Defaultable Bonds. Thought of the Day 133.0

equations

Defaultable bonds are bonds that have a positive possibility of default.  Most corporate bonds and some government bonds are defaultable.  When a bond defaults, its coupon and principal payments will be altered.  Most of the time, only a portion of the principal, and sometimes, also a portion of the coupon, will be paid. A defaultable (T, x) – bond with maturity T > 0 and credit rating x ∈ I ⊆ [0, 1], is a financial contract which pays to its holder 1 unit of currency at time T provided that the writer of the bond hasn’t bankrupted till time T. The set I stands for all possible credit ratings. The bankruptcy is modeled with the use of a so called loss process {L(t), t ≥ 0} which starts from zero, increases and takes values in the interval [0, 1]. The bond is worthless if the loss process exceeds its credit rating. Thus the payoff profile of the (T, x) – bond is of the form

1{LT ≤ x}

The price P(t, T, x) of the (T, x) – bond is a stochastic process defined by

P(t, T, x) = 1{LT ≤ x}e−∫tT f(t, u, x)du, t ∈ [0, T] —– (1)

where f (·, ·, x) stands for an x-forward rate. The value x = 1 corresponds to the risk-free bond and f(t, T, 1) determines the short rate process via f(t, t, 1), t ≥ 0.

The (T, x) – bond market is thus fully determined by the family of x-forward rates and the loss process L. This is an extension of the classical non-defaultable bond market which can be identified with the case when I is a singleton, that is, when I = {1}.

The model of (T, x) – bonds does not correspond to defaultable bonds which are directly traded on a real market. For instance, in this setting the bankruptcy of the (T, x2) – bond automatically implies the bankruptcy of the (T, x1) – bond if x1 < x2. In reality, a bond with a higher credit rating may, however, default earlier than that with a lower one. The (T, x) – bonds are basic instruments related to the pool of defaultable assets called Collateralized Debt Obligations (CDOs), which are actually widely traded on the market. In the CDO market model, the loss process L(t) describes the part of the pool which has defaulted up to time t > 0 and F(LT), where F as some function, specifies the CDO payoff at time T > 0. In particular, (T, x) – bonds may be identified with the digital-type CDO payoffs with the function F of the form

F(z) = Fx(z) := 1[0,x](z), x ∈ I, z ∈ [0,1]

Then the price of that payoff pt(Fx(LT)) at time t ≤ T equals P(t, T, x). Moreover, each regular CDO claim can be replicated, and thus also priced, with a portfolio consisting of a certain combination of (T, x) – bonds. Thus it follows that the model of (T, x) – bonds determines the structure of the CDO payoffs. The induced family of prices

P(t, T, x), T ≥ 0, x ∈ I

will be a CDO term structure. On real markets the price of a claim which pays more is always higher. This implies

P(t, T, x1) = pt(Fx1(LT)) ≤ pt(Fx2(LT)) = P(t, T, x2), t ∈ [0, T], x1 < x2, x1, x2 ∈ I —– (2)

which means that the prices of (T, x) – bonds are increasing in x. Similarly, if the claim is paid earlier, then it has a higher value and hence

P(t, T1, x) = pt(Fx(LT1)) ≥ pt(Fx(LT2)) = P(t, T2, x), t ∈ [0, T1], T1 < T2, x ∈ I —– (3)

which means that the (T, x) – bond prices are decreasing in T. The CDO term structure is monotone if both (2) and (3) are satisfied. Surprisingly, monotonicity of the (T, x) – bond prices is not always preserved in mathematical models even if they satisfy severe no-arbitrage conditions.

Collateral Debt Obligations. Thought of the Day 111.0

A CDO is a general term that describes securities backed by a pool of fixed-income assets. These assets can be bank loans (CLOs), bonds (CBOs), residential mortgages (residential- mortgage–backed securities, or RMBSs), and many others. A CDO is a subset of asset- backed securities (ABS), which is a general term for a security backed by assets such as mortgages, credit card receivables, auto loans, or other debt.

To create a CDO, a bank or other entity transfers the underlying assets (“the collateral”) to a special-purpose vehicle (SPV) that is a separate legal entity from the issuer. The SPV then issues securities backed with cash flows generated by assets in the collateral pool. This general process is called securitization. The securities are separated into tranches, which differ primarily in the priority of their rights to the cash flows coming from the asset pool. The senior tranche has first priority, the mezzanine second, and the equity third. Allocation of cash flows to specific securities is called a “waterfall”. A waterfall is specified in the CDO’s indenture and governs both principal and interest payments.

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1: If coverage tests are not met, and to the extent not corrected with principal proceeds, the remaining interest proceeds will be used to redeem the most senior notes to bring the structure back into compliance with the coverage tests. Interest on the mezzanine securities may be deferred and compounded if cash flow is not available to pay current interest due.

One may observe that the creation of a CDO is a complex and costly process. Professionals such as bankers, lawyers, rating agencies, accountants, trustees, fund managers, and insurers all charge considerable fees to create and manage a CDO. In other words, the cash coming from the collateral is greater than the sum of the cash paid to all security holders. Professional fees to create and manage the CDO make up the difference.

CDOs are designed to offer asset exposure precisely tailored to the risk that investors desire, and they provide liquidity because they trade daily on the secondary market. This liquidity enables, for example, a finance minister from the Chinese government to gain exposure to the U.S. mortgage market and to buy or sell that exposure at will. However, because CDOs are more complex securities than corporate bonds, they are designed to pay slightly higher interest rates than correspondingly rated corporate bonds.

CDOs enable a bank that specializes in making loans to homeowners to make more loans than its capital would otherwise allow, because the bank can sell its loans to a third party. The bank can therefore originate more loans and take in more origination fees. As a result, consumers have more access to capital, banks can make more loans, and investors a world away can not only access the consumer loan market but also invest with precisely the level of risk they desire.

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1: To the extent not paid by interest proceeds.

2: To the extent senior note coverage tests are met and to the extent not already paid by interest proceeds. If coverage tests are not met, the remaining principal proceeds will be used to redeem the most senior notes to bring the structure back into compliance with the coverage tests. Interest on the mezzanine securities may be deferred and compounded if cash flow is not available to pay current interest due.

The Structured Credit Handbook provides an explanation of investors’ nearly insatiable appetite for CDOs:

Demand for [fixed income] assets is heavily bifurcated, with the demand concentrated at the two ends of the safety spectrum . . . Prior to the securitization boom, the universe of fixed-income instruments issued tended to cluster around the BBB rating, offering neither complete safety nor sizzling returns. For example, the number of AA and AAA-rated companies is quite small, as is debt issuance of companies rated B or lower. Structured credit technology has evolved essentially in order to match investors’ demands with the available profile of fixed-income assets. By issuing CDOs from portfolios of bonds or loans rated A, BBB, or BB, financial intermediaries can create a larger pool of AAA-rated securities and a small unrated or low-rated bucket where almost all the risk is concentrated.

CDOs have been around for more than twenty years, but their popularity skyrocketed during the late 1990s. CDO issuance nearly doubled in 2005 and then again in 2006, when it topped $500 billion for the first time. “Structured finance” groups at large investment banks (the division responsible for issuing and managing CDOs) became one of the fastest-growing areas on Wall Street. These divisions, along with the investment banking trading desks that made markets in CDOs, contributed to highly successful results for the banking sector during the 2003–2007 boom. Many CDOs became quite liquid because of their size, investor breadth, and rating agency coverage.

Rating agencies helped bring liquidity to the CDO market. They analyzed each tranche of a CDO and assigned ratings accordingly. Equity tranches were often unrated. The rating agencies had limited manpower and needed to gauge the risk on literally thousands of new CDO securities. The agencies also specialized in using historical models to predict risk. Although CDOs had been around for a long time, they did not exist in a significant number until recently. Historical models therefore couldn’t possibly capture the full picture. Still, the underlying collateral could be assessed with a strong degree of confidence. After all, banks have been making home loans for hundreds of years. The rating agencies simply had to allocate risk to the appropriate tranche and understand how the loans in the collateral base were correlated with each other – an easy task in theory perhaps, but not in practice.

The most difficult part of valuing a CDO tranche is determining correlation. If loans are uncorrelated, defaults will occur evenly over time and asset diversification can solve most problems. With low correlation, an AAA-rated senior tranche should be safe and the interest rate attached to this tranche should be close to the rate for AAA-rated corporate bonds. High correlation, however, creates nondiversifiable risk, in which case the senior tranche has a reasonable likelihood of becoming impaired. Correlation does not affect the price of the CDO in total because the expected value of each individual loan remains the same. Correlation does, however, affect the relative price of each tranche: Any increase in the yield of a senior tranche (to compensate for additional correlation) will be offset by a decrease in the yield of the junior tranches.

Private Equity and Corporate Governance. Thought of the Day 109.0

The two historical models of corporate ownership are (1) dispersed public ownership across many shareholders and (2) family-owned or closely held. Private equity ownership is a hybrid between these two models.

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The main advantages of public ownership include giving a company the widest possible access to capital and, for start-up companies, more credibility with suppliers and customers. The key disadvantages are that a public listing of stock brings constant scrutiny by regulators and the media, incurs significant costs (listing, legal and other regulatory compliance costs), and creates a significant focus on short-term financial results from a dispersed base of shareholders (many of whom are not well informed). Most investors in public companies have limited ability to influence a company’s decision making because ownership is so dispersed. As a result, if a company performs poorly, these investors are inclined to sell shares instead of attempting to engage with management through the infrequent opportunities to vote on important corporate decisions. This unengaged oversight opens the possibility of managers potentially acting in ways that are contrary to the interests of shareholders.

Family-owned or closely held companies avoid regulatory and public scrutiny. The owners also have a direct say in the governance of the company, minimizing potential conflicts of interest between owners and managers. However, the funding options for these private companies are mainly limited to bank loans and other private debt financing. Raising equity capital through the private placement market is a cumbersome process that often results in a poor outcome.

Private equity firms offer a hybrid model that is sometimes more advantageous for companies that are uncomfortable with both the family-owned/closely held and public ownership models. Changes in corporate governance are generally a key driver of success for private equity investments. Private equity firms usually bring a fresh culture into corporate boards and often incentivize executives in a way that would usually not be possible in a public company. A private equity fund has a vital self-interest to improve management quality and firm performance because its investment track record is the key to raising new funds in the future. In large public companies there is often the possibility of “cross-subsidization” of less successful parts of a corporation, but this suboptimal behavior is usually not found in companies owned by private equity firms. As a result, private equity-owned companies are more likely to expose and reconfigure or sell suboptimal business segments, compared to large public companies. Companies owned by private equity firms avoid public scrutiny and quarterly earnings pressures. Because private equity funds typically have an investment horizon that is longer than the typical mutual fund or other public investor, portfolio companies can focus on longer-term restructuring and investments.

Private equity owners are fully enfranchised in all key management decisions because they appoint their partners as nonexecutive directors to the company’s board, and some- times bring in their own managers to run the company. As a result, they have strong financial incentives to maximize shareholder value. Since the managers of the company are also required to invest in the company’s equity alongside the private equity firm, they have similarly strong incentives to create long-term shareholder value. However, the significant leverage that is brought into a private equity portfolio company’s capital structure puts pressure on management to operate virtually error free. As a result, if major, unanticipated dislocations occur in the market, there is a higher probability of bankruptcy compared to either the family-owned/closely held or public company model, which includes less leverage. The high level of leverage that is often connected with private equity acquisition is not free from controversy. While it is generally agreed that debt has a disciplining effect on management and keeps them from “empire building,” it does not improve the competitive position of a firm and is often not sustainable. Limited partners demand more from private equity managers than merely buying companies based on the use of leverage. In particular, investors expect private equity managers to take an active role in corporate governance to create incremental value.

Private equity funds create competitive pressures on companies that want to avoid being acquired. CEOs and boards of public companies have been forced to review their performance and take steps to improve. In addition, they have focused more on antitakeover strategies. Many companies have initiated large share repurchase programs as a vehicle for increasing earnings per share (sometimes using new debt to finance repurchases). This effort is designed, in part, to make a potential takeover more expensive and therefore less likely. Companies consider adding debt to their balance sheet in order to reduce the overall cost of capital and achieve higher returns on equity. This strategy is sometimes pursued as a direct response to the potential for a private equity takeover. However, increasing leverage runs the risk of lower credit ratings on debt, which increases the cost of debt capital and reduces the margin for error. Although some managers are able to manage a more leveraged balance sheet, others are ill equipped, which can result in a reduction in shareholder value through mismanagement.