Financial Distress.

Financial distress is a term used to describe a situation where a company’s asset value (V) is less than the face value of its debt (D). This imbalance can lead to severe consequences for the company, including bankruptcy, restructuring, or liquidation. For instance, the American retail giant, Toys “R” Us, faced financial distress in 2017 when it filed for bankruptcy due to its inability to service its $5 billion debt. This situation is a critical factor to consider in investment decisions as it can significantly impact the company’s ability to generate returns.

The capital structure of a company refers to the mix of its various sources of funding, including debt and equity. It plays a crucial role in determining the company’s financial health and stability. For example, tech giant Apple Inc. has a capital structure that is heavily reliant on equity, with debt making up only a small portion. A closer examination of the capital structure is required in complex investment situations, particularly when a company is facing financial distress.

Merton Model: Equity as an Option on Firm Assets

In the theoretical construct, shareholder claims consist of the firm’s asset value \(V\) plus the right to deliver or “put” assets \(T\) to debtholders upon default at an exercise price of \(D \text{ }(\text{p at t=0})\). Debtholders, on the other hand, possess a risk-free debt claim at maturity \(D\) plus the put option sold to shareholders \(-p\). The concept of put–call parity in evaluating firm asset value \(V\) is described through the equation:

$$V_0 = c_0 + PV(D)_0 – p_0$$

Here, \(c_0\) represents the call option value on firm value, and \(PV(D)_0\) is the present value of risk-free debt, highlighting how the shareholder payoff is likened to a call option, while the debtholder payoff includes the put option sold (credit spread).

Structural (Merton) Models

Structural models, often termed as Merton models, are grounded in the foundational principles of the Black–Scholes–Merton (BSM) option pricing model. These models are pivotal in the context of corporate finance and risk management as they offer a sophisticated framework to assess a firm’s default risk by treating equity and debt as options on the firm’s assets.

A critical aspect of these models is equity value, \(E_t\), as a call option on the residual value of the firm’s assets over its debt obligations. Specifically, equity value can be represented by the following equation:

$$E_t = V_tN(d_1) – e^{-rT}DN(d_2)$$

This formula parallels the expression in the BSM model where the stock price minus the exercise price (\(S – X\)) is substituted by the firm’s net asset value over debt (\(V_t – D\)). The equation uses the firm’s asset volatility in place of equity volatility, reflecting a broader view of risk that encompasses the entire firm’s operations and financial structure.

The variables \(d_1\) and \(d_2\) in the equation are calculated as follows:

$$d_1 = \frac{\ln(\frac{V_t}{D}) + [r + \frac{1}{2}\sigma^2](T – t)}{\sigma\sqrt{T – t}}$$ $$d_2 = d_1 – \sigma\sqrt{T – t}$$

Here, \(N(x)\) signifies the cumulative distribution function of the standard normal distribution, indicating the probability that a variable takes a value less than \(x\). These calculations incorporate the risk-free interest rate (\(r\)), the volatility of the firm’s assets (\(\sigma\)), and the time to maturity (\(T – t\)), offering a probabilistic assessment of the firm’s ability to meet its debt obligations.

For debtholders, the model specifies that the value of risky debt prior to maturity (\(D_t\)) is essentially the difference between the firm’s asset value (\(V_t\)) and its equity value (\(E_t\)):

$$D_t = V_t – E_t$$

This formulation reflects the contingent claim nature of debt in the structural model framework. Debtholders are positioned to receive the face value of the debt at maturity, but the market value of this debt before maturity fluctuates based on the firm’s asset value and the perceived risk of default.

The application of the BSM option pricing model to corporate debt and equity, as embodied in the Merton model, provides a comprehensive method for evaluating financial risk. By analyzing equity as a call option on the firm’s assets, the Merton model offers insights into the dynamics between equity holders and debtholders, underlining the importance of asset volatility and the risk-free rate in determining the value of a firm’s securities.

Risky Debt Valuation and Credit Spreads

Risky debt prior to maturity \(D_t\) equals the difference between firm asset value \(V_t\) and equity value \(E_t\), reflecting the put option on firm value. The credit valuation adjustment, or the “price” of the put option, equates to the present value of expected loss. The equation for credit spread \(R – r\) over risk-free debt is given as:

$$\frac{1}{T – t}\ln\left(\frac{D_t}{[D]}\right) – r = R – r$$

Highlighting that a more valuable put option increases the credit spread, this equation underlines the inverse relationship between the value of equity and debt relative to asset value.

Limitations

The market value of a firm’s assets and asset price volatility are not directly observable but are estimated using equity prices and equity volatility. For example, the market value of Amazon’s assets is not directly observable but can be estimated using its stock price and the volatility of its stock price.

Debt profiles with staggered maturities, different levels of seniority and security, and contingency features complicate the put option calculation. For instance, a company like Microsoft may have different types of debt with different maturities and levels of seniority, which makes the calculation of the put option more complex.

It is difficult to calibrate models to sudden capital structure changes. For example, if a company like Google suddenly issues a large amount of debt, it can be difficult to adjust the Merton model to reflect this change.

Continuous trading and no-arbitrage pricing assumptions do not apply to firms in financial distress with less liquid debt and equity securities. For instance, a company in financial distress like Lehman Brothers may have less liquid debt and equity securities, which makes the assumptions of the Merton model less applicable.

The default probabilities and credit spreads resulting from the Merton model may require adjustments based on historical data or other factors to arrive at a default probability forecast. For example, the default probability of a company like Tesla may need to be adjusted based on its historical default rate and other factors such as its financial health and market conditions.

Capital Structure Arbitrage and the Merton Model

Capital Structure Arbitrage and the Merton Model are key concepts in financial analysis and portfolio management. They provide a framework for understanding and exploiting discrepancies in the pricing of securities issued by the same company in different markets. This guide will delve into these concepts, providing real-world examples and a glossary of terms for easy reference.

Capital Structure Arbitrage Strategies

Capital structure arbitrage strategies are investment strategies that involve taking multiple positions, typically a long and a short position, to capitalize on security mispricing in different markets for the same issuer. For instance, if Apple Inc.’s stocks are undervalued in the equity market and overvalued in the bond market, an investor could buy the stocks and short sell the bonds to profit from the price correction.

These discrepancies often arise due to the presence of different participants in equity, bond, loan, and CDS markets, as well as varying speeds of price adjustment.

Structural models, such as the Merton Model, are used as a basis to compare implied credit spreads across equity, bond, and CDS markets and predict changes based on market movements.

Implied Credit Spread

The implied credit spread is a measure of the additional yield that an investor requires for taking on the credit risk of a bond issuer over the risk-free rate. It is calculated from the equity value (S) as (R – r), where R is the yield-to-maturity on an issuer’s debt and r is the applicable risk-free rate.

The relationship between an issuer’s equity price and its implied credit spread is established using a structural model.

As share prices rise, the likelihood of default falls and credit spreads narrow. For example, if Amazon’s share price increases, the risk of the company defaulting on its debt decreases, leading to a reduction in its credit spread.

Capital Arbitrage Decision Rule

The capital arbitrage decision rule is a guideline used by investors to exploit mispricing between implied equity and bond spreads. It operates under the assumption that the price of credit risk between these spreads should generally be aligned.

If the observed bond spread exceeds the spread implied by the model, then the value of debt, and thus the bond price, are below that predicted by the model. For instance, if the bond spread for Microsoft is higher than the spread implied by the Merton Model, an investor could buy the bond and sell Microsoft’s stock short, expecting to profit as the mispricing falls to zero.

Hedge Ratio of Capital Arbitrage Strategy

The hedge ratio of a capital arbitrage strategy is determined using the Merton model, which accurately represents the default probability. The Black-Scholes-Merton (BSM) model is used to derive the delta, or expected change in bond value for a given change in equity value, to determine this ratio.

Interest Rate Hedging Strategies

Investors use interest rate hedging strategies, such as an asset swap, to isolate a bond’s spread component. For example, an investor could enter into an asset swap where they receive a fixed rate and pay a floating rate, effectively hedging against interest rate risk.

The swap offsets bond value changes due to interest rate risk, leaving the investor with price risk based on bond credit spread changes.

CDS Strategies in Managing Issuer Spread Risk

Credit Default Swap (CDS) strategies can be used to manage issuer spread risk. An investor can create a long bond spread position by borrowing at the Market Reference Rate (MRR) for the life of the debt, buying the bond, and entering a pay-fixed interest rate swap.

An investor may also create a synthetic long bond position to earn the total rate of return by depositing the bond purchase at a risk-free rate, selling CDS protection, and entering a receive-fixed swap.

Volatility Changes in the Structural Model

Volatility changes in the structural model add a third dimension that may create capital structure arbitrage opportunities. Investors may take an explicit capital structure arbitrage position based on a view that the implied equity volatility suggested by the credit spread/share relationship in the structural model deviates significantly from actual equity volatility.

Convertible bonds are a unique type of investment that combines the features of a straight bond with an embedded call option on the issuer’s shares. These bonds are typically sold to investors who have the option to exchange the debt into equity at a predetermined conversion price per share during a future period. Convertible bonds are often issued by early-stage or high-risk companies such as tech startups and are relatively illiquid securities. The call option contingency feature of these bonds attracts lenders who may not be willing to offer standard fixed-rate debt to the issuer. To attract capital more quickly, convertible bonds are often offered at a discount to investors compared to a typical equity or bond offering.

An investor can create a synthetic long convertible bond position by depositing the bond purchase price at a risk-free rate, selling CDS protection, entering a receive-fixed swap, and purchasing an equity call option that matches the bond’s conversion terms. The convertible bond issuer sells equity volatility to the investor, typically in the form of a lower debt coupon versus standard non-convertible debt. This is demonstrated by the investor’s initial outlay of the straight bond purchase price (D) plus the equity call option (cEt), which is greater than D in the case of standard fixed debt.

There are two key differences in capital structure arbitrage for convertible debt versus straight debt. First, convertible bond investors hold a long equity volatility position in the form of an embedded call option, unlike the indirect impact of equity volatility on the relationship between credit spreads and share prices in the structural model. Increasing volatility results in gains to the convertible bondholder due to increases in value on the embedded call option. Second, the conversion feature associated with convertible bonds imposes arbitrage bounds on convertible bonds that do not exist in the case of straight bonds under the structural model.

Investors can use a wide range of capital arbitrage strategies to isolate or offset equity, volatility, credit, and other exposures related to convertible bonds. These strategies include purchasing CDS protection to offset convertible bond issuer default risk (credit risk), paying fixed on an interest rate swap to convert the fixed-rate exposure on the convertible bond to MRR (interest rate risk), and using short equity positions or equity put options to hedge the equity market position of the convertible bond (equity volatility risk).

Glossary:

Financial Distress: A situation where a company’s asset value (V) is less than the face value of its debt (D), leading to potential bankruptcy, restructuring, or liquidation.

Capital Structure: The mix of a company’s various sources of funding, including debt and equity.

Building Blocks of Firm Value: The various components that contribute to the overall value of a company, including tangible and intangible assets, and financial assets.

Equity as an Option of Firm Assets: The Merton Model

Convertible bonds: A type of bond that the holder can convert into a specified number of shares of common stock in the issuing company or cash of equal value.

Straight bond: A bond that pays interest at regular intervals, and at maturity pays back the principal that was originally invested.

Call option: A financial contract that gives the option holder the right, but not the obligation, to buy a stock, bond, commodity or other asset or instrument at a specified price within a specific time period.

Equity volatility: A measure of the price fluctuation of an equity over a certain period of time.

Capital structure arbitrage: A strategy used by many directional, quantitative, and market neutral credit hedge funds. In essence, it is going long one security in a company’s capital structure while simultaneously going short another security in that same company’s capital structure.

Credit Default Swap (CDS): A financial derivative or contract that allows an investor to “swap” or offset his or her credit risk with that of another investor.

Interest Rate Swap: A financial derivative in which two parties agree to exchange interest rate cash flows, based on a specified principal amount from a fixed rate to a floating rate (or vice versa) or from one floating rate to another.

Equity: The value of an ownership interest in a business, including the equity stake of shareholders.

Debtholders: Individuals or entities that lend money to companies and are owed a debt by these companies.

Put option: A financial contract that gives the option holder the right, but not the obligation, to sell a specified amount of an underlying security at a specified price within a specified time.

Credit spread: The difference in yield between a U.S. Treasury bond and another debt security of the same maturity but different credit quality.

Default: The failure to pay back a loan. Default occurs when a debtor is unable to meet the legal obligation of debt repayment.

Capital Structure Arbitrage: An investment strategy that exploits pricing discrepancies between different securities issued by the same company.

Merton Model: A model used to assess the credit risk of a company by analyzing its equity, debt, and asset values.

Implied Credit Spread: The additional yield that an investor requires for taking on the credit risk of a bond issuer over the risk-free rate.

Capital Arbitrage Decision Rule: A guideline used by investors to exploit mispricing between implied equity and bond spreads.

Hedge Ratio: The ratio of the size of a position in the underlying asset to the size of the position in the derivative used to hedge.

Interest Rate Hedging: A strategy used to offset the risk of interest rate fluctuations.

Credit Default Swap (CDS): A financial derivative that allows an investor to “swap” or offset their credit risk with that of another investor.

Market Reference Rate (MRR): A benchmark interest rate used in financial markets.

Practice Questions

Question 1: Imagine you are an investment analyst evaluating a company that is currently facing financial distress. The value of the company’s assets is less than the face value of its debt. You are tasked with conducting a detailed analysis of the company’s situation to inform investment decisions. In this context, which of the following aspects would be most critical to examine in order to assess the company’s financial health and potential for recovery?

1. The company’s current marketing strategies and customer base.
2. The company’s capital structure, including the mix of its various sources of funding.
3. The company’s human resources policies and employee satisfaction levels.

Answer: Choice B is correct.

When evaluating a company that is currently facing financial distress, the most critical aspect to examine is the company’s capital structure, including the mix of its various sources of funding. The capital structure of a company is a critical determinant of its financial health and its ability to weather financial distress. It includes the mix of the company’s debt and equity financing, as well as the cost of this financing. A company with a high level of debt relative to equity may be at greater risk of financial distress, as it has a higher burden of debt repayments. On the other hand, a company with a balanced mix of debt and equity may be better positioned to weather financial difficulties. By examining the company’s capital structure, an analyst can gain insights into the company’s financial stability, its risk profile, and its potential for recovery.

Choice A is incorrect. While the company’s current marketing strategies and customer base are important aspects to consider, they are not the most critical when assessing the company’s financial health and potential for recovery. These aspects are more related to the company’s operational and strategic positioning, rather than its financial health.

Choice C is incorrect. The company’s human resources policies and employee satisfaction levels, while important for the overall health and productivity of the company, are not the most critical aspects to examine when assessing the company’s financial health and potential for recovery. These aspects are more related to the company’s internal operations and culture, rather than its financial stability.

Question 2: In the Merton Model, the equity value (E) can be expressed as a call option on residual firm value (V – D). The value of risky debt prior to maturity at time t (D) equals the difference between firm asset value (V) and equity value (E). Given these equations, how is the put option expressed in the Merton Model?

1. As a periodic credit spread, or the difference between a risky yield R and the risk-free rate r.
2. As a call option on residual firm value (V – D).
3. As the difference between firm asset value (V) and equity value (E).

Answer: Choice A is correct.

In the Merton Model, the put option is expressed as a periodic credit spread, or the difference between a risky yield R and the risk-free rate r. The Merton Model is a structural model of credit risk that treats a firm’s equity as a call option on its assets. In this model, the value of the firm’s debt is equal to the value of a risk-free bond minus the value of a put option on the firm’s assets. This put option represents the right to sell the firm’s assets at the debt’s face value. The value of this put option increases with the volatility of the firm’s assets and decreases as the firm’s asset value increases. The credit spread in the Merton Model is the yield difference between the risky debt and a risk-free bond, which is equivalent to the value of the put option. This credit spread compensates the debt holders for the risk of default.

Choice B is incorrect. In the Merton Model, the equity value is expressed as a call option on the residual firm value (V – D), not the put option. The put option is the right to sell the firm’s assets at the debt’s face value, which is different from the call option that gives the right to buy the firm’s assets.

Choice C is incorrect. The difference between the firm’s asset value (V) and equity value (E) is the value of the firm’s debt, not the put option in the Merton Model. The put option is the right to sell the firm’s assets at the debt’s face value, which is different from the value of the firm’s debt.

Private Markets Pathway Volume 2: Learning Module 5: Private Special Situations; LOS 5(c): Discuss the features of complex investment situations involving financial dislocation or stress