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

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1 , 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 1

2 RAROC % 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 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) 2

3 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 riskbased 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). 3

4 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 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 4

5 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. 5

6 Step 2. The Cost of Funding relative to the Fund Transfer Pricing curve Where Asset Liability Management and Transactions Meet 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. 6

7 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% % % = 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. 7

8 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 Net Cost (1) Customer Contributions (2) (3) (4) [(1)+(2)][1-(3)]/(4) 30 FRM 1.20 % 1.22 % 33% 11.8% 13.74% Tax Equity ratio 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 subitems 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. ROE 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. 8

9 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 9

10 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 Thomas Ho Company Ltd Tom.ho@thomasho.com

11 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. THE THC CONTENT IS PROVIDED AS IS, WITHOUT REPRESENTATIONS OR WARRANTIES OF ANY KIND. TO THE MAXIMUM EXTENT PERMISSIBLE UNDER APPLICABLE LAW THC HEREBY DISCLAIMS ANY AND ALL WARRANTIES, EXPRESS AND IMPLIED, RELATING TO THE THC CONTENT, AND NEITHER THC NOR ANY OF ITS AFFILIATES SHALL IN ANY EVENT BE LIABLE FOR ANY DAMAGES OF ANY NATURE WHATSOEVER, INCLUDING, BUT NOT LIMITED TO, DIRECT, INDIRECT, CONSEQUENTIAL, SPECIAL AND PUNITIVE DAMAGES, LOSS OF PROFITS AND TRADING LOSSES, RESULTING FROM ANY PERSON S USE OR RELIANCE UPON, OR INABILITY TO USE, ANY THC CONTENT, EVEN IF THC IS ADVISED OF THE POSSIBILITY OF SUCH DAMAGES OR IF SUCH DAMAGES WERE FORESEEABLE 11