Coval Flashcards
Structured finance security
Coval
pooling of economic assets (e.g. loans, bonds, and mortgages) and issuance of a prioritized capital structure of claims, or tranches, against these pools
Collateralized debt obligation (CDO)
Coval
prototypical structured finance security that uses tranches to prioritize payments with the most junior tranches absorbing losses first, working up to the most senior tranches
Purpose of CDOs and credit-ratings of senior tranches
Coval
differing tranche priorities enables CDOs to convert underlying assets with high credit risk into highly-rated investment vehicles (credit rating of senior tranches is > average credit rating of underlying assets)
Goal of structured finance
Coval
create as many senior tranches as possible with higher credit ratings than the average rating of securities in the pool
Problem with structured finance/CDO securities
Coval
high ratings are extremely sensitive to assumptions regarding underlying assets such as default probabilities, correlations, and recovery rates
Correlation and relative safety of the most senior tranches
Coval
lower correlation means relatively “safer” senior tranches
Overcollateralization of CDOs
Coval
degree of protection offered by the more junior tranches
more protection > higher rating of senior tranche
Notional value of CDO
Coval
total potential bond payout (payments are made if bonds do not default)
Default for junior and senior tranches
Coval
junior tranches default if at least 1 bond defaults
senior tranches only default if all bonds default
Probability that one, both, and neither bond default in a 2-bond CDO structure
(Coval)
P(NN) = no bond defaults
= (1 - prob. default)^2 + rho * prob. default * (1 - prob. default)
P(DD) = both bonds default
= prob. default^2 + rho * prob. default * (1 - prob. default)
P(ND) = prob. 1 bond defaults
= 1 - P(NN) - P(DD)
rho = default correlation
Probability of default with > 2-bond CDO structure
Coval
uses a binomial distribution
p(k) = (n choose k) * prob default ^ k * (1 - prob. default)^(n - k)
Senior and junior tranche payouts of CDOs
Coval
senior tranche payout = min(size of senior tranche, total payout)
junior tranche payout = min(size of junior tranche, total payout - senior payout)
Expected payout for each tranche
Coval
expected payout = probability weighted average of the tranche payouts
Relationships b/w expected payout of each tranche (2)
Coval
- generally E[payout(Jr)] < E[payout(Sr)] due to increased riskiness
- with perfect correlation (rho = 1), E[payout(Jr)] = E[payout(Sr)]
Relationships b/w correlation and default probabilities (3)
Coval
- when bonds are uncorrelated (rho = 0), default prob. of senior tranche is much < default prob. of junior tranche
- when bonds are perfectly correlated (rho = 1), prob. default for either tranche = prob. default for the individual bonds (senior tranche does not benefit from CDO)
- As correlation decreases, pr(default - senior) decreases and pr(default - junior) increases
Relationship between default probability and expected bond payout and tranche sensitivity
(Coval)
as default probability increases, expected payoff decreases (junior tranche is the most sensitive)
Relationship between default correlation and riskiness of senior tranche
(Coval)
as default correlation increases, more risk is shifted to the senior tranche
Price of a tranche in a CDO
Coval
price = PV(expected tranche payout)
Relationship between price, yield, and correlation of junior and senior tranches in a CDO
(Coval)
generally price(Jr tranche) < price(Sr tranche) and the junior tranche will have higher yield due to increased riskiness
w/perfect correlation, price(Jr tranche) = price(Sr tranche)
Ways to ensure as many tranches as possible have credit ratings > average credit rating of the underlying assets (2)
(Coval)
- increase the # of assets in the pool
2. apply the CDO structure more than once
CDO^2
Coval
CDO structure consisting of 2 or more junior tranches (ex: junior tranche from the original CDO + a junior tranche of a separate CDO)
Credit ratings are typically based on (2)
Coval
- likelihood of default
or
- severity of a loss, given default
> > measure of expected payoff
Issues with determining credit ratings of structured finance securities/CDOs (2)
(Coval)
- underlying pool may have many correlated assets
2. CDOs magnify the impacts of imprecise default estimates (and CDO^2s even more so)
Sub-prime mortgages and relationship to structured finance securities
(Coval)
mortgages that did not meet size & credit quality requirements to be packaged into mortgage-backed securities and resold on the capital markets with a government guarantee
sub-prime mortgages were repackaged into non-backed collateralized mortgage obligations (CMOs) that were similar to CDO^2s
Impacts of increased default rates on mortgage-backed securities during the sub-prime crisis (4)
(Coval)
there was:
- higher than expected default correlation from overlapping geography & vintages of mortgages
- higher than expected probability of default b/c of deteriorating credit quality of sub-prime borrowers
- lower than expected asset recovery values b/c of low housing prices
- prevalence of CMOs (= CDO^2s) magnified the impacts of the preceding assumptions differing from expectations
Systematic risk in the context of CDOs (and high and no systematic risk)
(Coval)
whether a security is more likely to default when there is a recession or stock market decline
high systematic risk when default likelihood is high when the economy is poor
no systematic risk when default likelihood is independent of economic state
Credit ratings and systematic risk
Coval
credit ratings do not consider systematic risk
Implication of credit ratings ignorance of systematic risk
Coval
possible for 2 securities with the same credit rating to have drastically different exposure to systematic risk
Yield spread with and without systematic risk
Coval
without systematic risk: yield spread is consistent with expected losses
with high systematic risk, a significant yield spread is required to compensate for additional systematic risk
Systematic risk of senior tranches in CDOs
Coval
high systematic risk exposure in senior tranches because losses are magnified as the economic conditions worsen
Reasons the yields on structured finance products (/CDOs) did not reflect the underlying risks (2)
(Coval)
- credit ratings understated default risks b/c they were based on favorable extrapolations of economic conditions
- yields did not account for exposure to systematic risk
Other issues related to the rise & fall of the structured finance market (4)
(Coval)
- rating agencies misestimated default probabilities and correlations
- banks were happy to collect fees for structuring and origination
- bond issuers pay for credit ratings > conflict of interest
- analysts & managers knew how actions would affect profits which conflicted with accurate risk assessments
Coval’s solution to parameter uncertainty in the structured finance market and its implication
(Coval)
use a Bayesian approach to acknowledge parameter uncertainty in the credit rating process
implication: fewer AAA-rated tranches
Recovery rate
Coval
amount of potential payment paid in the event of default
How to measure sensitivity of tranches to changes in default rates
(Coval)
calculate probability of jr & sr default before and after change
largest change is most sensitive (senior)
