CREDIT RISK
EXPECTED RETURN
Classes #13; Chap 11
Lecture Outline
2
Purpose: Gain a basic understanding of credit risk. Specifically,
how it effects loan returns

Brief Introduction to Credit Risk- what is it; why it is important?

How to calculate expected loan return



Contractually promised return
Expected return
Required return
What is Credit Risk?
3
Home Mortgage Losses
Settlement
It is the risk associated with a loan (or bond) having to do with a
borrower’s unwillingness or inability to pay.
Variation in asset prices due to the risk of default
Types of Loans




C&I loans: Secured and unsecured
Real Estate loans: Primarily mortgages
Fixed vs. Floating
Individual (consumer) loans:




Non-revolving loans (Automobile, mobile home, personal loans)
Revolving loans (Credit line)
Growth in credit card debt (Visa, MasterCard )
Other loans include:

Farm loans, Other banks, Nonbank FIs, Broker margin loans; Foreign
banks and sovereign governments, State and local governments
11-4
5
Loan Returns



Contractually Promised Return
Expected Return
Required Return
6
Contractually Promised Return
Contractually Promised Return
Definition
7
Definition:

The return that the bank realizes if the loan does not default (best case)
Rcontractual

Amount EarnedOrigination Fee  Interest Earned
Amount
Loan
AmCommitted
ount Com p. Balance Interest Expence Reserve Req.
Origination fee – a one-time payment at origination usually used to cover administrative costs
Interest Earned – total interest earned over the life of the loan
Compensating Balance – a fraction of the loan principal required to be held in demand deposits
at the bank
Interest Expense – includes all interest expenses over the life of the loan that the bank incurs
from issuing the loan
Reserve Requirements – Reserves sent to the fed to cover additional reserve requirements
incurred from issuing the new loan (from the compensating balance)
Contractually Promised Return
Loan Interest Rate
8
How does the bank determine
Loan Interest Rate
the interest rate it charges?
 Bank will usually charge a base rate that is related to their
funding costs (Libor) + some risk premium
LIBOR
Base Rate = 12%
Credit Risk Premium = 2%
Loan Interest Rate = 14%
FICO
Job/
Income
Contractually Promised Return
Book Formula
9

The book provides a formula so we should discuss why we do not follow
the book
1 k  1
of  (br  m)
[1  b(1  RR)]
k
of  (br  m)
[1  b(1  RR)]
Contractually Promised Return
Book Formula
10

The book provides a formula so we should discuss why we do not follow
the book
k
1.
of  (br  m)
[1  b(1  RR)]
Origination fee – Usually a one-time upfront payment but it is being
added in as if it were a continuous fee

It can be done by converting the one-time fee into annual payments an then asking what percent of the
loan value are those incremental payments – that gives you “of”
2.
Interest Expense – the formula only works if the compensating balance is
held in non-interest bearing demand deposits.
3.
Federal Reserve Interest – the formula does not take into account interest
paid on reserves held at the Fed.
Contractually Promised Return
Summary
11

So at this point we have k
k


Origination Fee  Interest Earned
Loan Am ount Com p. Balance Interest Expence Reserve Req.
This is the return on our loan if there is no possibility of default
(it is the best case scenario)

Do we always get that return? No!! – the loan can default

What happens if the loan defaults?


we do not get the promised return
we may not even get back the full principal committed
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Expected Return
Loan Expected Return
Uncertainty
13


Why do we need to calculate an expected return?
What don’t we know? If or when the loan will be paid back
This is the uncertainty – it is default risk: the
risk that the borrower will default on their loan

What can we do if we don’t know how things will turn out?
We can guess
Loan Expected Return
Expected Return
14


How to guess – we want our guess to be educated and reasonable
We have two cases:
1.
2.
The borrower has enough money to payoff the loan
The borrower does not have enough money to payoff the loan
Default
E(R) = P (1+k)
There is some likelihood
(probability) that the borrower
will payback the loan
+
In this case we get our full
return – but we know this
doesn't happen all the time
(1-P)(R)
We may be able to recover
some money in default
There are only 2 cases payment and
default. So the likelihood (probability)
of default is 1- probability of payment
Loan Expected Return
Expected Return
15


How to guess – we want our guess to be educated and reasonable
We have two cases:
1.
2.
The borrower has enough money to payoff the loan
The borrower does not have enough money to payoff the loan
Default
E(R) = P (1+k)
+
– 0.80) = 0.20
(1-P)(R) = (1
(1+k)
Recovery – is the percent of value recovered in default
– what is our return -80%

Suppose we can recover 20% of the principal?

When we talk about the recovery rate we just say R or 20% but it is really 1+kD where
kD is the loan return in default
Loan Expected Return
Default vs. payment (survival) probabilities
16


How to guess – we want our guess to be educated and reasonable
We have two cases:
1.
2.
The borrower has enough money to payoff the loan
The borrower does not have enough money to payoff the loan
Default
E(R) = P (1+k)
+
(1-P)(R)
What if I told you that the probability of payment was 90%
P = 0.90
1–P = 0.10
What if I told you that the probability of default was 15%
P = 0.85
1–P = 0.15
Loan Expected Return
Summary
17

The expected return on a loan adjusts for default risk

That is, it is a guess at what the loan return will be taking
into account the possibility of default
E(R) = P(1+k) + (1–P)(R)
Survival Probability
(prob of payment)
Recovery Rate
Default
Probability
Contractually
promised return
E(R) = (Survival Prob)(1+k) + (Default Prob)(R)
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Required Return
Required Return
19

How does a bank decide when they will issue a loan?
Economic
conditions
Required
Return
4%
To be profitable, the bank
needs to earn more than 4%
expected return on its loans
Funding Costs
Global Markets
In order to maintain positive expected profits the bank must only issue loans with an
expected return greater than or equal to the required return, which means:
1  Rrequired  ERloan 
Required Return
Net Present Value (NPV)
20

Anything above the bank’s required compensation is
positive value to the bank
Net Value = Loan Proceeds – Loan Cost
NPV = PV(Loan Proceed – Loan Cost )
Required Return
Net Present Value (NPV) – Example
21
Example: Consider a 1-year loan for $500M. Calculate the loan
NPV if its expected return is 6% and the bank’s required return is 4%
Net Value  (500M )(1.06)  (500M )(1.04)
NPV 
(500 M )(1.06)  (500 M )(1.04)
1.04
NPV 
(500 M )(1.06) (500 M )(1.04)

1.04
1.04
1.06
NPV  500 M
 500 M
1.04
NPV  $9.62 M
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Example
Loan Return Example
23
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of
6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%.
Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost
of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.
a) Calculate the contractually promised return
b) Calculate the expected return of the loan
c) Find the NPV of the loan
a) Contractually Promised Return
Step #1: Calculate interest Earned
Interest  (15,000,000)(1.063 ) 15,000,000  2,865,240
Step #2: Fee Income
Orignination Fee  (15,000,000)(0.02)  $300,000
 ($300,000)(1.033 )  $327,818.10
Loan Return Example
24
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of
6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%.
Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost
of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.
a) Calculate the contractually promised return
b) Calculate the expected return of the loan
c) Find the NPV of the loan
a) Contractually Promised Return
Step #3: Compensating Balance
Comp. Bal.  (15,000,000)(0.04)  $600,000
Step #4: Reserve Requirements
RR  (600,000)(0.10)  $60,000
Step #5: Interest Expense
Interest Expense (600,000 60,000)(1.0153 )  (600,000 60,000)  $24,666.3225
Loan Return Example
25
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of
6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%.
Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost
of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.
a) Calculate the contractually promised return
b) Calculate the expected return of the loan
c) Find the NPV of the loan
a) Contractually Promised Return
k
Amount Earned
Amount Committed
AmountEarned  2,865,240 327,818.10  3,193,058.10
AmountCommitted 15,000,000 600,000 60,000 24,666.32  14,484,666.32
k
3,193,058.10
 22.04%
14,484,666.32
Loan Return Example
26
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of
6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%.
Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost
of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.
a) Calculate the contractually promised return
b) Calculate the expected return of the loan
c) Find the NPV of the loan
b) Expected Return
What is P?
E ( R)  P(1  k )  (1  P)(R)
P  1  ( Default prob)  1  0.13  0.87
E ( R)  0.87(1  0.2204)  (0.13)(0.40)
k is the contractually promised
E (from
R) the
1.11
return
last slide
In this case you are given the default probability
so you need to calculate the survival probability
Loan Return Example
27
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of
6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%.
Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost
of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.
a) Calculate the contractually promised return
b) Calculate the expected return of the loan
c) Find the NPV of the loan
b) Expected Return
E ( R)  P(1  k )  (1  P)(R)
P  1  ( Default prob)  1  0.13  0.87
E ( R)  0.87(1  0.2204)  (0.13)(0.40)
E ( R)  1.11
1.11  (1  r )3
Expectedreturn  3.66%
This is the gross expected return it includes the
initial investment and tells us that we would expect
the have 111% of what we started with in 3 years.
Note this is not an annualized rate.
Annualize return: What rate would we need
to invest $1 at for 3 years to get $1.11?
Loan Return Example
28
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of
6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%.
Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost
of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.
a) Calculate the contractually promised return
b) Calculate the expected return of the loan
c) Find the NPV of the loan
C) Loan NPV
15,000,000(1.033 )
PV ( Loan cost ) 
 15,000,000
1.033
15,000,000(1.03663 )
PV ( Loan proceeds) 
 15,289,083.63
3
1.03
NPV  15,289,083.63  15,000,000  289,083.63
We expect our $15M investment to return
3.66% per year over the next 3 years so
this is the expected value in 3 years
Question: Why don’t we consider
interest payments fees …
The returns we have calculated – the
expected return and required return
are “all inclusive” – they include
interest fees …, remember when we
calculated the expected return we
took all of that into account
But the bank only requires 3% (that is the return
they need to break-even) so we discount at 3%
anything over 3% is positive value (gravy)
Example: ConocoPhillips borrows $3M from Bank of America for one year to cover a short-term capital shortage. They
agree to pay 9% interest per annum on the loan. Bank of America charges a 3% origination fee and requires an 8%
compensating balance to be held in demand deposits. Bank of America pays 2% on demand deposits. The Federal Reserve
requires that 10% of deposits be held in reserves at the Fed. In the case of default, Bank of America expects to recover 60%
of the loan value. Bank of America’s cost of capital is 2.5%
a) Find the contractually promised return
b) What is Bank of America’s maximum acceptable probability of default for ConocoPhillips over the coming year
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Lecture Summary
30

Loan Contractually Promised Return


Loan Expected Return



Is the total return that the bank realizes over the life of the loan if the
borrower does not default
Adjusts for the possibility that the firm will default
Decreases the return relative to the contractually promised
Loan NPV

Bank profit on the loan after taking into account the banks cost of
capital.