Pricing loans correctly is critical to your business. Underprice the loan, and you might get more customers -- but you also risk reducing profitability. Overprice the loan, and you risk losing customers. To price correctly, there are several assumptions on the expense side to determine the RAROC (ROE) on a loan; chief among them is the cost of funds.

We are big proponents of the Strip Funding method for calculating cost of funds (COF), but we know many financial institutions choose WAL (Weighted Average Life) funding, possibly because it's simpler to calculate.

We set out to analyze the profitability of each method using historical data. The results firmly establish Strip Funding (sometimes referred to as Match Funding) as the more accurate way to price loans.

In the first part of this blog, we're going to walk though how each method is calculated and then identify some situations in which Strip and WAL funding produce different COF calculations.

In Part 2, we'll dig deeper into those differences and the historical data. We'll show that the differences in accuracy between Strip and WAL funding are significant and can be costly to your institution.

## Cost of Funding Basics

There are many expense elements in a loan. These include the cost of origination and servicing as well as loan loss provisions. However, usually the main expense item is the COF. This includes the cost to raise funds to lend to the borrower, some interest rate risk premium and perhaps optionality expense. The main determinant in calculating COF is a funds transfer pricing (FTP) curve. This curve is often based on a form of the Libor/Swap curve with some adjustments. However, for many community banks in the U.S., a Federal Home Loan Bank (FHLB) fixed-rate advance curve is frequently used. Alternatively, some banks (mostly outside of the US) may also use the local national government treasury curve.

## The Math Behind Strip Funding

Most reliable loan pricing and profitability solutions use a strip funding method on fixed and adjustable rate loans. This method examines the timing of each cash flow with the associated FTP rate. The weighted average rate, or COF, is then determined.

Let's examine a few examples to show the mathematics behind this method. These examples use an FTP curve with six periods as shown in the next table. For illustrative purposes, we have not specified the exact definition of the periods. They could be months, quarters, or years.

The loan rate in these examples is 6% based on an actual/365-day basis. The loans are fixed rate.

If this is an interest-only loan (no amortization of payments) with a term of six periods, the COF is simply the sixth-period point on the FTP curve, or 4.5%. However, if the loan is fully amortizing or a balloon type amortizing loan the calculations are more complex.

The next table shows the beginning balances and payments for six periods for both the fully amortizing and a balloon type loan which amortizes over twelve periods. All payments are made at the end of each period.

The interest expense in the first period is the sum of the product of each periodic payment (p_{i}) and corresponding FTP rate (r_{i}). The effective COF for the first period is this sum divided by the initial loan amount (Bi) or (∑ p_{i} * r_{i} )/ B_{1} where i =1 to 6. We perform the same calculation for the second period, except the initial period information is excluded or i=2 to 6 and B_{2} is used. We perform similar calculations for each period. We show, in the next table, the calculations as well as each period's COF and the overall COF for the loan or COF = [∑ i * p_{i} * r_{i} ]/ ∑B_{i}. In this example,** the COF is 3.69%**.

For the balloon loan with a six-period term, but 12-period amortization, the calculations are the same. But instead of each period principal payments being similar, the final payment is significantly greater than the combined sum of all the others. This last payment will have an out-sized weighting on the calculations, and a **4.26% COF** compared to the 3.69% for the fully amortizing example.

Note, we have assumed all FTP rates (r_{i}) have the same interest day count method. This may not always be true, particularly when the FTP periods are under twelve months.

## Exploring the WAL Method

Weighted Average Life (WAL) is the other method used in some models to determine the COF. The calculations are somewhat less complex than the Strip funding methodology, but may lack accuracy. When you use this method, you need to determine the weighted average life of the loan. The FTP rate associated with the maturity date of the calculated WAL of the loan becomes the COF rate.

In the case of an interest-only loan, the results are identical with the strip method. However, there is often a difference for amortizing loans. To calculate WAL for COF, you take the sum of each period's loan's outstanding balance and divide this by the initial loan amount. When you use this calculation as the average term of the loan, the associated rate from the FTP curve is used. For the fully amortizing loan as described in the previous section, the WAL is $3,669.6/1000 or 3.67 periods. In this case, the WAL can either be rounded to the 4th-period rate of 3.3% or the interpolated value between three and four periods - 3.0 +(3.3 -3.0)/.67, **or 3.2%**. In the case of the balloon loan, the WAL is 5.04 ($5,036.43/1000), and the **COF is 4.0%**. This compares with the 3.69% and 4.26%, respectively, found in the Strip method.

## Comparing Strip to WAL Funding

For the amortizing fixed-rate loan in the above example, the COF is higher for the Strip method. However, that is not always a typical scenario. Let's look at examples that involve the kinds of loans your institution is likely to make. In all the following examples, the loans will have monthly periods, and the loan rate will be 0.422% -- or a 5.0% per annum (assume actual/360 interest day count calculation). As of late August 2017, the FTP curve to the US dollar Libor/Swap curve had the following rates:

We interpolate the months in between those in the charts. Rates for less than one year have been adjusted for actual/360 interest day count. To determine the COF based on the WAL and Strip funding methods, we developed a model with calculations described earlier. We show the results of that model below. There is a 60-month fully amortizing loan and a 60-month balloon with a 120-month amortization. Both assume no prepayments (constant prepayment rate (CPR) is set to zero), and an initial loan amount of $1 million.

## Where Strip and WAL Funding Calculations Differ

In both cases, the Strip method results in a higher COF by about 5 basis points. Here's another way of looking at it -- a recommended rate based on a RAROC/ROE target would be about 0.05% higher using this method. Often the difference depends on the shape of the yield curve. The chart below shows different configurations of FTP curves over time.

Some are relatively flat or even downward sloping (Dec 2006), others show a significant upward trend (Sep 2001 and Sep 2013). In general, the flatter the curve (when prepayment assumption is zero), the more likely that WAL funding will have a higher COF than Strip. More importantly, in the majority of cases, __there is a difference between the two. And in many cases, it can be significant.__

## What's Next

In part 2 of our WAL vs. Strip funding blog post, we look at 16 years worth of historical data that includes 4,163 observations and stretches over two economic cycles. When you study Strip vs. WAL in this kind of depth, you'll understand why Strip Funding is the better way to calculate your COF.