CREDIT RISK EXPECTED RETURN
Classes #13; Chap 11
Lecture Outline
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
2
What is Credit Risk?3
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
Home Mortgage Losses Settlement
11-4
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
Loan ReturnsContractually Promised Return Expected ReturnRequired Return
5
Contractually Promised Return
6
Contractually Promised Return Definition
Definition: The return that the bank realizes if the loan does not default (best case)
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)
7
ExpenceInterestBalanceCompAmountLoan
EarnedInterestFeenOriginatio
.
Rcontractual Reserve Req.CommittedAmount
EarnedAmount
Rcontractual
Loan Interest Rate Bank will usually charge a base rate that is related to their
funding costs (Libor) + some risk premium
8
Base Rate = 12%Credit Risk Premium = 2%
Loan Interest Rate = 14%
Contractually Promised Return Loan Interest Rate
Job/Income
FICOLIBOR
Tied to funding cost
Tied to borrower credit risk
How does the bank determine the interest rate it charges?
The book provides a formula so we should discuss why we do not follow the book
Contractually Promised ReturnBook Formula
9
)]1(1[
)(11
RRb
mbrofk
)]1(1[
)(
RRb
mbrofk
The book provides a formula so we should discuss why we do not follow the book
1. 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 ReturnBook Formula
10
)]1(1[
)(
RRb
mbrofk
So at this point we have k
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?
What happens if the loan defaults? we do not get the promised return we may not even get back the full principal committed
11
Contractually Promised ReturnSummary
ExpenceInterestBalanceCompAmountLoan
EarnedInterestFeenOriginatio
.
k
Reserve Req.
No!! – the loan can default
Expected Return
12
Loan Expected ReturnUncertainty
Why do we need to calculate an expected return? What don’t we know?
What can we do if we don’t know how things will turn out?
13
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
We can guess
Loan Expected ReturnExpected Return
14
How to guess – we want our guess to be educated and reasonable We have two cases:
1. The borrower has enough money to payoff the loan
2. The borrower does not have enough money to payoff the loan
(1+k)P (1-P)
Default
(R)
There are only 2 cases payment and default. So the likelihood (probability) of default is 1- probability of payment
We may be able to recover some money in default
In this case we get our full return – but we know this
doesn't happen all the time
There is some likelihood (probability) that the borrower
will payback the loan
E(R) = +
How to guess – we want our guess to be educated and reasonable We have two cases:
1. The borrower has enough money to payoff the loan
2. The borrower does not have enough money to payoff the loan
Recovery – is the percent of value recovered in default 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 ReturnExpected Return
15
(1+k)P (1-P)
Default
(R)E(R) = +
– what is our return -80%
= (1 – 0.80) = 0.20= (1+k)
How to guess – we want our guess to be educated and reasonable We have two cases:
1. The borrower has enough money to payoff the loan 2. The borrower does not have enough money to payoff the loan
Loan Expected ReturnDefault vs. payment (survival) probabilities
16
(1+k)P (1-P)
Default
(R)E(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
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
17
Loan Expected ReturnSummary
E(R) = P(1+k) + (1–P)(R)Survival Probability(prob of payment)
Default Probability
Contractually promised return
Recovery Rate
E(R) = (Survival Prob)(1+k) + (Default Prob)(R)
Required Return
18
Required Return
How does a bank decide when they will issue a loan?
19
Economic conditions
Funding Costs
Global Markets
Required Return
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:
loanrequired RER 1
4%To be profitable, the bank
needs to earn more than 4% expected return on its loans
Anything above the bank’s required compensation is positive value to the bank
20
Required ReturnNet Present Value (NPV)
Net Value = Loan Proceeds – Loan Cost
NPV = PV(Loan Proceed – Loan Cost )
Example: Consider a 1-year loan for $500M. Calculate the loan NPV if its expected return is 6% and the bank’s required return is 4%
21
)04.1)(500()06.1)(500( MMValueNet
04.1
)04.1)(500()06.1)(500( MMNPV
04.1
)04.1)(500(
04.1
)06.1)(500( MMNPV
MMNPV 50004.1
06.1500
MNPV 62.9$
Required ReturnNet Present Value (NPV) – Example
Example
22
Loan Return Example
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of 6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%. Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.a)Calculate the contractually promised returnb)Calculate the expected return of the loan c)Find the NPV of the loan
23
a) Contractually Promised Return
Step #1: Calculate interest Earned
240,865,2000,000,15)06.1)(000,000,15( 3 Interest
Step #2: Fee Income
000,300$)02.0)(000,000,15( FeeonOrigninati
10.818,327$)03.1)(000,300($ 3
Loan Return Example
Asolo bank issues a 3-year $15M balloon payment loan to Kemp Inc. The loan has an annual interest rate of 6%, origination fee of 2% and compensating balance of 4% to be held in demand deposits that pay 1.5%. Kemp has a 13% probability of default over the next 3 years and expected recovery rate of 40%. Asolo’s cost of capital is 3% and the fed requires 10% of demand deposits to be held on reserve.a)Calculate the contractually promised returnb)Calculate the expected return of the loan c)Find the NPV of the loan
24
a) Contractually Promised Return
Step #4: Reserve Requirements
3225.666,24$)000,60000,600()015.1)(000,60000,600( 3 ExpenseInterest
Step #5: Interest Expense
000,60$)10.0)(000,600( RR
Step #3: Compensating Balance
000,600$)04.0)(000,000,15(. . BalComp
Loan Return Example
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 returnb)Calculate the expected return of the loan c)Find the NPV of the loan
25
a) Contractually Promised Return
Committed
Amount
EarnedAmountk
10.058,193,310.818,327240,865,2 EarnedAmount
32.666,484,1432.666,24000,60000,600000,000,15 CommittedAmount
%04.2232.666,484,14
10.058,193,3k
Loan Return Example
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 returnb)Calculate the expected return of the loan c)Find the NPV of the loan
26
b) Expected Return
))(1()1()( RPkPRE
87.013.01) (1 probDefaultP
What is P?
In this case you are given the default probability so you need to calculate the survival probability
)40.0)(13.0()2204.01(87.0)( RE
k is the contractually promised return from the last slide11.1)( RE
Loan Return Example
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 returnb)Calculate the expected return of the loan c)Find the NPV of the loan
27
b) Expected Return
))(1()1()( RPkPRE
87.013.01) (1 probDefaultP
)40.0)(13.0()2204.01(87.0)( RE
11.1)( RE
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.3)1(11.1 r
%66.3 returnExpectedAnnualize return: What rate would we need
to invest $1 at for 3 years to get $1.11?
Loan Return Example
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 returnb)Calculate the expected return of the loan c)Find the NPV of the loan
28
C) Loan NPV
000,000,1503.1
)03.1(000,000,15)cos (
3
3
tLoanPV
63.083,289,1503.1
)0366.1(000,000,15) (
3
3
proceedsLoanPV
63.083,289000,000,1563.083,289,15 NPV
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
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
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
29
Lecture Summary
Loan Contractually Promised Return Is the total return that the bank realizes over the life of the loan if the
borrower does not default
Loan Expected Return 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.
30