Where Asset Liability Management and Transactions Meet

Loan Pricing Profitability

key words: loan pricing, rates, RAROC, profitability measure, fund transfer pricing, approaches

THC Asset-Liability Management (ALM) Insight

Issue 7

Introduction

Loan pricing is important to community banks and credit unions, as it can impact customer relationships,

change loan volume and margin, and also impacts the balance sheet risk exposures. Because multiple factors

affect loan pricing, the process in determining a loan price can be complex.

For example, ALCO and loan officers are often motivated differently in loan pricing. The loan officers tend to

be pressured by the customer’s needs, while the ALCO tends to be pressured by risk management. The loan

pricing process should consider the needs of all stakeholders. In the end, both are unified in efforts to

increase risk-adjusted margin.

This article describes a systematic methodology in pricing loans ensuring direct costs are covered and indirect

and overhead costs are properly allocated. This enables ALCO and loan officers to make informed decisions

in product offerings and secondary market transactions. Ultimately, the underlying profitability driver are

assumed and pricing objectives are met.

In particular, do ALCO and loan officers alike know which products provide the highest value? How much (if

any) rate concession can the loan officer offer to borrowers given the loan policy, secondary market pricing

and risk analysis? Can ALCO adjust the rate cap to meet the borrower’s needs without changing the loan offer

rate?

This article explains. In particular, this article describes the Dynamic Cash Flow method in measuring

profitability on loan pricing across a broad range of loan types. The relative profitability measure enables the

ALCO and loan officers to jointly decide:

•

•

the appropriate loan rate in negotiating with a customer in certain occasions;

most profitable loan products given the loan market competitive rates, combining the market

intelligence from the loan officers and ALCO balance sheet strategies;

the growth potential of certain profitable loan products as the loan market supply and demand are

continually changing

•

•

the bank’s risk-adjusted return on capital (RAROC) against the loans in the secondary market to

expand profitable opportunities.

Figure 1 below depicts the RAROC profitability of loan pricing based on a bank’s loan offer rates and a sample

of secondary market loan rates. These results are relative measures of profitability of loans benchmarked

against the secondary market offer prices. While the RAROC has adjusted for the expected credit loss rates

of the loans, the profitability has not adjusted for the credit risk premium. The risk premium has to be

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Where Asset Liability Management and Transactions Meet

determined by the risk culture of the bank. Therefore, RAROC is institutional specific, depending on the

bank’s risk aversion, balance sheet structure and local economic activities.

Figure 1. Loan Pricing RAROC: Risk Adjusted Return on Capital

based on Bank's Loan Rates and Secondary Market Loan Rates

25.00

20.00

15.00

10.00

5.00

0.00

Loan Types "market" denotes secondary market rates

The RAROC chart enables ALCO and loan officers to determine their pricing strategies in managing their

balance sheet profitability.

Measures of Profitability

Banks often use Net Interest Margin (NIM), as a measure of a loan profitability. However, such a profitability

measure has to be adjusted to compare fixed rate residential mortgages (FRM) and adjustable rate mortgages

(ARMs) due to the two loan types have significantly different cashflow characteristics. Also, NIM does not

consider caps and floors for ARMs and fails to compare profitability across loan types such as commercial

real estate (CRE) loans and auto-loans. Indeed, Margin has limited use for pricing loans.

One common approach to Loan Pricing is to use the Static Cash Flow Approach. This method uses return on

equity (ROE) as a relative profitability measure, where the equity is the allocated capital to support the

purchase of the loan. This method uses Fund Transfer Pricing (FTP) and the Risk Adjusted Return on Capital

(RAROC) model, which I have described in Insight #3. I will first describe this method in brief below. In the

following sub-section, I will describe the Dynamic Cash Flow approach that can mitigate some of the

shortcomings of the Static Approach

Consider a 30-year fixed rate 1-4 family mortgage: loan size $100,000, FICO 750, current LTV 80%, owner

occupied and detached home, with a loan rate of 4.52%.

Static Cash Flow Approach: Fund Transfer Pricing (FTP) and Risk Adjusted Return on Capital (RAROC)

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Where Asset Liability Management and Transactions Meet

Step 1. Calculate the loan Net Interest Margin by the loan rate net of the funding cost

The bank can calculate the weighted average interest costs and the servicing cost of the deposits. Currently,

under regulation, the servicing cost has to be provided in the Economic Value of Equity (EVE) report. Suppose

the total funding cost is 0.85%. Then the Net Interest Margin is 4.52% net of 0.85%.

Step 2. Calculate the loan loss provision and cost of options embedded in the loan. The bank can use risk-

based valuation models to estimate the credit loan loss rate and the prepayment cost (borrowers option

cost); the total cost is then used to deduct from the Net Income Margin.

Step 3. Calculate the FTP.

FTP is the rate spread to compensate for the interest rate sensitivity between the loan and funding portfolio.

Using the Fund Transfer Pricing Method, the spread can be calculated to be 0.71% which is the funding cost

of the loan cashflows based on the Treasury rates net of the total actual funding cost (%) based on deposits

and borrowings as described in Step 2.

Step 4. Determine the expense charge in servicing the loans.

Assume the bank has calculated the cost of servicing the loan to be 0.15%. Let us also assume the initial

origination fees pay for the expense in underwriting the loan. We further assume, for this example0 that the

bank does not allocate other overhead cost to holding the loan. I do not make assumptions on cost allocation

because assigning overhead costs to business units is a complex process that the bank needs to determine

internally.

Step 5. Calculate the ROE.

I assume that the capital, as assigned to the purchase of the loan, to the loan size is the equity ratio of the

bank. That is, C/L = E/A, where C is the assigned capital, L the loan size, E the total equity, and A the total

assets of the bank. This way, I do not assume that the bank has certain preference or aversion to certain loan

types.

The ROE is specified as follows. Since the annualized loan net income is ((Net Income Margin – Provisions –

Fund Transfer Pricing – servicing cost)(1 – tax) L), then, the ROE can be derived as shown below:

ROE = (Net Income Margin – Provisions – Fund Transfer Pricing – servicing cost)(1 – tax_rate) L]/C

= (Net Income Margin – Provisions – Fund Transfer Pricing – servicing cost)(1–tax_rate)/EquityRatio

The Table below provides a summary worksheet in calculating the ROE, where I assume the tax rate and

equity ratio to be 33% and 11.8%, respectively. Since the ROE has adjusted for the credit risk and interest

rate risk, the return on equity is the risk-adjusted return on capital (RAROC).

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Where Asset Liability Management and Transactions Meet

The Static Cash Flow approach provides a methodology that can systematically compare the profitability of

all fixed rate loans. Using ROE as a profitability measure, ALCO and loan officers can have a systematic way

to compare profitability of loan pricing across a spectrum of loan types and can then determine the loan

pricing that meets both the customer’s needs and the bank’s performance requirements.

However, this static approach has multiple significant shortcomings. For example, what is the loan income

for an ARM, as the loan rate is not fixed? How is the loan Fund Transfer Rate determined when there are

caps and floors, where the income depends on the rate scenarios?

The static cash flow method fails when the loan cash flows are not predetermined; ARM cashflows and

callable CRE depend on the interest rates, for example. Regulators call this the “option risk.” But most balance

sheet items have rate dependent interest payments and therefore option risk cannot be ignored. Option risk

is an important consideration in loan pricing. To deal with this option risk, I now describe the Dynamic Cash

Flow Approach.

Dynamic Cash Flow Approach

The impact of option risk on the profitability of a whole loan purchase is apparently recognized by the Federal

Housing Finance Agency (FHFA). AB-3-2017 Bulletin has suggested that Federal Home Loan Banks(FHLBs)

should adopt an Option Adjusted Spread (OAS) approach to measure profitability when purchasing loans.

FHFA suggested using the OAS approach not because FHLBs have different loan types or a different loan

acquisition process, but because the method is more accurate.

In this section, I describe this OAS approach in the context of the balance sheet of a community bank, and

the method is called the Dynamic Cash Flow Approach.

I will follow the 5-step procedure analogous to the static cash flow approach. They are:

Step 1. Calculate the loan’s Risk-Adjusted Margin (RAM) based on the Fund Transfer Pricing (FTP) curve.

Step 2. Calculate the weighted average cost of funding (WCF) and servicing cost based on the FTP curve

Step 3. Calculate the Customer Contribution on the funding side

Step 4. Determine the expense charge

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Where Asset Liability Management and Transactions Meet

Step 5. Calculate the RAROC.

Steps 4 and 5 are identical to the Static Approach. The main differences between the Static and Dynamic

Approaches are twofold. First, the dynamic approach calculates the Risk Adjusted Margin (RAM). RAM is

calculated using over 1,000 interest rate scenarios to determine the net interest income for all the scenarios,

instead of one static scenario, to capture the impact of optionality of the loans. Second, the dynamic

approach calculates the profitability of the loan and funding separately. This approach can clearly identify

the profitability attributed to the loan pricing, isolated from the funding strategies. This attribution enables

ALCO and loan officers to adjust the bank’s ALCO strategies and the loan pricing with transparent

assumptions to make decisions.

Step 1. Risk Adjusted Margin of a Loan

The Option Adjust Spread (OAS) method assumes a constant spread off the Treasury curve to discount the

mortgage loan projected cashflows using Monte Carlo interest rate simulation. The Monte-Carlo

methodology projects over 1,000 interest rate scenarios and the respective loan cashflows to calculate the

net interest income under each scenario. Therefore, the OAS is the net interest incomes over 1,000 interest

rate scenarios. The Risk-Adjusted Margin is the OAS that has also isolated the expected credit loss from the

income in addition to the interest rate optionality. Therefore, Monte-Carlo simulation can isolate the impact

caps and floors and dynamic interest rates of ARMs have on profitability.

For example, the 30-year Fixed Rate Mortgage loan is 4.52% priced by the bank as described above. The

Monte-Carlo model has calculated the Risk Adjusted Margin to be 120 bpts, where the option cost and credit

charge are 14 bpt and 25 bpt, respectively, which are calculated based on the Monte-Carlo simulations. A

sample report is provided below.

The estimated cost of servicing is assumed to be 15 bpt.

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Where Asset Liability Management and Transactions Meet

Step 2. The Cost of Funding relative to the Fund Transfer Pricing curve

The cost of funding can be determined as the weighted average cost of deposits and borrowings. The

weighted average interest cost can be calculated from the Economic Value of Equity (EVE) report, since the

report provides the deposit and borrowing rates and their corresponding face values. For a hypothetical

bank, the weighted average funding cost is 70 bpt.

The bank should estimate the weighted average servicing cost of funding the loan purchase. I will assume

that the weighted average funding cost is 15 bpt. Furthermore, the EVE report provides the duration of the

funding portfolios, which in this example, is 1.57 years. These results are provided by the EVE report,

presented below.

Step 3. Customer Contribution: Fund Transfer Pricing Adjustment

The yield curve is not flat but often upward sloping. Therefore, the appropriate margin between the loan and

the funding cost should take the yield curve shape into account, as the loan has a higher duration than that

of the funding in this example. The appropriate margin and the customer contribution, based on the Fund

Transfer Pricing, are depicted below.

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Where Asset Liability Management and Transactions Meet

In this numerical example, the Treasury rate for the 1.57 year is 2.06%. The funding cost is 0.70%. Therefore,

referring to the diagram above, the customer contribution is 2.06% - 0.70% - 0.15% = 1.21%

Step 4. Expense Charge

There are two types of overhead costs to consider that affect the pricing: the origination cost and the

servicing cost. These costs depend on the loan size and the complexity of origination. For example, low credit

borrowers may lead to higher expense in originating the loan. Mitchell Epstein provides in When Setting

Your Loan Pricing Assumptions, sample tables of the overhead costs, which are provided below.

This is beyond the scope of this article to discuss cost allocation and servicing costs. As noted before, for the

30-year fixed rate mortgages, I assume that the origination fee covers the upfront cost and the servicing cost

is 15 bpt, which is taken into account by the RAM calculation.

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Where Asset Liability Management and Transactions Meet

Step 5. Calculate the ROE

I have shown that the net interest income margin is the sum of RAM and the customer contribution. The ROE

can then be calculated as in the Static Approach. The results are summarized below.

RAM

Customer

Tax Equity ratio

ROE

Net Cost Contributions

(1)

(2)

(3)

33%

(4)

11.8%

[(1)+(2)][1-(3)]/(4)

13.74%

30 FRM

1.20 %

1.22 %

Therefore, based on the assumptions of the model, the RAROC is 13.74%. This calculation can be applied to

other loan types. For clarity of the exposition, I present the results of both the Static and Dynamic

methodologies below. The results show that the two methods provide the same RAROC, but with the sub-

items arranged differently. The calculated RARACs are the same because the Option Models with Monte-

Carlo Simulations are the same in both examples, and therefore the FTP rates are specified correctly for the

Static Approach. Otherwise, FTP rates can be incorrect without using the option model. More importantly,

the Dynamic Approach can be applied to ARMs and many other loan types, while the Static Approach is

confined to static cash flow loan types.

Comparing the ROE calculations between the Static and Dynamic Approaches

A sample of loans’ ROE (RAROC) is presented below for illustration using the Dynamic Approach. The results

show that the profitability measures can be analyzed by the attributions of the rate. Risk premiums should

be considered for each loan type to adjust for the RAROC. For example, the SBA 7a can be priced at 111.

Therefore, the premium (priced above par) risk due to prepayments of SBA 7a can be significant. The HELOCs

may require significant credit premium particularly when the bank has significant concentration of HELOCs

in one region. However, it is beyond the scope of this article to discuss the specifications of risk premiums.

RAROC of Hypothetical Bank’s Loans based on the Bank’s Offer Rate Sheet. I also provide the RAROC of a

sample of loans offered in the loan market.

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Where Asset Liability Management and Transactions Meet

A consistent profitability measure enables ALCO and Loan Officers to evaluate the appropriateness of their

loan offer rates and to benchmark against the secondary market loan rates. Such a framework enables the

bank to execute balance sheet strategies coherently in loan pricing, funding, and risk management.

The scattered plot below illustrates the loan pricing across different loan types, showing how the loan

market’s market risk premium increases with the credit risk. Since RAROC is a relative profitability measure

based the bank’s internal loan pricing, adjusted for the institutional specific risk capacity, a secondary market

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Where Asset Liability Management and Transactions Meet

loan can be preferred by one bank and not the other. Therefore, incorporating the secondary market loans

in the RAROC analysis can expand the bank’s profitability opportunities.

The Scattered Plot of Risk Adjusted Margin (RAM) against CECL across different loan types of a hypothetical

bank

Conclusions

This article describes the Dynamic Cash Flow method in measuring profitability on loan pricing across a broad

range of loan types. The relative profitability measure enables the ALCO and loan officers to jointly decide:

•

•

the appropriate loan rate in negotiating with a customer in certain occasions;

most profitable loan products given the loan market competitive rates, combining the market

intelligence from the loan officers and ALCO balance sheet strategies;

•

•

the growth potential of certain profitable loan products as the loan market supply and demand are

continually changing

the bank’s RAROC against the loans in the secondary market to expand profitable opportunities.

This article focuses on the loan pricing methodology. I will discuss the specification of Risk Premiums that

should be deducted from the loan profitability based on the bank’s perceived Risk Capacity. I will also discuss

the issue of non-interest cost allocation in later issues of Insight. These issues are beyond the scope of this

article.

I welcome your comments.

Regards,

Tom Ho PhD

President

1-212-732-2878

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Where Asset Liability Management and Transactions Meet

About THC

THC is a financial technology company founded by Dr. Thomas Ho, a former professor at New York

University, who introduced the first balance sheet valuation (Ho-Lee model 1986) called "option model" by

regulators and key rate durations (1992), one of the most popular interest rate risk measures.

THC was selected as the sole provider of the risk reporting to all regulated institutions under a federal bank

regulator. THC continues to dedicate its research and resources to supporting community banks.

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