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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.
-What is the bank's net profit from securitization without communication?
A)$1.57
B)$3.98
C)$4.28
D)$5.66
E)$8.75

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Use the following information for questions 
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.
-What is the bank's net profit from securitization without communication? 
A)$1.57
B)$3.98
C)$4.28
D)$5.66
E)$8.75

Quizplus · Accepted Answer

The expected value of the portfolio S is:

E(S) = 0.8($250) + 0.2($80) = $220

The expected value of the portfolio R is:

E(R) = 0.6($250) + 0.4($80) = $190

The expected value of the portfolio, taking into account the investors' belief, is:

E(V) = 0.5($220) + 0.5($190) = $205

The bank's net profit from securitization without communication is:

0.02($205) - $2.50 = $1.57

If the bank communicates the true value of the portfolio, the investors will always choose the portfolio with higher expected value, which is S. The bank's net profit from keeping the portfolio on the books is:

0.03($250) - $2.50 = $5.50

The cost of communicating the true value of the portfolio is $18, which reduces the net profit from keeping the portfolio on the books to:

$5.50 - $18 = -$12.50

Therefore, the best choice for the bank is to securitize the portfolio without communication, with a net profit of $1.57.

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