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ROA Methods and Relationship ROA

August 16, 2014
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If you are using the ROA profitability method to evaluate the relative profitability of a relationship, you would like it to approximate how ROA is calculated at the institution level. So how do we calculate the ROA of a single relationship? We certainly know how to do this at the institution level; we take annual net income and divide by institution total assets. Can we just do the same thing with a relationship? That is, take net income for the relationship (we’re already calculating it) and divide by the total assets in the relationship?

There are a number of reasons why that approach is not accurate. First, and most importantly, relationships contain more than financial assets. In addition to the loan or loans that make up a relationship, there are likely to be deposit balances belonging to that relationship. And in many cases, the deposit balances are an inseparable part of the relationship. If the mortgage loan leaves the institution, it isn’t unusual for some or all of the deposit balances to leave as well.

In LoanEDGE we calculate the income of both loans and deposits when calculating the net income portion of the ROA (the numerator). If you paused for a moment when I said we calculate the income of a deposit, hold that thought. We will get to the deposit “income” topic in a moment. Just assume for now that we have total relationship income as our numerator. What should we divide by to get ROA?

If we use the total of loans and deposits as the denominator, we are understating the return of that relationship. We would also understate the return if we just use relationship loans as the income source. To see why, imagine that your institution has one customer and that customer has two products – a loan representing your entire loan portfolio and a deposit representing total deposits. Each product produces income after costs.

In this case let’s just say the deposit product produces some decent fee income and by coincidence, the loan and the deposit each produce exactly the same amount of net income after costs. If in this case we take the relationship income and divide by the total of loans and assets, we will end up calculating the relationship ROA as half of the institution ROA. Institution ROA would simply be the relationship income divided by total assets, which is the same as total loans in our simplified relationship.

The next step is to realize that some relationships have more loans than deposits, while some have more deposits than loans. We are trying to consistently calculate the ROA of every relationship, and the only way to make it consistent with institution ROA is to average out that imbalance by using (relationship loans + relationship deposits) divided by 2 as the denominator. Please note – if a relationship has equal loan to deposit ratio, then (relationship loans + relationship deposits) / 2 is the same as loans balance.

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We call this method the balance sheet method of calculating relationship ROA, and it is the default method selected when we configure an institution on LoanEDGE. However, we do support the traditional method if an institution prefers it – which is to use loans plus deposits as the denominator. Some existing loan pricing systems use that method, and to some, it is more intuitive.

It seems non-intuitive to calculate the ROA of one loan by taking half of the average balance as the denominator. But the reason this is not obvious is because we are forgetting that when calculating institution ROA, we assume a balance sheet relationship where assets = liabilities + capital, and we also assume that some deposits produce income. In the individual loan case, we are conveniently forgetting about the other side of the balance sheet equation.

Another reason it seems intuitive to simply use total loans as a denominator is that we often discount the value of deposits. It is easy to think of a deposit as only representing an expense (the interest expense), especially if there is no fee income associated with it. But in LoanEDGE we use the FTP (funds transfer pricing) method of calculating both the income of the loan and the value of a deposit. With FTP, we assume that the spread between loan yield and deposit cost is not simply loan income. We calculate the cost of the loan’s funds based on an independent wholesale curve and for the purpose of the loan income, we ignore your actual deposit cost. FTP recognizes that the difference between the cost of the deposit and the wholesale alternative cost of those same funds is also an income source. We have a separate tutorial illustrating the FTP case with deposits, but keep in mind it is an accepted method of recognizing that the spread between asset income and funding cost represents income that is attributed to both your loan production and deposit gathering activities of your institution. So for that reason as well, the balance sheet method of calculating ROA is appropriate because we are not using the entire loan spread as the income or numerator, and thus we should not be using the total loan balance as the denominator.

So our recommendation is to use the balance sheet method of calculating relationship ROA. This is important when you are including relationship deposits (and their value) in the relationship evaluation, but it is especially important because LoanEDGE uses FTP methodology to measure the income of a loan and FTP does not attribute the entire loan spread to the loan. The traditional method of calculating relationship ROA is available if you simply want to measure the ROA contribution of individual loans and you do not want to attempt to measure the contribution of deposits at the relationship level. Keep in mind that when using the traditional ROA method, you are assuming that net income for your institution is only generated from interest on loans and investments and is only based on the spread between the loan yield and a wholesale cost of funds. Income from deposit transactions and fees is discounted when using the traditional method with LoanEDGE.


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