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Suppose that the Second United Bank has originated a portfolio of loans.The bank knows that the aggregate payoff on this portfolio call this portfolio S) will be $250 with probability 0.8 and $80 with probability 0.2.However, investors are unable to distinguish portfolio S from portfolio R.Portfolio R has an aggregate payoff of $250 with probability 0.6 and $80 with probability 0.4.Nevertheless, the investors believe that there is a 0.5 probability that the portfolio is S.The cost of communicating the true value of the portfolio is $18.If the bank keeps the portfolio on the books, its net profit is 3% of the true value minus a fixed cost of $2.50.The bank's net profit from origination and servicing is 2% of the value of the securitized portfolio.Everybody is risk-neutral.
-Suppose the cost of communication drops to $5.Should the bank securitize the loans with communication relative to funding and keeping them on the books?
A)Yes, this generates a net profit of $3.58.
B)Yes, this generates a net profit of $4.22.
C)Yes, this generates a net profit of $5.76.
D)No, this generates a net loss of $3.98.
E)No, this generates a net loss of $6.88.

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Suppose that the Second United Bank has originated a portfolio of loans.The bank knows that the aggregate payoff on this portfolio call this portfolio S) will be $250 with probability 0.8 and $80 with probability 0.2.However, investors are unable to distinguish portfolio S from portfolio R.Portfolio R has an aggregate payoff of $250 with probability 0.6 and $80 with probability 0.4.Nevertheless, the investors believe that there is a 0.5 probability that the portfolio is S.The cost of communicating the true value of the portfolio is $18.If the bank keeps the portfolio on the books, its net profit is 3% of the true value minus a fixed cost of $2.50.The bank's net profit from origination and servicing is 2% of the value of the securitized portfolio.Everybody is risk-neutral.
-Suppose the cost of communication drops to $5.Should the bank securitize the loans with communication relative to funding and keeping them on the books?
A)Yes, this generates a net profit of $3.58.
B)Yes, this generates a net profit of $4.22.
C)Yes, this generates a net profit of $5.76.
D)No, this generates a net loss of $3.98.
E)No, this generates a net loss of $6.88.

Quizplus · Accepted Answer

- First, let's calculate the expected payoff of portfolio S and R:
- Portfolio S: $250 x 0.8 + $80 x 0.2 = $220
- Portfolio R: $250 x 0.6 + $80 x 0.4 = $190
- Next, let's calculate the expected value of the portfolio if it is securitized:
- Expected value = 0.5 x $220 + 0.5 x $190 = $205
- The cost of communicating the true value of the portfolio is irrelevant since it is the same for both securitization and keeping the portfolio on the books.
- If the bank securitizes the loans, its net profit is 2% x $205 = $4.10.
- If the bank keeps the portfolio on the books, its net profit is 3% x $250 - $2.50 = $5.50.
- Therefore, the bank should keep the portfolio on the books if the cost of communication is higher than $5, and securitize the loans if the cost of communication is lower than $5.
- In this case, the cost of communication is $5, so the bank should securitize the loans and generate a net profit of $4.10. Therefore, the answer is B.

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