Coval

Question 1

Explain how a collateralized debt obligation is created

Answer 1

A CDO is formed by pooling together fixed-income assets such as loans, bonds and mortgages and prioritizing payments into tranches.

Question 2

Describe how CDOs can be used to convert underlying assets with high credit risk into highly-rated investment vehicles.

Answer 2

The prioritization of losses allows senior tranches to obtain higher credit ratings than underlying assets.

Since junior tranches absorb losses first, senior tranche is protected, which drives credit rating up for senior tranches.

More protection leads to higher rating.

Question 3

Explain how 2008 financial crisis showed these securities were far riskier than originally advertised

Answer 3

Ability of structured finance to repackage risks and create safe assets from otherwise risky collateral led to dramatic expansion in issuance of structured securities.

2008 financial crisis showed that these securities were far riskier for 2 main reasons:
1. Most securities could only have received high credit ratings if rating agencies were extremely confident about their ability to estimate default risks and how likely defaults were correlated.
2. Process substitutes risks that are largely diversified for risks that are highly systematic. Securities produced have far less chance of surviving a severe economic downturn than traditional corporate securities of equal rating.

Question 4

Calculate the number of fixed income assets that default

Answer 4

pNN = (1-pD)^2 + rhopD(1-pD)

pDD = PD^2 + rhopD(1-pD)

pND = 1 - pNN - pDD

Question 5

What is the relationship between correlation and safety of senior tranche?

Answer 5

The lower the default correlation, the more improbable is that all assets default simultaneously.

Thus, the safer senior-most claim can be made.

Question 6

What is the relationship between default probability and expected payoff. Which tranche is the most impacted?

Answer 6

As pD increases, expected payoff on collateral decreases monotonically.

Junior tranche is the most impacted by increase in pD.

Question 7

Calculate the junior and senior tranche payout.

Answer 7

Senior payout = min(senior width, tot payout)

Junior payout = min(junior width, tot payout - senior payout)

Question 8

Explain what it means if senior tranche of CDO has attachment point equals to 50% - 100% of notional principal.

Answer 8

This means senior tranche begins to absorb losses once portfolio loss exceeds 50% (at least one defaults) and continue to do until portfolio loss reaches 100% (both default)

Question 9

Calculate the price of a tranche

Answer 9

Price = PV of expected tranche payout

Question 10

Does junior or senior tranche has lowest price? Is there an exception?

Answer 10

Except when correlation = 1, junior tranche has lower price.

Question 11

Explain why junior tranches have higher promised yields than senior tranches.

Answer 11

Junior tranches are riskier, thus they have a higher promised yield.

This is meant to compensate investors for the increased risk.

Question 12

Describe 2 ways to increase number of tranches with credit ratings higher than average rating of underlying pool of assets.

Answer 12

1. Increase the number of assets in underlying pool.
   This will reduce default risk of tranches and allow more of them to obtain AAA-rating.
2. Create a CDO^2 by applying CDO construction 2 times.
   We can construct a second CDO where the underlying pool of assets is comprised of the junior tranches from original CDO and junior tranche of a separate CDO.

Question 13

Identify 2 components that underlie credit ratings and why they overstate true credit risk of security.

Answer 13

1. Likelihood of default
2. Severity of loss given a default

These components understate true credit risk of security because they fail to consider systematic risk:
1. The default probability of CDO tranches is significantly impacted by correlation
2. CDOs magnify the effects of imprecise estimates of default probability and default recovery amounts, as well as model errors.

Question 14

Briefly describe a solution proposed by regulators to account for uncertainty

Answer 14

Regulators proposed using a “.SF” rating modifier for structured finance instruments instead of typical rating scores due to uncertainty in default and correlation estimates.

Question 15

Fully describe how sub-prime mortgages contributed to great recession.

Answer 15

1. Sub-prime mortgages were not eligible for purchase by government agencies. They were either helpful by original issuer of mortgage or sold directly in secondary markets.
2. Eventually, many of these mortgages found their way into private mortgage-backed bonds without government guarantee.
3. These mortgage-backed bonds were often repackaged into CMO which operated like CDO^2.
4. As house prices decline, there were significant increase in default rates. The impact on CMOs was much worse than expected due to overlap in geographical and vintages in mortgage pools.
5. In addition, prob of default was higher than expected due to deterioration in credit quality of subprime borrowers.
6. The final result was a massive decline in asset values due to assets being sold off for extremely low prices.

Question 16

Explain how exposure to systematic risk impacts yield spread for a security.

Answer 16

Credit ratings are based on security’s expected payoff.

They do not take into account whether or not a security is more likely to default when there is a stock market or an economic recession.

Thus, it’s possible for 2 securities with the same credit rating to have drastically different levels of exposure to systematic risk.

The degree of systematic risk present in a security has a meaningful impact on potential yield spread for the security:

1. If a security’s default likelihood is indecent of economic state, the its yield spread will be consistent with compensation for expected losses.
2. If a security’s default likelihood is at its highest when economy is poor, then it should commande a significant yield spread to compensate for additional systematic risk.

Investors in senior tranches of CDOs are exposed to significant systematic risk since their losses are magnified as economy worsens.

As a result, they ought to earn a yield spread proportional with level of risk they are bearing, which means greater than single-name securities with same credit rating.

Question 17

Describe 2 reasons why yields associated with senior tranches of CDOs did not adequately reflect the underlying assets.

Answer 17

1. Credit ratings understated the default risks of these products since they were based on rating agencies’ extrapolation of favorable economic conditions.
2. The yields did not account for exposure of CDOs to systematic risk. As a result, senior tranches investors were under-compensated for their risk exposure and junior tranche investors were over-compensated for their risk exposure.

Question 18

Identify 3 model errors that contributed to improper CMOs credit ratings.

Answer 18

1. Failed to consider the possibility of declines in home prices.
2. Failed to capture impacts of imprecise estimates of default correlations.
3. Failed to capture impacts of imprecise estimates of default probabilities.

Question 19

In addition to model error, explain how regulators and investors also contributed to improper CMOs credit ratings.

Answer 19

Regulators and investors failed to recognize that small errors in model assumptions were magnified when dealing with CDOs.

Question 20

Briefly explain the conflict of interest in CDO rating. What was the conclusion?

Answer 20

Issuer, not investor, pays for rating.

Process and complexity of creating structure finance products require rating agencies to become part of UW team rather than acting as agents for outside investors.

Conclusion:
1. No more severe for structured finance products than for single-name credit products.
2. Reputation is a strong force against bad behaviour in both markets.
3. No fundamental difference in rating process.

Question 21

Briefly explain why investment banks were hit particularly hard during fall of structured finance assets.

Answer 21

Capital requirements for AAA-rated securities are half as much as other investment-grade securities.

Naturally, the banks gravitated to AAA-rated securities that offered the most attractive yields (senior tranches of CDOs).

In reality, yield spreads were not high enough to compensate exposure to systematic risk.

Investment banks also had a false sense of security due to apparently “safe” ratings.

When investment bank was unable to sell a senior tranche, it would hold onto it.

When market collapsed, investment banks were left holding a large pool of low-quality assets such as subprime mortgages.

Question 22

List 2 takeaways from Coval paper.

Answer 22

1. Small errors that would not have material impact in single-name market are magnified when dealing with CDOs and CDO^2s.
   To solve this during credit rating process, a Bayesian approach can be used to explicitly acknowledge parameter uncertainty.
2. CDOs are often more exposed to systematic risks than single-named securities which can lead to massive losses during economic downturns.
   Credit ratings fail to account for exposure to systematic risk.

Question 23

Consider 3 securities: a cat bond, a junior tranche on CDO and a senior tranche on CDO^2. Which is preferred under CAPM?

Answer 23

Cat bond since uncorrelated with market risk, while CDOs risk is highly sensitive to market risk.

Question 24

Consider 3 securities: a cat bond, a junior tranche on CDO and a senior tranche on CDO^2. Describe the impact of an increase in default probability.

Answer 24

Junior tranche absorbs first losses and is affected the most if default probability increases.

Cat bond is uncorrelated with other bonds, so its probability of default increases 1-to-1.

Senior tranche is least affected as it is the las tranche to absorb losses after junior and mezzanine.

Question 25

Consider 3 securities: a cat bond, a junior tranche on CDO and a senior tranche on CDO^2. Describe the impact of an increase in default correlation.

Answer 25

CAT bond is not impacted by correlation. Junior tranche price will increase as risk shifts to higher tranche. Senior tranche price will decrease as risk increases from correlation defaults.

Question 26

Discuss 3 ways in which CAT bond CDOs differ from CMOs.

Answer 26

1. Cat bonds are not correlated with market returns, so they should not drop in value during market downturn. 2. Cat bonds can be selected to cover different geographical areas and therefore will not suffer from geographical concentration. 3. Cat reinsurance market is small compared to overall finance market, therefore is likely to be absorbed by market. 4. Cat bonds are fully collaterized therefore are not subject to credit risk like mortgages are. 5. Cat bonds have a credit rating provided, where individual subprime mortgages did not. Therefore, when packaged, we have a better idea of individual risk.

Question 27

Discuss 2 potential challenges from widespread CAT bond CDOs that could contribute to future financial crisis.

Answer 27

1. Global warming may cause flood more frequently occurs and if cat bond focuses on flood exposures, then it would increase the correlation. 2. It is very difficult to model cat events, so there is modelling error (model risk) associated with estimating probability of happening and triggering payment. 3. CAT risk being passed to investors may pose challenges as they may not truly understand the risk they would be taking on. Just like CMO investors did not fully understand. 4. Investors may misinterpret (assume naming convention discipline) AAA rating on CAT bond CDOs which would lead them to underestimating risk of default that could be caused by even one large catastrophe.

Question 28

Propose 2 possible regulations to alleviate challenges imposed by CAT bond CDOs.

Answer 28

1. Regulators could thoroughly review rating agency's models and mandate them to put in some conservative reduction in its ratings to account for greater level of uncertainty. 2. Regulators could put greater scrutiny on underlying assumptions used to rate the bonds and to determine default rates. This could lead to more transparency around uncertainty and error risk. 3. Put limits in place on how much investors could use CAT bond CDOs in their portfolios. 4. CDOs should be rated by independent rating agencies, not those hired by insurers/issuers of CDOs since this presents a conflict of interest.

Question 29

Assume single-name unrelated bond is rated AA by S&P. Propose a reasonable rating for senior tranche of CDO.

Answer 29

Senior tranche and unrelated bond may have similar assumed default risk, but senior tranch is much more sensitive to underlying assumptions, thus should receive lower rating. Reasonable answers could vary from A to C range. I would lean away from A given high correlation. A grade C denotes substantiak risk. D is in default so not applicable here.