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

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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

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Contractually Promised Return

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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)

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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

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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

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)]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

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)]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

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Contractually Promised ReturnSummary

ExpenceInterestBalanceCompAmountLoan

EarnedInterestFeenOriginatio

.

k

Reserve Req.

No!! – the loan can default

Expected Return

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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?

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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

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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

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(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

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(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

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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

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Required Return

How does a bank decide when they will issue a loan?

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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

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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%

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)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

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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

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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

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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

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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

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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

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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

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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

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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.

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