An investment bank has created a CDO by pooling 100 bonds which will either pay off $0 (in case of default) or pay off $1.
The CDO has three risk classes rated AAA, BBB, and CCC with face values of $70, $20, and $10, respectively.
The current prices of the tranches are respectively, $66, $12, and $1.
Consider the strategy of buying one unit (out of 100 units) of the BBB class and shorting one unit of the AAA tranche.
How many bonds will have to default for this portfolio to make money?
Please help. I really don't know where to begin on this one. I really need help. thank you for helping.
To determine how many bonds will have to default for the portfolio to make money, we need to calculate the net profit or loss from the strategy of buying one unit of the BBB class and shorting one unit of the AAA tranche.
Let's begin by understanding the structure and payoff of the CDO. The CDO is created by pooling 100 bonds, each with a payoff of either $0 (in case of default) or $1. The CDO has three risk classes: AAA, BBB, and CCC. The face values of these tranches are $70, $20, and $10, respectively.
Now, let's analyze the payoff for each tranche:
- AAA tranche: This is the highest-rated tranche with a face value of $70. It will be the last to face losses. If there are no defaults, it will pay off $70. If any of the 100 bonds default, it will lose $1 for each defaulted bond.
- BBB tranche: This tranche has a face value of $20. It will absorb losses after the AAA tranche but is still relatively safe. If there are no defaults, it will pay off $20. If any of the 100 bonds default, it will lose $1 for each defaulted bond.
- CCC tranche: This tranche has a face value of $10. It is the riskiest tranche and will absorb the first losses. If there are no defaults, it will pay off $10. If any of the 100 bonds default, it will lose $1 for each defaulted bond.
Now let's calculate the net profit or loss from the strategy of buying one unit of the BBB class and shorting one unit of the AAA tranche:
- Buying one unit of the BBB class at a price of $12 means we pay $12.
- Shorting one unit of the AAA tranche means we receive $66 (since the current price is $66, shorting means selling at that price).
So, the initial net cash flow for this strategy is $66 (received from shorting AAA) - $12 (paid for BBB) = $54.
To make money from this strategy, the total loss from defaults should exceed the initial net cash flow. Since each defaulted bond causes a loss of $1 for both the AAA and BBB tranches, we need the number of defaulted bonds to be greater than $54.
Therefore, the portfolio will make money if the number of defaults is greater than 54.
Note: This analysis assumes that the CDO tranches are priced identically to their expected payout in an efficient market. It's important to note that the pricing and risk associated with CDOs can be complex and influenced by various factors, so this answer is a simplified explanation based on the given information.