8/3/2019 11B F2011 Contractual_return_er

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Ch 11 Par t b Ret urn on a Loan:

The rate on the loan is not the return due tovarious structural factors and due to defaults

,Promised Return on a Loan

This ignores defaults

Per the text:

1+k= 1+

of+

BR+m

/ 1-b

1-RR

Can be simplified to:

k= (of+ (BR+ m ))/(1-[b(1-RR)])

11-2

Contract ua l ly Promised Return on a Loan:

Factors that determine the stated rate on theloan:

.Libor

m = Margin. The margin in excess of the baserate.

BR + m = stated rate

11-3

Contrac tua l ly Promised Return on a Loan:

Factors that add to the profitability of theloan: of = Origination fees. Note that there are some

simplifying assumptions in the way that these aretreated. First, the we just add them in, we are makingthe implicit assumption either that the loan is for one or

that we collect the fees each year. Second we actuallyreceive them at origination but they are treated thesame as year-end cash flows.

. -bearing deposit the borrower must maintain at the bankfor the duration of the loan. This improves profitabilityby essentially requiring less funds to lend whilecollecting interest on the gross amount.

11-4

Contract ua l ly Promised Return on a Loan:

Factor that reduces profitability of the loan:

RR = Reserve requirement. This factor has aver minor im act on the return. Recall thatreserves are required to be held againstdeposits, not loans. The reserve requirement

that is included in this calculation is the reserveamount required for the deposit received as acompensating balance (if there is one).

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8/3/2019 11B F2011 Contractual_return_er

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Contrac tua l ly Promised Return on a Loan:

Back to the calculation:

= + + - -

k = (income received) / (money lent)

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Sens i t i v i t y to Money Lent Factors

10% Base Rate, 1.5% origination fees, 2.5% margin

+ = .

Reserve Compensating Balances

Reqt. 5% 10% 15% 20%

5% 14.70% 15.47% 16.33% 17.28%

10% 14.66% 15.38% 16.18% 17.07%

15% 14.62% 15.30% 16.05% 16.87%

11-7

Loan Er : Now Inc lude Defaul ts

Er = (1 + k)*P + (0)*(1-P)*(1+k) -1

Where P= probability of complete repayment of loan, so

(1-P) is probability of default

Er = (1 + k)*P + (0)*(1-P)*(1+k) - 1

Collected if loan fully paid

* * *

r = + + - + -Recovery in default

Note that text never varies from the assumption thatrecoveries = 0%. We will investigate the impact ofrecoveries.

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Er Wi th Defaul ts & Recover ies

k = 12%

Probabilityof

Collection

0% 20% 40% 60%

98% 9.76% 10.21% 10.66% 11.10%

95% 6.40% 7.52% 8.64% 9.76%

90% 0.80% 3.04% 5.28% 7.52%

70% 21.60% 14.88% 8.16% 1.44%