Pricing Bonds Untested by Time and Convention

Just because some cute girl likes the same weird music you do, that doesn’t make her your soul mate.

Just because there is a new type of capital vehicle out there that picks up 150 bps over sub debt doesn’t make it the right match for your money.

Contingent capital notes look great through an equity-buyer lens. If you are looking at these notes from a bond-buyer lens—as if they are a flashy new note that offers you more yield than the lame old bond-buyers and more safety than equity, well you are soon to be a hipster carcass. Being lame is not so bad. It’s just what happens when one finally grows up. Some of us enjoy it far more than we enjoyed being hip.

Consider a bond that defaults not when coupon payments are skipped or missed. This goofy bond untested by time and convention is not concerned with default. It triggers by a type of balance sheet weakness called capital inadequacy. To define capital (in)adequacy, we first set a capital position as assets net of liabilities. We set financial institutions in a space X of random variables on some probability space (W, F, P) representing the future states of the world. At any state w ∈ W, an institution with capital position X ∈ X can meet its obligations whenever X(w) ≥ 0 and be insolvent whenever X(w) < 0.

A financial institution is deemed to be adequately capitalized if its capital position belongs to a pre-specified subset A of X, where A is X(w) ≥ a, a close to insolvency. Our new type of bond stops paying coupons whenever X(w) < a. When events become even more dire and X(w) < b, b < a then the bond converts to equity at market prices, or it marks to 0. This bond is a new object called a contingent convertible bond, or an alternative tier I/II instrument.

This set-up highlights the fundamental puzzler. Equity marks to zero in insolvency X(w) = 0. Contingent convertibles can trigger before equity marks down. So much for debt seignority to common.

North American banks do not issue them. They are largely a European phenomenon. There are a couple of reasons why North American banks don’t issue AT1s. One, North American banks issue preferred shares to accomplish the same purpose. There is a stronger equity culture in the Anglo-Saxon financial culture. The continental European culture has always been bond-centric. Equity in Europe started as something banks bought to enforce their loan and debt covenant requirements. Second, European bank balance sheets are in much worse shape in terms of capital, provisioning, and leverage.

I can easily see AT1s as a transitory European blip in history that fold after the first wash-out, but maybe they will have some staying power. After all, the spectrum of bank funding instruments is myriad: perpetuals, preferred securities, hybrid callable and step-upable notes and just plain old subordinated debt. They are all treated by buyers as fixed income instruments. AT1s look far more like equity than any of these notes. Capital market issuers of AT1s look to convert the fixed income-like products listed above with a quasi-maturity and quasi-coupons into equity with no maturity and optional dividends. If investors in AT1s are essentially equity buyers looking for a safer equivalent of bank shares, fine and good. Otherwise you have a bunch of bagholders that were expecting some measure of fixed income in their fake equity.

The question at hand is not whether they will survive some future, wholly trivial apocalypse. The question is how to price capital notes with no maturity (easy enough, just a perpetual) and optional dividends (different, but analogous to something you know). The trick is switching the model formulation from default to a less lenient trigger. Other than that, deploy the tools in the credit modeling toolkit.

The basic cornerstone of price determination for debt is the present value of future cash flows. But this isn’t the whole story. Distressed debt guys earn their bread by buying at extremely discounted prices defaulted corporate bonds and then try to induce debt re-structuring. It is clear from the viability of the business model that these instruments have some value outside of their present cashflows. Instead of cashflow or some derivative of it, debt looks to the balance sheet, specifically, the assets of the issuer and where the bond sits in the capital structure. For a bond, recovery value is a strong function of the balance sheet. Future cash flows don't come from thin air; they come from assets.

Here is where things change, and really what makes contingent capital non-debt: AT1s have no recovery option upon trigger, save conversion to equity. So an AT1 is bond-like prior to triggering.

After this, the bond’s valuation at best depends on bank equity and the conversion into equity comes from the income statement. Contingent capital notes are bond-like prior to hitting their trigger. So it is important to evaluate their propensity to trigger.

An approach to evaluating “triggerable” (analogous to “defaultable”) AT1 bonds is the structural model. In a structural model, AT1 trigger events occur when the firm value approaches the inability to repay debt, that is, when the firm value reaches a certain lower threshold (called “trigger” barrier) from the above. Such a default can be expected and thus we call it expected default. In a distressed/default setting, structural credit risk modeling would look at the defaulted bond as a call option on the assets of the firm. In the contingent capital setting, it would look at defaulted bond as equity or marked to zero.

In addition to the firm-specific data captured on a balance sheet, it is clear that systematic risks play a significant role in the credit space, especially in bank debt. The big AT1 losses will likely come via rare systemic shocks for which no amount of diversification into other contingent capital vehicles will remedy. In short, they will all mark to zero together. Systematic defaults not only destroy most value, they explode like a chain reaction especially when the financial and banking sector is the focal point. This is the way of the credit universe: A place of extended periods of low risk seasoned with somewhat frequent less impactful idiosyncratic events and punctuated by rare high-impact credit crises.

To capture the effect of systematic risk on AT1s, the reduced-form approach is used. Reduced-form models intuitively assume that there are too many individual factors that contribute to credit and “trigger” risk, and they are best captured by a single aggregating random process. Thus the probability of an AT1 trigger is treated as a random event obtained from a random process. In this case, the trigger event can occur without any correlation with the firm value and such a default is called unexpected trigger. In the reduced-form approach, if the trigger probability in time interval [t, t+s] is Lt, then L is called the trigger intensity.

The structural approach works well if an investor knows all information about the firm value and default barrier in every time. Such perfect knowledge is unrealistic. An investor can not exactly know true firm value or how close a bank is to levels that trigger an AT1 and hurt investors. There is definitely an incentive for a bank to not disclose pertinent information or misreport it. Further, bank asset value can change quickly in cases of systematic credit crisis or if, well, this is why the reduced form model is used.

The best approach is to blend these structural and reduced-form models into a hybrid. The blend could be in the form of a switching model where idiosyncratic, structural factors dominate 95% of the time and a stress-indicator (for example, the bond price moves 10% down) switches pricing to a reduced form model. Even better, you have a truly integrated structural-reduced form hybrid model that reflects both idiosyncratic and systematic factors at all times, allowing one to dominate the other depending on credit conditions. This is a cross-over between two world views, reflecting the “tail risk” of really bad systemic outcomes and the fundamental bottom-up approach that evaluates banks on their own merit.

Please note: there really is no prediction to these models; these models do not predict, they merely reflect a conception of fair value based on inputs. Incorrect firm value in the structural model yields occasional idiosyncratic losses in a diversified portfolio of contingent convertible bonds when financial conditions are not stressed. When the financial system is stressed, these contingent bonds will convert to equity, driven by some correlated process that reflects a changing environment in the credit ecosystem. This systematic component is the most important. It also makes these notes bidless when you try to sell them.

Which is OK if you are looking at contingent capital notes through an equity lens.

If you are looking at these notes from a bond lens, as if they are a flashy new note that offers you more yield than the lame old bond-buyers and more safety than equity, well you are soon to be a hipster carcass. Being lame is not so bad. It’s just what happens when one finally grows up. Some of us enjoy it far more than we enjoyed being hip. Don’t fight it.


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