank has nothing with which to repay the CoCo holders. Because their claims remain valid, the CoCo holders can demand repayment. In this case, the government must pay the CoCo holders back on behalf of the bank in order to prevent liquidation.

Suppose instead that the signal falls short of the threshold. Accordingly, trigger activation is imminent. In practice, the CET1 capital ratio is the most popular signal used in rule-based CoCos, and financial regulators monitor this capital ratio. Thus, a financial regulator could realize that the capital ratio is about to fall sharply in the near future and hence may consider recapitalizing the bank preemptively just before the activation of the trigger. In this sense, I consider the situation in which the government could enact a preemptive bailout on the brink of trigger activation. In doing so, the government bears the cost of the bailout, δ(1+ r)m . If the government does not choose the preemptive bailout option and lets the CoCo holders absorb losses, it incurs the bail-in cost, θ + π_rc(m). Note that the political cost parameter π_r is smaller than π_d and hence the political cost π_rc(m) is not very sensitive to the number of CoCo holders. Thus, the following assumption may or may not hold:

Assumption 2. π_r[c(m¹) − c(m⁰)] > δ[(1 + r¹)m¹ − (1 + r⁰)m⁰].

The following proposition characterizes the rational expectations equilibria in the rule-based trigger case (see Figures 3 and 4). If the difference in the political cost parameters (π_d − π_r) is moderate and hence Assumption 2 holds, the equilibrium structure is then similar to that of the discretion-based trigger case. However, if the difference is large and Assumption 2 therefore does not hold, there is no rational expectations equilibrium if the shock cost is at an intermediate level.

FIGURE 3.

DISCRETION VS. RULE (IN CASE WHERE )

FIGURE 4.

DISCRETION VS. RULE (IN CASE WHERE ASSUMPTION 2 DOES NOT HOLD)

Proposition 2. (Rule-based trigger case): Suppose that Assumption 1 holds.

(Subcase 1) Suppose further that the Assumption 2 holds. Then, there are and such that ,

(i) (q^* = 0, r⁰, m⁰) is the unique equilibrium if ,

(ii) both (q^* = 0, r⁰, m⁰) and (q^* = 1, r¹, m¹) are equilibria if , and

(iii) (q^* = 1, r¹, m¹) is the unique equilibrium if

(Subcase 2) Suppose instead that the Assumption 2 does not hold. Then, there are and such that ,

(i) (q^* = 0, r⁰, m⁰) is the unique equilibrium if ,

(ii) There is no equilibrium if , and

(iii) (q^* = 1, r¹, m¹) is the unique equilibrium if .

Proof. Via Assumption 1 and the fact that π_r < π_d, there exists unique and such that and . The proof of subcase 1 is analogous to the proof of Proposition 1. Consider subcase 2. Because Assumption 2 does not hold, it follows that .

(i) If , I have δ(1 + r⁰)m⁰ ≥ θ + π_rc(m⁰). and δ(1 + r¹)m¹ > θ + π_rc(m¹). Thus, q^* = 0 is a unique equilibrium. (iii) If , it follows that δ(1 + r⁰)m⁰ ≤ θ + π_rc(m⁰) and δ(1 + r¹)m¹ < θ + π_rc(m¹). Then, q^* = 1 is a unique equilibrium. (ii) If , I have δ(1 + r⁰)m⁰ < θ + π_rc(m⁰) and δ(1 + r¹)m¹ > θ + π_rc(m¹). Thus, the bailout cost exceeds the bail-in cost when investors expect a bailout. Moreover, the bail-in cost is larger than the bailout cost when investors believe a bail-in will occur. Thus, neither a bailout nor a bail-in constitutes an equilibrium. ■

3. Comparison

By comparing Propositions 1 and 2, one can assess the effectiveness of a CoCo as a bail-in tool. For both types of triggers, a bail-in constitutes the unique equilibrium if the shock cost θ is small enough while a bailout constitutes the unique equilibrium if the shock cost is large enough. If we focus on the unique equilibrium, it is clear that a rule-based trigger is better than a discretion-based trigger in terms of the implementability of a bail-in, as the following corollary shows.

Corollary 1. Suppose that Assumption 1 holds. The region in which a bail-in constitutes the unique equilibrium is larger while the region in which a bailout constitutes the unique equilibrium is smaller if the trigger is rule-based rather than discretion-based.

Proof. Note that and .

Suppose that Assumption 2 holds. Then, a bail-in constitutes the unique equilibrium if , k = {d, r}, while a bailout constitutes the unique equilibrium if θ > θ^′′ under both types of triggers. Because and , the proof is completed.

Suppose instead that Assumption 2 does not hold. Then, with a rule-based trigger, a bail-in constitutes the unique equilibrium if while a bailout constitutes the unique equilibrium if . Because and , it follows that . Also, as and according to Proposition 2. ■

If the shock cost is at an intermediate level, the model does not make a definitive prediction, as there are either multiple or no equilibria. Nevertheless, one can determine that a bail-in arises more likely as an equilibrium if the trigger is rule-based rather than discretion-based in the following sense. Whenever there are multiple equilibria under the discretion-based trigger case, a bail-in constitutes the unique equilibrium or there are multiple equilibria under the rule-based trigger case (see Figures 2-4). Moreover, whenever there are multiple equilibria under the rule-based trigger case, a bailout constitutes the unique equilibrium or there are multiple equilibria under the discretion-based trigger case. Furthermore, whenever there are no equilibria under the rule-based trigger case, a bailout constitutes the unique equilibrium under the discretion-based trigger case.

4. Biased Threshold

Thus far, I have focused on the case where the threshold of the signal x is unbiased in the sense that the probability of the trigger being activated is equal to the probability of insolvency (see Definition 1).

However, in practice, thresholds appear to be biased upwardly. For instance, most CoCos with rule-based triggers in the real world are based on the CET1 capital ratio, and the threshold is around 5% (see Table 3). In principle, a bank is insolvent if its assets fall below its liabilities and, therefore, 0% appears to be an unbiased threshold level. Nevertheless, banks are encouraged or required by market or financial regulators to use a threshold higher than 0% when they issue CoCos based on the CET1 capital ratio.

Suppose that the threshold is higher than the unbiased level (i.e., x > x^′). In this case, the probability that a rule-based trigger is activated is higher than the probability of insolvency p, as the error of false activation increases while the error of negligence decreases (see Equation (1)). As the bail-in risk increases, the CoCo demand shrinks. Thus, the equilibrium interest rate and bail-in risk premium rise (see Equation (6)). In contrast, the equilibrium interest rate and bail-in risk premium with a discretion-based trigger are unchanged.

Analogously, one can find that the equilibrium interest rate and bail-in risk premium for a CoCo with a rule-based trigger fall if the threshold is downwardly biased.

5. Unique Equilibrium

If the size of the shock cost parameter θ is moderate, there are multiple equilibria or no equilibria, as investors can perfectly observe the shock cost parameter. In such a case, all investors know whether the government chooses a bailout or a bail-in. However, if they can observe only an imperfect signal of the parameter, some investors believe that the government will choose a bailout while others expect a bail-in. Therefore, investors behave differently. In this case, the model can generate a unique equilibrium for all θ. In Appendix 1, I explore the possibility of having a unique equilibrium based on the global game approach suggested by Morris and Shin (1998). The main result is that the equilibrium is unique and the implementability of a bail-in is improved if the trigger is changed from discretion-based to rule-based.

1. Hypothesis

A main finding of the previous theoretic model is that the bail-in risk as measured by the interest rate at issuance—the coupon rate—is most likely lower under a discretion-based trigger than under a rule-based trigger with an unbiased level of threshold. In this section, this theoretical prediction is tested empirically. In particular, I consider the following hypothesis:

Hypothesis 1. The bail-in risk is lower (i.e., the likelihood of government assistance is higher) under a discretion-based trigger than under a rule-based trigger.

2. Measures of the Bail-in risk: Coupon Rate and Coupon Residual

The coupon rate is a measure of the bail-in risk. In theoretical model, I assume that the bank is never allowed to be liquidated due to its systemic importance and, hence, there is no default risk. The coupon rate r can then be decomposed into two parts: the risk-free benchmark rate and the bail-in risk premium (see Figure 1). Therefore, if the risk-free rate can be properly controlled, the coupon rate is a good measure of the bail-in risk. However, as the bankruptcy of Lehman brothers showed, even a systemically important bank can be liquidated, though it is very unlikely. This is why default indicators such as bank CDS premiums are positive. As the coupon rate in real-life reflects the default risk as well, it is an imperfect measure of the bail-in risk.

In addition, the validity of the coupon rate as a measure of the bail-in risk depends on whether CoCos are AT1 or T2 instruments. Tier 2 (T2) instruments are subordinated bonds for which a bail-in clause is added. Additional Tier 1 (AT1) instruments have more complicated structures. They are de facto perpetual bonds with bail-in clauses and two special options. First, with a call option, the issuer can opt to repay the bond before the maturity. Because this option is usually exercised, the market panics if the issuer does not exercise the option—the call option risk. Secondly, the issuer can choose to suspend or even default on the interest payment if business conditions are unfavorable—the interest payment risk.16 The coupon rate of AT1 CoCo reflects the call option risk and interest payment risk as well as the default risk and bail-in risk.

An alternative measure of the bail-in risk is the coupon residual, which is obtained after subtracting a benchmark sovereign bond rate and a relevant CDS premium from the coupon rate.

For T2 instruments, this coupon residual is conceptually an ideal measure of the bail-in risk. Tables 1 and 2 describe how the coupon rates of CoCos are determined in real life.

TABLE 1

INTEREST STRUCTURE OF WOORI BANK’S T2 COCO

Note: 1) The CoCo (ISIN: US98105FAC86) was issued in April 30, 2014. The maturity is ten years. The face value is $10 billion. 2) * The coupon residual = the coupon rate - the benchmark rate - the default risk premium.

TABLE 2

THE INTEREST STRUCTURE OF BARCLAYS’S AT1 COCO

Note: 1) The CoCo (ISIN: XS1274156097) was issued in August 11, 2015. The maturity is 34 years. The face value is $15.6 billion. 2) * The coupon residual = the coupon rate - the benchmark rate - the default risk premium.

Woori Bank (a Korean bank) issued a T2 CoCo (in USD) on April of 2014 at the coupon rate of 4.75%. The coupon rate can be decomposed into the benchmark country rate of 3.17% (measured by a similar-term US Treasury bond rate), the default risk premium of 1.40% (measured by the CDS premium on a similar-term Woori Bank subordinated bond), and a residual of 0.18%. Because it is a T2 instrument, investors are concerned only about the default risk and bail-in risk but not the call option risk or interest payment risk. As the CDS premium accounts for the default risk, the coupon residual could be construed as a good measure of the bail-in risk.

The coupon residual, however, is not an ideal measure of the bail-in risk of an AT1 CoCo. Table 2 illustrates this point. Barclays issued an AT1 CoCo in August of 2015 at the coupon rate of 7.86%. As it is an AT1 instrument, the coupon rate reflects not only the default risk and bail-in risk but also the call option risk and interest payment risk. However, it is difficult to find objective measures of the call option risk premium and interest payment risk premium.

Despite its drawbacks, the coupon rate could still be a good measure of the bail-in risk. Although the coupon residual is conceptually a better measure at least for T2 instruments, only a few samples are available, as many CoCos in real life have no counterpart sovereign bonds or subordinated bonds for which CDSs are traded. The maturity of CoCos is mostly ten years or thirty years, but many countries do not issue 10-year or 30-year sovereign bonds. The problems are even worse with CDS contracts. For many banks, CDSs are not traded at all on any subordinated bond. In contrast, if the coupon rate is used as the bail-in risk measure, the available sample size triples in size.

In the following empirical analyses, I use two different approaches. Firstly, I use the coupon rate as the primary measure of the bail-in risk and attempt to control the default risk as much as possible. Various different specifications are considered, and robustness checks are conducted. Secondly, I choose the coupon residual as an alternative measure of the bail-in risk.

3. Data

I utilize a dataset of CoCos issued by banks from January of 2010 to September of 2016. The sources of the dataset are Moody’s Quarterly Rated and Tracked CoCo Monitor Database (2016 3Q) and a Bloomberg terminal. The data also contain information on issuing banks and their countries of domicile. The data cover 632 distinct CoCo instruments issued by 222 banks. The aggregate face value is $460 billion. (Short-term CoCos that mature within three years are excluded because CoCos are designed as a long-term debt.)

Figures 5 and 6 provide an overview of CoCo issuance. The number of issuance increases steadily during the sample period. The volume of CoCos increased to 185 billion US$ until 2014 and then decreased to $124 billion in 2015. According to the convention of international bond markets, I classify countries into five regions—Asia Pacific, EU Euro, EU non-Euro, North and Latin America, and Middle East and Africa. Asia-Pacific banks have been major issuers, accounting for 44% (281 issues) of all issues and 45% ($207 billion) of the total volume. European banks in the Euro area and in the non-Euro area issued 19% ($87 billion) and 24% ($112 billion) of the total volume, respectively. A country-level comparison shows that Chinese banks have been the largest issuers ($107 billion, 23% of the total volume). Then follows UK ($57 billion), Swiss ($41 billion), Australian ($40 billion), Canadian ($29 billion), French ($20 billion), Japanese ($18 billion), Spanish ($15 billion), Korean ($14 billion), Irish ($12 billion), and Brazilian ($11 billion) banks. The average country-wide volume is $10 billion.

FIGURE 5.

YEARLY COCOS ISSUANCE

FIGURE 6.

REGIONAL COCOS ISSUANCE

4. Country-wide Comparison

Of many variables in the dataset, the coupon rate is a key variable. (A definition of each variable is given in Table A7) Table 3 shows that the coupon rate is 5.75% on average, with a standard deviation of 2.66%. Consider the aforementioned eleven major countries. Figure 7 shows that Japanese banks have been able to borrow at the world's lowest interest rate of 1.66% on average. Korean and Canadian banks have also borrowed at low interest rates of 3.57% and 4.02% on average, respectively. In contrast, French (7.34%), Brazilian (7.89%), Spanish (8.28%), and Irish banks (9.00%) borrowed at double or even higher interest rates.

TABLE 3

SUMMARY STATISTICS: VARIABLES

Note: 1) * Only rule-based and mixed-trigger CoCos are considered. 2) ** Only T2 instruments considered as AT1 instruments are deemed perpetual.

Another key variable is the type of trigger. There are two types of triggers: CET1 and PONV. First, the CET1 trigger is a rule-based trigger based on the ratio of common-equity tier 1 (CET1) capital to the risk-weighted assets. The Basel III accord classifies capital into various groups according to the capacity of loss absorbency. Common-equity tier 1 capital has the greatest such capacity, as it mainly consists of common equity. Under the CET1 trigger, the write-down or conversion is activated if the CET1 ratio falls below a predetermined threshold. The threshold for most issues is 5.125%, as the Basel III accord deems 5.125% the minimum capital ratio that a going-concern bank should maintain. (Table 3 shows that the threshold is on average equal to 5.38% with a small standard deviation of 1.28%.) Second, the PONV trigger is a discretion-based trigger. Under this trigger, the government activates a write-down or conversion if it determines that the issuing bank is at the point of non-viability (PONV). See Table 4. The ratio of CoCos with a discretionbased trigger to all CoCos is 49.1% in terms of the number of issuances and 35.4% in terms of the total volume.

TABLE 4

SUMMARY STATISTICS: COCO TYPES

Note: * Face values are denominated in USD according to the exchange rate at the issue date. The unit is $1 billion.

In fact, there is an additional type of trigger—the mixed trigger. Under the mixed trigger, write-down or conversion is activated if either the CET1 ratio falls short of the threshold or the government determines that the issuing bank is at the point of non-viability. Usually, the PONV condition is deemed more difficult to be met than the CET1 condition, as the point of non-viability corresponds to the case in which assets are less than liabilities (i.e., 0% of the CET1 ratio). In this sense, I regard the mixed trigger as a rule-based trigger. However, Japan is special. According to the Japanese Comprehensive Guidelines for the Supervision of Major Banks, such as III-2-1-1-3 (2), a bank that issued a CoCo with a mixed trigger can avoid the activation of write-down or conversion even when the CET1 condition is met (but the PONV condition is not yet met) if the bank submits a resolution plan to the supervision authority and gains approval of it (see Lee and Pang, 2014). For this reason, I regard the mixed trigger of Japanese banks as a discretion-based trigger in the following empirical analysis.

Figure 7 shows that the discretion-based trigger ratio varies across countries.17 Japan, Korea and Canada represent one extreme case. The trigger of every CoCo is discretion-based. France, Brazil, and Ireland are at the other extreme. The trigger of every CoCo is rule-based. Australian, Swiss, Chinese, and UK banks use both types of triggers during CoCo issuances.

The country-level comparison of the discretion-based trigger ratio and that of the coupon rate suggest that there is a negative relationship between the two variables. See Figure 7. In Japan, Korea, and Canada, banks have issued only discretion-based trigger CoCos and the coupon rates are low. In France, Brazil, Spain, and Ireland, only rule-based trigger CoCos have been issued and the coupon rates are high. In other countries, both types of CoCos have been issued and the coupon rates are at an intermediate level.

FIGURE 7.

COUPON RATE AND DISCRETION-BASED TRIGGER RATIO (CORRELATION: -0.88)

One can argue that the negative relationship between the coupon rate and discretion- based trigger ratio is spurious, as the coupon rates are primarily explained by the low sovereign credit risk rather than the discretion-based trigger ratio. However, Figure 8 shows that the CDS premium on 5-year sovereign debt does not appear to be strongly related to the country-wide coupon rate.18 French banks pay high interest rates despite the fact that the CDS premium on France is the lowest. In contrast, Japanese, Korean, and Chinese banks pay low interest rates even if the sovereign CDSs are relatively high. The correlation between the sovereign CDS and the coupon rate is as low as 0.33, while the correlation between the discretion-based trigger ratio and the coupon rate is as high (in magnitude) as −0.88. Although the country-wide comparison is consistent with Hypothesis 1, a more formal empirical analysis is required.

FIGURE 8.

COUPON RATE AND 5-YEAR CDS PREMIUMS (CORRELATION: 0.33)

1. Coupon residual based on a CDS contract on subordinated debt

Initially, I conduct a simple T-test to illustrate the empirical relationship briefly, as shown in Table 8. The average coupon residual of discretion-based trigger CoCos is −0.40%, which is lower by 3.06%p than the average coupon residual of rule-based trigger CoCos. The difference in the coupon residual is significant at the 1% level.

TABLE 8

T-TEST: COUPON RESIDUAL (SUB) AND TRIGGER TYPE

It appears to be odd that the average coupon residual is negative in cases of CoCos with discretion-based triggers. In principle, the coupon residual cannot be negative as the bail-in risk is at least as much as zero. However, the ‘measured’ coupon residual could have a negative value if the bail-in risk is low and the measurement of the default risk (i.e., the CDS premium on the benchmark bond) is imperfect. The difference in the measured coupon residuals due to the difference in the trigger type is not significantly exposed to this measurement problem because errors can be canceled after taking the difference.

Next, I conduct a regression analysis. I exclude Country rate_i and Credit score_i from the set of control variables because Country rate_i is a measure of the benchmark rate and Credit score_i is a measure of the default risk premium. I also exclude State bank_i because its inclusion causes a severe multi-collinearity problem.

Table 9 provides the estimation result. I consider four different model specifications. The coefficient of Discretion_i is negative in all specifications and significant in all but specification 2. The size of the coefficient (in specifications (1), (3), and (4)) is meaningfully large.

TABLE 9

REGRESSION FOR THE COUPON RESIDUAL (SUB)

Note: 1) The dependent variable is the coupon residual (= the coupon rate - the benchmark rate - the default premium). 2) The Huber-White robust standard errors are in parentheses. *, **, and *** indicate significance at 10%, 5%, and 1%, respectively.

2. Coupon residual based on a CDS contract on senior unsecured debt

Consider a simple t-test. See Table 10. The coupon residual is lower by 3.46%p if the trigger is discretion-based rather than rule-based. This difference is significant at the 1% level.

TABLE 10

T-TEST: COUPON RESIDUAL (SENIOR) AND TRIGGER TYPE

Next, I conduct a regression analysis. Unlike the case where the CDS on subordinated debt is used, State bank_i can be included in the regression model. The estimation result is provided in Table 11. The coefficient of Discretion_i is negative and significant in all four specifications. Except for specification 2, the measured discount is as high as 3.41-3.50%p.

TABLE 11

REGRESSION FOR THE COUPON RESIDUAL (SENIOR)

Note: 1) The dependent variable is the coupon residual (= the coupon rate - the benchmark rate - the default premium). 2) The Huber-White robust standard errors are in parentheses. *, **, and *** indicate significance at 10%, 5%, and 1%, respectively.