**The return adjusted to the risk of capital or RAROC for its acronym in English (Risk-adjusted return on capital) is a methodology that proposes a variation to the ratio of ****financial return or ROE**** . Its objective is to calculate the profit margin that a ****bank**** obtains for a product or customer portfolio.**

Unlike **ROE** , RAROC takes into account that the risk of default varies according to the type of **credit** and **debtor** . Thus, at higher risk, the financial institution assigns higher provisions.

The function of RAROC is as follows:

## RAROC elements

The elements of the RAROC are the following:

**Financial margin :**It is calculated by subtracting the interest charged to clients less the**financial expenses**incurred to obtain the borrowed funds.**Commissions:**It is a payment that the debtors make as a percentage of the loan received.**PE or expected losses:**They result from the multiplication of three factors as we see in the following equation:

The first variable (PD) is the probability that the debtor does not comply with repaying the loan. The second data (LGD), which is interpreted as the severity of the loss, is the part of the credit that, once all the collection efforts have been made, is irrecoverable.

These two factors (PD and LGD) are estimated based on information from credit bureaus. Another alternative is for the bank to search for historical data from its own clients. Also, in case of new debtors, you can use user figures or transactions with similar characteristics.

Finally, the EAD is the amount that the financial institution is pending to collect from its borrowers.

**BC or Capital Benefit:**It is the profitability obtained by the financial institution when investing the economic capital.**Economic capital (EC)**is the heritage that keeps the company to protect itself from the**credit risk**,**market risk**and**systematic risk**. It is invested in low risk assets such as**treasury bills**. Unlike the legal reserve, it does not depend on the mandate of the regulator, but on the criteria of each company. This concept is further developed in the**RORAC**note .**Operating expenses :**These are the administrative costs necessary to keep the business running.**t:**It is the rate paid for**Corporation tax**.

## RAROC objective

The objective of RAROC is to estimate the profitability of a financial activity with greater precision than ROE. For this reason, credit risk is included, that is, the probability that clients do not pay back the entire **loan** received.

The usefulness of this ratio is that it allows to distinguish between the performance obtained by different products. In the case of business loans, for example, the possibility of default (the PD factor of expected losses) is higher compared to **consumer loans** .

**RAROC variations**

Within the RAROC methodology, up to three variations can be distinguished:

**RAROC:**When, in relation to ROE, only the numerator varies.

**RORAC:**When, compared to financial profitability, only the denominator changes.

**RARORAC:**When both the numerator and the denominator of the ROE are adjusted according to the risk.

**RAROC example**

Let’s see a simple example of RAROC application. Suppose a bank wants to estimate the performance of its consumer loan portfolio of $ 150,000.

The **interest rate** of the loans analyzed is 14% on average. In turn, the rate the bank pays for raising these resources stands at 7%.

With these data, we can calculate the financial margin that is 7% (14% -7%). To this is added the opening commission charged to debtor clients of 0.25%.

Another fact that we know is that the administrative expenses incurred by the financial institution were US $ 7,000.

Likewise, the probability of default of the analyzed portfolio is 5%, while the severity of the loss is 40%. Therefore, the expected loss will be:

**PE =** 0.05 x 0.4 x 150,000 = US $ 3,000

Let us also suppose that the Economic Capital is 8% of the portfolio, that is, US $ 12,000. By investing this equity, a return of 3% is obtained in the analysis period.

So, we can calculate the risk-adjusted benefit, considering a tax rate of 25%:

**Economic capital =** US $ 12,000

**RAROC =** 926.25 / 12,000 = 7.72%