Chap 23 - Introduction to Structuring

Question 1

What is structuring ?

Answer 1

Structuring is the process of engineering
unique financial opportunities from existing asset exposures. An example of a structured product is an investment specially designed to provide downside protection against losses while offering potential profits through exposure to increases in the value of an index or an underlying portfolio.

However, a forward contract on an equity index would not be commonly described
as a structured product because most forward contracts do not provide a substantially altered exposure to the fundamental characteristics of the underlying asset.

Question 2

What is Heterogeneous liquidity preference ?

Answer 2

Heterogeneous liquidity preferences are accommodated by structuring an asset into short-term claims for investors who place a high value on liquidity and long-term claims for investors less concerned about liquidity.

Question 3

How does the structure of CDOS work ?

Answer 3

CDOs are structures that partition the risk of a portfolio into ownership claims called tranches which differ in seniority. More senior tranches tend to be the first to receive cash flows and the last to bear losses. The tranching of CDOs performs a function quite similar to the capital structure of an operating corporation. Investors can select a tranche that best meets their preferences for risk and return.

Question 4

What are some of the motives for a buyer of structured products ?

Answer 4

The motivation to the buyer could be risk management, tax minimization, liquidity enhancement, or some other goal. From the perspective of a financial economist, the primary economic role of structured products is usually market completion.

Question 5

What are some of the motives for a saller of structured products ?

Answer 5

The primary direct motivation of the issuer is usually to earn fees—either explicit fees or implicit fees.

Question 6

What is market completion (complete market) ?

Answer 6

A complete market is a financial market in which enough different types of distinct
securities exist to meet the needs and preferences of all participants. For example, consider a world without any risk, uncertainty, taxes, or transaction costs. In such a world, the only difference between securities would be the timing of their cash flows. A complete market in this idealized example would exist when investors could assemble a portfolio that offered exactly the cash flows they desired on every possible date.

Question 7

What is a state of the world ( state of nature state) ?

Answer 7

Incomplete markets are understood in the context of “states of the world.” A state of the world, or state of nature (or state), is a precisely defined and comprehensive description of an outcome of the economy that specifies the realized values of all economically important variables. For example, a particular state of the world might be briefly summarized as being when an equity market index closes at $X, a bond market index closes at $Y, the gross domestic product (GDP) of a particular nation reaches $Z, and so on. The concept is theoretical since it is impossible to fully describe the entire world or all states that could occur.

Question 8

Although markets can never be complete, the primary role of structured products is to move them toward being more complete. For example, most investors would define the states of the world as including the condition of their physical properties. How can investors prepare for the potential that fire might destroy their real estate? The answer, of course, is to purchase fire insurance.

Answer 8

In a incomplete markets (centuries ago), investors might not have been able to purchase fire insurance and so would have had to bear the very undesirable and highly diversifiable risk of losing substantial wealth due to fire. But in a complete market, investors could purchase fire insurance, a “security” that pays a substantial payoff in states in which the real estate burns and pays nothing in other states.

Question 9

What is a CMO ?

Answer 9

Collateralized mortgage obligations (CMOs) assemble mortgage assets and finance those assets by issuing securities. They then divide the cash flows from assets such as mortgage pools or other mortgage-related products and distribute them with varying characteristics to different classes of security holders.

The key distinguishing feature between and other investment pools, such as mutual funds or the mortgage-backed securities , is the use extensive structuring.

Question 10

What is a tranche ?

Answer 10

A tranche is a distinct claim on assets that differs substantially from other claims in such aspects as seniority, risk, and maturity. Each tranche is typically tradable in units that may differ in size.

Question 11

What is a sequential-pay collateralized mortgage obligation ?

Answer 11

The sequential-pay collateralized mortgage obligation is the simplest form of CMO. In a sequential-pay CMO, each tranche receives a prespecified share of the interest payments based on each tranche’s coupon and principal amount. Each tranche also
potentially receives principal. When there is no default risk, it is the seniority to principal payments that is the focus of CMOs.

Question 12

What is extension risk ?

Answer 12

Fluctuations in interest rates and other factors that drive mortgage prepayments
cause a phenomenon known as extension risk. Extension risk is dispersion in economic outcomes caused by uncertainty in the longevity—especially increased
longevity—of cash flow streams.

For example, when interest rates rise, prepayment rates usually fall, and the life of most tranches, especially the more junior tranches, is extended, thereby increasing or extending the expected life of the tranche further than originally expected.

Question 13

What is Contraction risk ?

Answer 13

Contraction risk is dispersion in economic outcomes caused by uncertainty in the longevity—especially decreased longevity—of cash flow streams.

Question 14

How does the Z-Bond work ?

Answer 14

In actual CMO structures, there is typically an accrual tranche, or Z-bond, that receives no promised interest or coupon payments. Rather, the tranche serves as a residual, equity-like claimant, with rights to cash flows that remain after all fixed-income tranches have been satisfied.

Question 15

What is a Planned Amortization Class Tranches: Planned amortization class (PAC) ?

Answer 15

Planned Amortization Class Tranches: Planned amortization class (PAC) tranches receive principal payments in a more complex manner than do sequential pay CMOs. Investors in some PAC tranches have high priority for receiving principal payments as long as the prepayment rates are within a prespecified range (the planned prepayment levels). When prepayments diverge from what was à originally projected, the relative priorities of tranches can shift. PAC tranches, it is possible that a tranche will contract in longevity as prepayment rates accelerate to a certain point but then extendin longevity beyond that point. In other words, a tranche might have high priority to receiving principal payments in one range of prepayment speed and low priority if other prepayment speeds occur. Thus, PAC tranches can be riskier and more complexto analyze.

Question 16

In a sequential-pay structure, the relation between tranche longevity and prepayment rates is somewhat linear,meaning that each tranche’s longevity to changes in prepayment speeds is somewhat stable at various levels of prepayment.

Question 17

What is a Targeted Amortization Class Tranches: Targeted amortization class (TAC) ?

Answer 17

Targeted Amortization Class Tranches: Targeted amortization class (TAC)
tranches receive principal payments in a manner similar to PAC tranches but generally with an even narrower and more complex set of ranges. The amortization procedures tend to identify narrower ranges of prepayment speeds within which tranches have particular priorities for receiving principal payments and interest. These prepayment ranges can be viewed more as targeted outcomes than as planned outcomes. A sensitive TAC tranche can quickly switch from being quickly paid off to receiving no principal payments (and vice versa), even when prepayment speeds change by only a small amount.

Question 18

What are Principal-Only Tranches (PO) and Interest-Only Tranches (IO) ?

Answer 18

Principal-Only Tranches and Interest-Only Tranches: Principal-only (PO) tranches receive only principal payments from the collateral pool, whereas interest-only (IO) tranches receive only interest payments from the collateral pool. Both tranches are therefore created by dividing cash flows from the mortgage collateralinto the portion that is principal repayment and the portion that is interest. Theprincipal repayment cash flows are distributed to one bond, the PO, and the interestcash flows are distributed to a second bond, the IO. Investors in PO bonds are ultimately paid the face value of their bonds as borrowers eventually make the principal payments on their mortgages. The logic behind a PO is that investors buy these bonds at a discount from face value and eventually receive the face value through the scheduled principal repayments and prepayments received from the mortgages. PO tranches are positively exposed to extension risk in that their values decline when prepayments slow, since they receive no coupons. An IO bond has a notional principal used to compute each interest payment. The cash flows received by investors in IOs decline as the principal is paid down. IO tranches are positively exposed to contraction risk in that their values decline when prepayments accelerate, since their payments are only interest because the notional principal is not repaid.

Question 19

How does PO and IO tranches react to interest rates ?

Answer 19

Prepayment sensitivity tends to be severe for POs and IOs, with one generally
profiting when the other suffers. For example, in the case of POs on fixed-rate mortgages, when interest rates decline, the speed of prepayments typically accelerates. This contraction in longevity reduces the life of both the IO and the PO. PO tranches benefit from quicker receipt of their only cash flows: principal repayments in the fixed amount of the PO’s face value. IO tranches suffer from principal reductions, since their only cash flows (interest payments) are proportionately reduced. On the other hand, when interest rates increase, the speed of prepayments declines, and the PO investor is paid the face value further in the future, lowering its effective return, while the IO receives a longer annuity of interest payments. Both tranches can be issued with adjustable- and fixed-rate underlying mortgages.

Question 20

What is a Floating-Rate Tranches and a inverse floater tranche ?

Answer 20

Floating-rate tranches earn interest rates that are linked to an interest rate index, such as the London Interbank Offered Rate (LIBOR), and are usually used to finance collateral pools of adjustable-rate mortgages. A collateral pool of adjustable-rate mortgages provides a stream of variable interest rate payments that can flow through to floating-rate tranches, which also have floating coupons. Floating-rate tranches can be structured to have rates that move more than the underlying index (e.g., twice the floating rate) or even in the opposite direction, which is known as an inverse floater tranche. An inverse floater tranche offers a coupon that increases when interest rates fall and decreases when interest rates rise.
Floating-rate tranches can have specified upper and lower limits to their adjustable
coupons.

Question 21

The emergence of structured mortgage products in the past
several decades coincides with substantially reduced mortgage rate spreads, suggesting that structured products have enabled hundreds of millions of homeowners to enjoy substantially lower financing costs.

Question 22

The senior, investment-grade-rated tranches are generally viewed as fixed-income securities, since they have limited expected exposure to default risk and are therefore primarily analyzed in the context of interest rate risk. In contrast, the most junior tranches are generally viewed and analyzed as risky securities substantially influenced by the risks of the underlying real estate rather than being influenced primarily by interest rate risks. Even a single large default can have a considerable impact on the performance of these junior securities.

Question 23

What is Structural credit risk models ?

Answer 23

Structural credit risk models use option theory to explicitly take into account credit risk and the various underlying factors that drive the default process, such as
(1) the behavior of the underlying assets, and (2) the structuring of the cash flows (i.e., debt levels). Typically, structural models directly relate valuation of debt securities
to financial characteristics of the economic entity that has issued the credit security. These factors include firm-level variables, such as the debt-to-equity ratio and the volatility of asset values or cash flows. The key is that credit risk is understood
through analysis and observation of the entity’s underlying assets and its financial structure.

Question 24

How does Merton’s call option view of capital structure works ?

Answer 24

The call option view of capital structure views the equity of a levered
firm as a call option on the assets of the firm. The call option implicit in equity has a strike price equal to the face value of the debt and an expiration date equal to the maturity date of the debt. If the firm does well, the firm pays its debt holders fully when the debt matures, and the assets of the firm belong to the shareholders. If the firm does poorly, the shareholders can declare bankruptcy and walk away from the firm, leaving the assets to the debt holders.

Question 25

Specifically, if the value of the assets of the firm equals the sum of the liabilities plus equity, and if equity is a call option, then owning debt is equivalent to owning the assets and writing a call option. In other words, owning debt is equivalent to owning a covered call, meaning being long assets and short a call option on those assets.

Question 26

How does Merton’s put option view of capital structure works (throught put-call parity ) ?

Answer 26

The put option view of capital structure views the equity holders of a levered firm as owning the firm’s assets through riskless financing and having aput option to deliver those assets to the debt holders. The risky debt of a levered firm can be viewed as being equivalent to owning a riskless bond and writing a put option that allows the stockholders to put the assets of the firm to the debt holders without further liability (i.e., in exchange for the debt).

Question 27

How does the intrerest conflict between the stockholders and the bondholders works ?

Answer 27

There is an inherent conflict between the stockholders and the bondholders with regard to the optimal level of risk for a firm’s assets. The equity holders, with their long position in a call option, prefer higher levels of risk, especially when the value of the firm’s assets is near or below the face value of the debt. This is because the value
of the equity at the maturity of the debt is the maximum of zero and the difference between the value of the firm’s assets and the face value of the debt. Conversely, bondholders prefer safer projects and reduced asset volatility, as seen through their short position in a put option. The conflict of interest may be viewed as a zero-sum game in which managers can transfer wealth from bondholders to stockholders by increasing the risk of the firm’s assets (or vice versa).

Question 28

What is the view of Assets using put-call parity (equation) ?

Answer 28

Assets = [Call] + [Riskless Bond − Put]

Call = Equity
Riskless Bond = Debt
The reduction in the value of the debt by the value of the put option is the market’s price for bearing the credit risk of the firm.

Question 29

How to find the value of the put on a corporate debt using a bond ? Ex:

Answer 29

Consider a firm with $50 million in assets and $25 million in equity value. The
firm has one debt issue: a zero-coupon bond maturing in one year with a face
value of $30 million. A riskless zero-coupon bond of the same maturity sells
for 90% of its face value. What is the value of the firm’s debt? What is the value
of a one-year put option on the firm’s assets with a strike price of $30 million?
Since the assets are worth $50 million and the equity is worth $25 million,
the firm’s risky debt must be worth $25 million, since Assets=Equity + Risky
Debt. Since the riskless bond in Equation 23.3 is worth $27 million, the put
option must be worth $2 million.

Question 30

What are the 2 Merton’s structural model and its extensions major potential advantages ?

Answer 30

1- The structural approach tends to rely on data from equity markets, such as observed stock price volatilities or implied stock price volatilities backed out of option prices. Since equity markets are generally more liquid and transparent than corporate bond markets, some argue that equity markets provide more reliable information than credit markets provide.

2- Structural models are well suited for handling different securities of the same issuer, including bonds of various seniorities and convertible bonds. The different securities or tranches rely on the same assets with the same asset parameters.

Question 31

What are the 3 Merton’s structural model and its extensions major potential disadvantages ?

Answer 31

1- . If equity prices are highly unreliable, then estimates of asset volatility and values are also highly unreliable. For example, private equity or real estate equity valuations may be unreliable sources to the extent that the valuations are not based on liquid markets.

2- Current data on a firm’s or structure’s liabilities may be unreliable and, in the case of sovereign issuers, may be unworkable.

3- The valuations generated by simple structural models are sometimes unreasonable, especially for short-term, very high-quality debt and for debt that is very near default.

Question 32

What happens in an interest rate cap ?

Answer 32

In an interest rate cap, one party agrees to pay the other when a specified reference rate is above a predetermined rate (known as the cap rate, which is similar to the strike price of a European call option).

Question 33

What is a caplet ?

Answer 33

A caplet is an interest rate cap guaranteed for only one specific date.

Question 34

What is a cap ?

Answer 34

A cap is a series of caplets, and its price is equal to the sum of the prices of the caplets, which, in turn, can be valued using various term-structure models and a procedure similar to the Black-Scholes option pricing model.

Question 35

Example of intrest cap:

Answer 35

The contract is for three years, the
strike rate is 3%, the reference rate is three-month LIBOR, settlement is every three months, and the notional value is $10 million. Thus, every three months for the next three years, B will pay A if three-month LIBOR exceeds the strike rate of 3% at settlement. For example, suppose that the three-month LIBOR (i.e., the reference rate) is 4% on a settlement date. In this case, B will pay A $25,000, which is given by (4% – 3%) × $10,000,000/4=$25,000.

Question 36

What is the maximum a purchaser of an interest rate cap or floor can lose ?

Answer 36

If the LIBOR is below the strike rate, there will not make any payment to the purchaser. Thefore the maximum amount that can be lost from entering into this options contract is the up-front premium that was paid for the option.

Question 37

What happens in an interest rate floor?

Answer 37

In an interest rate floor, one party agrees to pay the other when a specified reference rate is below a predetermined rate (known as the floor rate, which is analogous to the
strike price of a European put option).

Question 38

What is a floorlet ?

Answer 38

A floorlet is an interest rate floor guaranteed for only one specific date.

Question 39

What is a floor ?

Answer 39

A floor is a series of floorlets, and its price is equal to the sum of the prices of the floorlets. Similar to caps, floors can be valued using derivative pricing models like the Black-Scholes option pricing model.

Question 40

Why would an investor enter into an interest rate cap or floor ?

Answer 40

Issuers of floating-rate debt can buy caps contracts to hedge against the possibility of increases in short-term interest rates (insurance). –> Buy with a premium

Floors can be purchased by lenders in floating-rate debt to hedge against the possibility of declining short-term interest rates. A seller in an interest rate floor is compensated for guaranteeing the interest rate.

Question 41

Example of intrest floor:

Answer 41

Party A buys the interest rate floor from party B with the following terms: The contract is for four years, the strike rate is 3%, the reference rate is three-month LIBOR, settlement is every three months, and the notional value is $20 million. Thus, every three months for the next four years B will pay A if three-month LIBOR is less than the strike rate of 3% at settlement. For example, suppose that the three-month LIBOR (i.e., the reference rate) is 1% on a settlement date. In this case, B will pay A $100,000, which is given by (3% – 1%) × $20,000,000/4=$100,000. Suppose instead that three-month LIBOR is 4% on a settlement date. In this case, B will not make any payment to A.

Question 42

How does default on a bond portfolio affect the waterfall cash flow distribution ? Ex:

Answer 42

Suppose that the CDO depicted in Exhibit 23.5 experiences defaults in $50 million of the assets with 30% recovery. What will happen to the tranches? First, note that the 30% recovery reduces the losses to 70% of $50 million ($35 million). After the equity tranche is eliminated due to the first $10 million in defaults, the mezzanine tranche is eliminated due to the next $20 million in defaults. The remaining $5 million of defaults will bring down the notional value of the senior tranche from $70 million to $65 million. The senior tranche has first priority to the recovered value of the bonds ($15 million), which may be distributed to the senior tranche, further reducing its notional value to $50 million.

Question 43

What are lower attachment and upper attachment point ?

Answer 43

The first percentage loss in the collateral pool that begins to cause reduction in a tranche is known as the lower attachment point, or simply the attachment point. The higher percentage loss point at which the given tranche is completely wiped out is known as the upper attachment point, or the detachment point.