Question

1. Borrowers Yash and Zara each are supposed to pay off their loans of $100,000 each next year. The bank which issued the loans has bundled the two loans and sold the cash flow to investors Alice and Bob. Alice will receive first $120,000 and Bob will receive any remaining cash flow.

If a borrower does not default, then he or she repays the loan in full. If a borrower defaults, 40% of the loan amount is recovered. Yash and Zara are both likely to default with probability 10%. Calculate the expected cash flows of Alice and Bob (no discounting needed) under the following probability distributions:

a.

	Zara defaults	Zara does not default
Yash defaults	1%	9%
Yash does not default	9%	81%

b.

	Zara defaults	Zara does not default
Yash defaults	5%	5%
Yash does not default	5%	85%

c.

	Zara defaults	Zara does not default
Yash defaults	10%	0%
Yash does not default	0%	90%

Answer 1

First, calculate the cash flows in case of the four scenarios mentioned:

Cash flows (CF):	Zara defaults	Zara does not default
Yash defaults	40,000+40,000 = 80,000	40,000+100,000 = 1,40,000
Yash does not default	100,000+40,000 = 1,40,000	100,000+100,000 = 2,00,000

a).

Probability (P)	Zara defaults	Zara does not default
Yash defaults	1%	9%
Yash does not default	9%	81%
Probability weighted cash flow	(P*CF)	(P*CF)
(P*CF)	800	12,600
(P*CF)	12,600	1,62,000

Sum of all (P*CF) = 188,000

In this case, Alice will get 120,000 first and Bob will received 188,000-120,000 = 68,000

b).

	Zara defaults	Zara does not default
Yash defaults	5%	5%
Yash does not default	5%	85%
Probability weighted cash flow	(P*CF)	(P*CF)
(P*CF)	4,000	7,000
(P*CF)	7,000	1,70,000	1,88,000

Sum of all (P*CF) = 188,000

In this case, Alice will get 120,000 first and Bob will received 188,000-120,000 = 68,000

c).

	Zara defaults	Zara does not default
Yash defaults	10%	0%
Yash does not default	0%	90%
Probability weighted cash flow	(P*CF)	(P*CF)
(P*CF)	8,000	-
(P*CF)	-	1,80,000	1,88,000

Sum of all (P*CF) = 188,000

In this case, Alice will get 120,000 first and Bob will received 188,000-120,000 = 68,000