978-0077861667 Chapter 20 Lecture Note Part 4

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Chapter 20 – Managing Credit Risk on the Balance Sheet 6th Edition

1. Calculating the Return on a Loan

a. Return on Assets (ROA) (The traditional approach)

Factors that affect a FI’s return on a loan include:

The base lending rate on the loan (BR)

The credit risk premium (m)

Fees earned as a result of the loan (e.g. origination fee and credit line fees)

Whether the borrower repays in full on time

The value of collateral and ease and cost of collections if the borrower defaults

The nonprice terms and conditions on the loan (other than fees), e.g., compensating

balance requirements

The base lending rate (BR) is the minimum rate required to hit a certain profit target,

such as a markup over the lender’s cost of funds, it may be called the prime rate,

although the meaning of the term prime rate has changed over time. Historically the

prime rate was the rate of interest a bank charged its best or ‘prime’ customers on loans of

$1 million or more. Subprime lending became common due to the competitiveness of the

lending market and the prime rate term has evolved to mean the base lending rate.

Variable rate business loans are now very common, especially for loans with a maturity

greater than one year. In these cases loan rates may fluctuate with LIBOR or the bank’s

prime rate.

Nonprice terms:

Origination fee (f), usually no more than 1% of the loan amount and less for larger

loans.

Compensating balances (b) are non-interest bearing deposits that the borrower is

required to hold at the bank while the loan is outstanding. These may be a percentage

of a credit line and/or the percentage of the drawdown on a credit line.

Reserve requirements (RR) on the compensating balances.

If k is the gross return on the loan per dollar lent, or the bank’s gross ROA on that loan

then

)]RR1(b[1

)mBR(f

1k1 





Example 1: A bank has a base lending rate of 8% (BR), and charges a certain customer a

110 basis point risk premium (m). The bank also charges a 1% origination fee (f). The

bank requires the borrower to maintain compensating balances (b) of 7% of the loan

amount. The reserve requirement (RR) is 10% and the loan amount is $1 million.

)]10.1(07.0[1

)011.008.0(01.0

1k1 





or k = 10.78%

Teaching Tip:

Total income to the bank (ignoring the timing of the receipts) is

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Chapter 20 – Managing Credit Risk on the Balance Sheet 6th Edition

$ 80,000 = 0.08  $1 million (base loan rate)

$ 11,000 = 0.011  $1 million (credit risk premium)

$ 10,000 = 0.01  $1 million (loan origination fee)

$ 101,000 = Total income

The amount of funds invested by the bank is:

$1,000,000 (the loan amount)

($ 70,000 ) (the compensating balance)

$ 7,000 (the bank’s reserve requirement on the compensating balance)

$ 937,000 = Net funds invested

The gross ROA on the loan is then $101,000 / $937,000 = 10.78%.

These days the compensating balance requirement may be eliminated or the borrower

may be allowed to meet the requirement with interest bearing time deposits.

Teaching Tip: If the fee and compensating balance requirements are more complicated,

the above equation will not work. For instance, banks may charge a fee for the unused

portion of a credit line and may charge different compensating balances for the

drawdown amount and the total line. In these cases the concept remains the same, but the

calculation method has to incorporate the different amounts involved and you can’t easily

calculate the cost rate per dollar lent with the above formula. The following example, the

idea for which was drawn from Gardiner, Mills and Cooperman, Managing Financial

Institutions: An Asset/Liability Approach, Dryden Press, 2000 illustrates this concept:

Example 2: A corporate customer obtains a $1 million line of credit from a bank. The

customer agrees to pay a 9% interest rate and agrees to make compensating balances of

6% of the total credit line and 3% of the amount actually borrowed. These will be held in

non-interest bearing transactions deposits at the bank for one year. The bank charges a

1% loan origination fee on the amount borrowed and a 0.25% commitment fee on the

unused line of credit. The expected draw down (loan amount) is 60% of the line for one

year. Reserve requirements are 10%. What is the expected rate of return to the bank?

$600,000 is the expected drawdown amount, and $400,000 is the unused portion of the

line. The numerator is comprised of the pretax income to the bank and the denominator

is the funds lent net of compensating balances and reserve requirements on those

balances.

Income to the bank: [($600,000  0.09) + ($600,000  0.01) + ($400,000  0.0025)] =

$61,000

Net funds lent [$600,000 – (0.90 ((0.06  1,000,000) + (0.03  600,000))] = $529,800

Gross ROA of loan = Income to the bank / Net funds lent

= $61,000 / $529,800 = 11.51%

As in the text this example ignores the timing effects of when the fees and interest are

earned.

Teaching Tip: Example 3: The credit risk premium (m) can be set based on historical

default rates on loans of this category and rates of return on defaulted loans. For instance

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Chapter 20 – Managing Credit Risk on the Balance Sheet 6th Edition

in order to earn the base loan rate of say 9% if the default history of a given loan category

is as follows:

% of loans Default experience Rate of return on given category

98% No default 9% + m

1.5% Limited default 0%1

0.5% Total writeoff -100%

The given credit risk premium required so that the average rate of return earned on this

loan category is 9% can be found as 0.09 = (0.98(0.09+m)) + (0.0150) + (0.005-1) or

m = 0.0069, or m = 69 basis points.

Teaching Tip: Conceptually a bank can calculate the ROE as well as the ROA on a loan.

If a bank has 10% equity capital and lends out $100, only $10 of that loan is funded with

equity. If the bank earns 9% on the loan or $9 and the interest and noninterest cost to

provide the loan is $7 then the bank nets $2 and earns an ROA of $2/$100 or 2% and a

ROE of $2 / $10 = 20%. If the bank has established a target ROA that is needed to hit a

given ROE target as is illustrated in the Gardiner, Mills and Cooperman cite above, then

it doesn’t really matter which measure is used. A conceptual problem with both

approaches is the lack of an objective risk adjustment for the loan. For example, these

approaches do not use any direct means to increase the required ROA or ROE for more

risky loans. The RAROC measure below attempts to add a risk adjustment.

b. RAROC Models

The risk adjusted return on capital (RAROC) originated by Banker’s Trust is now widely

used instead of the ROA method of loan pricing presented above.

riskatfundsofAmount

loantheonincomepretaxnetryeaOne

RAROC 

The numerator is the gross income on the loans (the numerator of the ROA model) minus

the cost of funds. The denominator is not the actual net funds invested. Instead, the

‘amount of funds at risk’ is measured as the product of the extreme loss rate times the

percentage of loans that are NOT eventually recovered in the event of default. The

amount at risk can be estimated as

Dollar value of the loan * Unexpected default rate * Loss rate given default

Example 4: Continuing with Example 1 from above and adding the additional necessary

information will illustrate how to calculate the RAROC:

The loan had income of $101,000. Suppose the dollar cost rate (including interest and

noninterest costs) of providing the loan is 10.3%. The net loan amount was $937,000 so

the dollar cost is thus $96,511 (=$937,000  0.103). Suppose that typical default rates on

this loan type are 0.3% in a given year. However, according to historical default rates,

the 99th percentile, or the extreme loss rate, for this loan category is 3%.2 This means

1The percent of loans and the rates of return numbers should both be net of recoveries

2Loan loss rates are not normally distributed. They have limited upside returns and long

tail downside risks. Hence, a bank may wish to calculate the extreme loss rate using a

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Chapter 20 – Managing Credit Risk on the Balance Sheet 6th Edition

that the bank believes that in the worst case scenario (which in this case should happen

only once every hundred years), 3% of the loans will default instead of the typical 0.3%.

Suppose further that based on historical data the bank can expect to eventually recover

25% of the loans that default. One can now calculate the capital at risk per dollar lent

under an extreme loss rate scenario as 0.03  0.75 = 0.0225, or for the $1 million loan,

the capital at risk is $22,500 = (0.0225  $1,000,000). The RAROC is thus ($101,000 –

$96,511) / $22,500 = 19.95%. The RAROC is then compared to the lender’s ROE. If the

RAROC is greater than or equal to the lender’s ROE the loan is acceptable with the given

terms.

1.1.1.1 Appendix 20A: Loan Portfolio Risk and Management (available on

Connect or from your McGraw-Hill representative)

The appendix applies the principle of efficient diversification to determine the best

diversified loan portfolios at given levels of rates of return. In general, correlations of

loan loss rates on different types of loans to different borrowers are likely to be low and

substantial diversification benefits can be achieved by holding multiple loan types. This

also implies that the total risk of the loan portfolio is substantially below the sum of the

risks of the individual loans. One can use the efficient frontier methodology to

theoretically determine the minimum risk loan portfolio.

Teaching Tip: Loan policies will normally specify maximum loan amounts by loan type

to help ensure diversification. Lenders may also participate in loans originated by other

FIs and achieve additional geographic diversification of the loan portfolio.

1.1.1.2 VI. Web Links

http://www.federalreserve.gov/ Website of the Board of Governors of the Federal

Reserve

http://www.fdic.gov/ The Federal Deposit Insurance Corporation website

has net charge off rates for banks and thrifts.

http://www.moodyskmv.com/ The website of KMV corporation, the developer of

the KMV option based credit scoring model.

http://www.americanbanker.com/ ABA website.

http://www.moodys.com/ Website of Moody’s Rating Agency. Unfortunately

there is not much available here without a

subscription.

http://www.standardandpoors.com/ Website of Standard & Poor’s. This is a better

number greater than two standard deviations below the mean in order to be sure they

have the 99th percentile. Bank of America has used 6.

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Chapter 20 – Managing Credit Risk on the Balance Sheet 6th Edition

website than Moody’s and there is some data

available here without a subscription.

http://www.wsj.com/ Website of the Wall Street Journal Interactive

edition. The web version of the well known

financial newspaper can be personalized to meet

your own needs. Instructors can also receive via

e-mail current events cases keyed to financial

market news complete with discussion questions.

http://www.loanpricing.com/ The Loan Pricing Corporation Website

http://consumeraid.org/scoring.htm Consumer group website with some information

about credit scoring models

1.1.1.2.1.1

1.1.1.2.1.2 VII. Student Learning Activities

1. Large banks are increasing internationally active lenders and investors. How

has the growth of international banking affected a bank’s overall portfolio loan risk?

Defend your answer.

2. Research the appraisal industry. What does it take to become an appraiser?

What level of income can an appraiser expect to make at the entry level? In ten years?

3. Go to http://www.epic.org/privacy/creditscoring/ and read the criticisms of

credit scoring models. How valid are the criticisms? Should credit scoring not be

allowed? Is it inherently discriminatory? Defend your answer.

4. At the website http://www.moodyskmv.com/ report on what major loan