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Merton model | Debt/equity, relative value & asset volatility

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“The only perfect hedge is in a Japanese garden”

In this update, we present an alternative bottom-up framework for evaluating relative value opportunities between fixed income assets and equities, which often leads to countervailing conclusions compared to those reached by Wall Street analysts using mainstream methods.

Member's follow-up question

We received a great follow-up question from a member regarding our previous update in which we explored the concept of asset values as an alternative framework for analyzing relative value opportunities between bonds and equities. We will try our best to address the question here. While many of you may already be familiar with the concepts discussed, we apologize in advance if some of this seems redundant, as we will draw from our previous updates.

Let's delve into the topic…

Cross-asset relative value

First and foremost, it's crucial to acknowledge that most equity and fixed income money managers typically operate within their respective silos, and their perceptions of relative value are often shaped within the confines of their specific asset classes, rather than considering cross-asset valuations. This approach can result in inconsistent valuations across the capital structure and the persistence of market dislocations. Corporate credit, where companies issue both equity and debt, serves as the intersection of these two asset classes.

Credit default swaps (CDS)

For the purpose of our discussion, let's assume that a company has publicly traded shares and bonds outstanding. The creditworthiness of an issuer is reflected in the additional spread over the risk-free rate, typically measured relative to interest rate swaps, demanded by bond investors. For larger, benchmark issuers, the preferred measure of credit risk often lies in the credit default swap (CDS) spread. A CDS contract effectively functions as insurance against potential losses in the event of a default.

Firm enterprise value

The enterprise value of a firm (A) can be calculated as the sum of its market capitalization (E) and the total nominal value of its debt (V), represented as A = E + V. Essentially, A approximates the amount a private equity (PE) buyer would need to pay to acquire the entire company. In most cases, a PE acquirer must offer a market premium to entice existing shareholders to sell their stake in the company.

Merton firm value model

In the Merton framework, equity can be conceptualized as a call option on the firm's assets (A) minus its liabilities (V). Shareholders enjoy limited liability, which introduces optionality into equity ownership. In contrast, bondholders, as investors, forgo potential upside in exchange for a fixed revenue stream through coupon payments. In essence, creditors are akin to being short an out-of-the-money put option on the future net asset value of the firm. The premium for this put option is reflected in the credit spread of the bond. The Moody's KMV model employs a similar framework to estimate bond issuer default probabilities.

Equity options & asset volatility

With this foundational understanding in place, it becomes evident that there exists a connection between equity put options and CDS spreads. Default probabilities are contingent upon a firm's leverage (the ratio of debt to equity) and the uncertainty (volatility) of its cash flows. High-leverage firms should theoretically trade at higher implied volatility levels when compared to less-leveraged counterparts. Once we adjust for differences in leverage ratios, we can make like-for-like comparisons of equity volatility, effectively reducing it to a comparison of asset volatilities.

For instance, two companies within the same sector with similar valuations can display significant differences in implied volatilities in the equity options market, even if their asset volatilities are identical.

Understanding the entire capital structure

While a firm's asset value can be approximated by its enterprise value, asset volatility is an abstract concept that is not directly observable or traded in markets. Nevertheless, both asset values and volatilities do change and fluctuate over time, albeit less dynamically than market capitalizations and corresponding equity implied volatilities. Therefore, considering equity or bond valuations in isolation may lead to misleading conclusions.

Trading ‘fallen angels'

In terms of trading strategies, the Merton debt-equity framework proves particularly effective when applied to “fallen angels”—companies with substantial amounts of publicly traded equity and debt securities that are on the verge of receiving a sub-investment grade rating or have recently been downgraded. Investment-grade funds typically are prohibited from holding non-investment grade bonds. As these downgraded bonds fall out of benchmark indices, investment managers are compelled to sell them rapidly. Bank dealers often have limited capacity to absorb these trades and hold the positions on their balance sheets. Consequently, these bonds tend to trade at a discount until new buyers, such as high-yield bond investors, emerge.

Hedging and pricing large bond flows 

During this interim period, unconstrained market investors can hold these bonds and hedge their positions with other instruments. For example, they might hedge credit and interest rate risk using credit default swaps (CDS) and interest rate swaps (IRS), a strategy commonly referred to as a basis trade, particularly when bonds trade at a discount relative to derivatives. Alternatively, dealers may be obligated to purchase CDS contracts to reduce their credit exposure while holding the bonds. In another scenario, a client might decide to sell CDS contracts (to the dealer) at elevated spreads and hedge their credit exposure by purchasing equity put options if the differential in implied asset volatility (between CDS spreads and equity volatilities) is enticing enough.

Different perspectives and incentives

Relative value opportunities, or arbitrage opportunities, often emerge due to the varying mandates and incentives of market participants. This is what creates a dynamic market. In our example, the role of the market maker is to match buyers and sellers while earning a small margin. The cross-asset trader might perceive the forced selling of bonds by real money investors as irrational behavior. These bond sellers are primarily concerned with their performance relative to benchmarks, regardless of absolute returns. For them, it is often preferable to realize a 10-20% loss on a bond downgrade within a diversified portfolio rather than risk potentially larger losses and the associated complications. On the other hand, the equity specialist might be inclined to sell downside put options following a significant negative announcement and a substantial decline in the stock price, especially when implied volatilities are elevated. From their perspective, the actions of the cross-asset trader might appear irrational.

When relative value opportunities continue to widen

If the fundamental outlook for the company continues to deteriorate, market dislocations may widen further. In such a scenario, real money investors may find solace in the fact that they exited their positions earlier. The equity volatility trader might be compelled to pay a premium to cover their short put position. The cross-asset investor may be disinclined to unwind the trade since it serves as a hedge against another (bond) position, and they may even seek to add to the position. This can further drive up equity option premiums.

Every dog has its day, back the right one

What initially seems like a well-conceived, model-driven investment strategy that capitalizes on cross-asset dislocations can quickly become complex when multiple factors come into play, particularly if market liquidity deteriorates. Most trading strategies thrive in specific market environments but struggle during paradigm shifts. As the saying goes, “horses for courses”.

Charging for liquidity provisioning

Regardless of the relative value strategy employed, the key is to provide liquidity to other market participants at the right price. Therefore, it is paramount to understand what motivates their actions, both in the present and the future. Without a catalyst and other market participants seizing upon pricing discrepancies, crowded positions and capital constraints can impede performance. It is generally an ominous sign if a market dislocation persists despite the increasing size of the relative value trade. Such anomalies should ideally revert to historical levels unless a significant imbalance is at play.

Financial ruin

The path to financial ruin often emerges when one group of market participants appears to possess an advantage over others solely due to access to cheap funding and leverage. In the absence of a complete understanding of the details involving the parties concerned, the US Treasury cash-futures basis trade we discussed earlier this week seems to have all the hallmarks of an impending disaster.

Hopefully, this gives a flavor for debt/equity trading strategies.

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Merton model | Debt/equity, relative value & asset volatility

Credit-equity relative value trades with CDS and equity options