Credit and equity divide the claims on the same assets of a corporation. Capital structure arbitrage tries to benefit from any mispricing between them. Yet, as often is applied, the term “arbitrage” is misnomer. Credit and equity are different markets. Mispricings discovered will often involve taking some sort of risk. Still, a careful observer can draw insights from the relative pricing between them, and might even be able to profit from them.
One of the simpler ways of checking pricing information between credit and equity markets involves mapping credit spreads versus dividend yields. For instance, the following graph shows the 5y CDS spreads versus indicated dividend yields of select US corporations as of mid January 2009:
Should we expect any simple relationship between the credit spreads and dividend yields? Let’s look at the market by segmenting into three parts: high spread, medium spread and low spread companies:
- On the high spread segment of the market, dividend yields may range from very high to zero. These are all stressed companies running a serious risk that their dividend would have to be cut. We would expect companies whose debt trades at high spreads would have high dividend yields reflecting this risk (like CIT, XL), unless they have already taken action to cut it down.
- On the low spread segment of the market, is natural to see low dividend yields. Companies placed here, by and large, are those that do not have serious issues with any debt payment. Stability in their profits would usually allow them to plow their earnings back to business. This is especially so if they are in the growth markets as opposed to mature markets. A new crop of corporations in this segment involve those whose credits are backstopped by government.
- In the medium spread markets, we would observe companies exposed to an event risk, such as an impending merger or acquisition (for example CTL, DOW). These can have high or low dividend yield depending on the expected structure after the event.
Still, the relationships between the credit spreads and dividend yields seem to be more complex than the basic relationships described above. There are some companies with relatively high dividend yields in all segments even without obvious event risks. MO and CBS are some examples that stand out.
Is there any inconsistency between the equity and credit markets for these companies? If we exclude the special cases, such as those corporations with unstable dividend payment policy or near term liquidity issues, would we be left with hard to explain cases, or potential mispricings?
First thing to note is that each example may have very good reasons to have its credit and equity trade at those prices. Capital structure is often complex. Existence of bank loans above the senior debt and any subordinated debt and preferreds between the senior debt and common equity would affect the pricing relative to equity. Credit claims can range from debt due immediately to those with 50 years maturity and those with equity warrants or hybrids or converts. All of this means, a sweeping generalization would be misleading.
It may yet be possible though to discover some “information” reflected in one market but not the other. A proof of that would use a trading strategy based on historical data. The first step in creating such a trading strategy would involve taking the CDS spreads, normalizing them by index spreads and mapping them against the dividend yield and equity prices. Second step is the creation of a mechanical trading rule that focuses on outliers. Third step involves the elimination of false signals by excluding the special cases.
Before looking at the results of such a trading strategy, let’s review whether such a trading strategy would make sense fundamentally. The most basic relationship between the credit and equity is through Merton’s capital structure model. The key model of this insight is that the equity owners have a call option on the balance sheet of a company. Equity is then priced a call option on the value of the assets of the company.
where A signifies the value of assets, F signifies the face value of equity and σA is the volatility of assets. Asset volatility is again determined through the Black-Scholes formula from the equity volatility:
d2 above is a measure of distance-to-default, and N(-d2) signifies the risk-neutral probability of default. Thus, the part of credit spreads due to expected loss can be derived in the Merton framework. This model yields a simple inverse relation between the credit spreads and indicated dividend yields.
There are, of course, many many issues with this model which is based on extremely simplified assumptions. (For example, insolvency does not necessarily lead to default in real world). This basic model has been enhanced in many directions by researchers. Some involve the use of non-zero barriers and pricing of knock-and-out options. Some involve stochastic volatility. Some focus on distance to default and a more elaborate representation of capital structure (such as in KMV models).
However, the basic Merton model is still useful in the sense that, it reminds us the following:
Asset/equity volatility is a key parameter in the debt-equity relationship.
Going back to our question on whether there is any mispricing, it is clear that we cannot ignore the equity volatility if we try to exploit information from one market in another.
Thus, we must modify the above trading strategy by incorporating the equity volatility as a parameter for the beginnings of a model...
