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Bank A plans to invest a 3-year unsecure par bond issued by ABC Corp. with a face value of
$100,000,000 that pays a 6% coupon annually. The marginal default rates (conditional on no previous
default) during the first , second, and third years are 2%, 3% and 4% respectively. The recovery rate is
10% in the event of default. Bank A also wants to hedge its exposure by having a total return swap (TRS)
with Bank B and promises to pay the interest plus the change in the market value of the bond in
exchange for LIBOR plus 30 basis points. Please answer the following questions
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What is the value change of the bond under the modified duration method, given the
assumption of yield rising is 1%?
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2
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What is the cumulative probability of default over the next three years and average annual
credit risk premium?
6
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3
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If the market value of the bond has decreased by 2% and LIBOR is 5% after one year, What
would be the net obligation of Bank A?
6
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4
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A portfolio analyst of Bank A wants to evaluate RAROC of the bond alone with the following
additional assumptions of internal prospects. What would be RAROC ?
7
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Funding Cost=$2,000,000
Operational Cost=$1,000,000
Economic Capital=$2,000,000
Return on the Economic Capital=$50,000
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In 2014 world cup, 8 European teams and 8 American teams entered the playoff games. Let Q be
the event that there are 4 European teams and 4 American teams in the quarter-final; S be the event that
there are 2 European teams and 2 American teams in the semi-final; and F be the event that there are
one European team and one American team in the final. Assuming every team in the playoff has the
equal probability to win in each game, and is matually independent.
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Find
the probabilities of the events Q, S∩Q and F∩S∩Q.
15
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2
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Find
the probability of the event S given that the event Q had been happen. That
is P(S|Q).
5
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3
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Find
the probability of the event F given that event Q and S had been happen.
That is P(F|S∩Q).
5
(note: To get full credit, you need to express your answer in fraction form with numerator
and denominator as relative primes. Get partial credit for answer with formula only.)