In class, we constructed a CDO utilizing three bonds. We saw that by utilizing “pooling”, and “prioritizing” default claims, we created securities with attractive characteristics. Essentially, we “re-packaged” existing debt that is “paripassu” into priority claims on the collateral of the pool. The result is, a portion of the issued debt has reduced probability of default and is of higher quality than the collateral of the pool – that securitizes the debt.
a) Assume you purchase four bonds. Create a CDO and issue four tranches of bonds.
Model the pool and display the probabilities of default, the pay-offs, and recovery rates. Calculate the current price of each bond and the YTM. Calculate the total market value of the pool.
Collateral:
1) The collateral has a total value of 400 with 100 allocated to each bond
2) Bonds are risky, speculative grade bonds
3) Defaults are independent and occur only at maturity
4) At maturity, each bond pays 100
5) Each bond has a 8% probability of default
6) Each bond has a 50% recovery rate 7)Risk free rate is 3.5%
b) Issue four tranches of bonds, the size of each tranche will be as follows:
1) Senior Tranche ?
2) Mezzanine Tranche ?
3) Subordinated Mezzanine Tranche ?
4) Subordinated Tranche ?
c) Calculate the price, YTM, default probability and recovery rates for each issue. Were you successful in creating a CDO with superior characteristics than the individual bonds?
d) Given, your answer to item C, make any changes you like to the size of the tranches to improve the characteristics of the bonds being issued.
e) Why do we assume defaults are independent?
The attached spreadsheet displays the format and necessary calculations. Please follow this format.
GSBM 698
1) Construct a CDO with 3 risky, speculative-grade bonds
2) Defaults are independent and occur only at maturity of the bond
3) At maturity each bond pays 100
4) Each bond has a 10% risk-nuetral probability of default
5) Each bond has a 40% recovery rate
6) Risk Free Rate is 6%
1) Price the Bonds
Price: $ 88.53 =EXP(-RiskFreeRate)*((1-DefaultProb)*Princ+(DefaultProb*(RecoverRate*Princ)))
Defaults Prob. Payoff Senior Mezzanine Subordinated
0 72.90% 300 140 90
1 24.30% 240 140 90
2 2.70% 180 140 40
3 0.10% 120 120 0
Price 131.83 83.40 50.35
Yield 0.0601 0.0761 0.3296
Defaul Prob. 0.001 0.028 0.271
Avg Recovery 0.8571 0.4286 0.1281
experience a default. Avg Recovery is Recovery Amount divided by the tranche’s
original principlemultipled by the ratio of Probability of Default and Cumulative Probability of Default.
Assuming Bond Defaults are Correlated
Number of Total Bond Payoff
Defaults Prob. Payoff Senior Mezzanine Subordinated
0 90.00% 300 140 90 70
1 0.00% 240 140 90 10 2 0.00% 180 140 40 0
3 10.00% 120 120 0 0
Price 129.96 76.28 59.33
Yield 0.0744 0.1654 0.1654
Defaul Prob. 0.100 0.100 0.100
Avg Recovery 0.8571 – –
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