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Structured finance security


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)


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


CDOs and credit-ratings of senior tranches


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


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


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


lower correlation means relatively "safer" senior tranches


Overcollateralization of CDOs


degree of protection offered by the more junior tranches

more protection > higher rating of senior tranche


Notional value of CDO


total potential bond payout (payments are made if bonds do not default)


Default for junior and senior tranches


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


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


uses a binomial distribution

p(k) = (n choose k) * prob default ^ k * (1 - prob. default)^(n - k)


Senior and junior tranche payouts of CDOs


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


expected payout = probability weighted average of the tranche payouts


Relationships b/w expected payout of each tranche (2)


1. generally E[payout(Jr)] < E[payout(Sr)] due to increased riskiness
2. with perfect correlation (rho = 1), E[payout(Jr)] = E[payout(Sr)]


Relationships b/w correlation and default probabilities (3)


1. when bonds are uncorrelated (rho = 0), default prob. of senior tranche is much < default prob. of junior tranche
2. 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)
3. As correlation decreases, pr(default - senior) decreases and pr(default - junior) increases


Relationship between default probability and expected bond payout


as default probability increases, expected payoff decreases (junior tranche is the most sensitive)


Relationship between default correlation and riskiness of senior tranche


as default correlation increases, more risk is shifted to the senior tranche


Price of a tranche in a CDO


price = PV(expected tranche payout)


Relationship between price, yield, and correlation of junior and senior tranches in a CDO


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)


1. increase the # of assets in the pool
2. apply the CDO structure more than once




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)


1. likelihood of default


2. severity of a loss, given default

>> measure of expected payoff


Issues with determining credit ratings of structured finance securities/CDOs (2)


1. 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


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)


there was:
1. higher than expected default correlation from overlapping geography & vintages of mortgages
2. higher than expected probability of default b/c of deteriorating credit quality of sub-prime borrowers
3. lower than expected asset recovery values b/c of low housing prices
4. 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)


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


credit ratings do not consider systematic risk


Implication of credit ratings ignorance of systematic risk


possible for 2 securities with the same credit rating to have drastically different exposure to systematic risk


Relationship b/w degree of systematic risk and yield spread (2)


1. if there is no systematic risk, yield spread is consistent with expected losses
2. if there is high systematic risk, a significant yield spread is required to compensate for additional systematic risk


Systematic risk of senior tranches in CDOs


high systematic risk exposure in senior tranches because losses are magnified as the economic conditions worsen