## RAROC/RARORAC

##### Published: May 2010

Risk-adjusted return on capital (RAROC) is a profitability metric that can be used to analyse return in relation to the level of risk taken on. It can be used to compare the performance of several investments with differing levels of risk exposure. It should not be confused with RORAC (return on risk-adjusted capital) which adjusts the capital invested based on the risks being taken. RAROC instead adjusts the return itself. RAROC was developed by Bankers Trust in the late 1970s and early 1980s in response to regulatory interest in the capital ratios of financial institutions and the implementation of capital adequacy regulations. RAROC is often used by banks to determine the amount of capital required to support the bank’s activities.

### How is it calculated?

$$\mathrm{RAROC} = \frac{revenue\:– \:expenses\: – \:expected \:loss\:+ \:income\: from\: capital}{capital}$$

• ##### Expected loss.

This is the average anticipated loss over the period being measured. It will include the cost of doing business as well as any loss incurred from default or operational risk.

• ##### Income from capital.

This is calculated by multiplying capital charges by the risk-free rate. This is because, since capital is set aside to support a risky transaction, it should theoretically be invested in something ‘risk free’.

• ##### Capital.

Economic capital is the amount of capital that a financial institution needs to ensure that the company remains solvent. It should be sufficient to support any risks that the company takes on.

### Example

Consider the following example:

$$\mathrm{RAROC} =\frac{16,434\:–\:15,615\:–\:221\:+\:66}{8,623}={8,623}={0.08\:or \:\%} {risk-adjusted \:return \:on \:capital}$$

### RARORAC and Basel II

RARORAC, the risk-adjusted return on risk-adjusted capital, combines RAROC with RORAC to adjust both the return and the capital based on the risks being taken. An example of this is Basel II which specifies regulations regarding the basic capital requirement to be held by international banks. Basel II states that banks must adjust their capital levels in relation to the level of credit risk, market risk and operational risk involved in the bank’s operational activities. The formula used to calculate the minimum level required is roughly as follows:

$$\frac{capital}{credit \:risk\:+\:market\: risk\: + \:operational\: risk}≥8\%$$

As a result, RARORAC is being used more and more as a measure to assess the risk-adjusted economic capital and the risk-adjusted return on an investment, where the risk adjustment for capital is based on the capital adequacy guidelines shown above.

### Points to consider

The use of risk-adjusted capital enables companies to determine the level of risk in each individual line of business and thus allocate the required amount of capital accordingly. The use of risk adjusted returns can be used to measure performance, which can aid the effective diversification of the composition of an investment portfolio. Shareholder value can similarly be increased by the reallocation of capital to areas of the business based on the economic value added. It is important to remember that although these ratios allow for the incorporation of market risk, credit risk and operational risk, they do not encompass systemic risks, so these must be calculated separately.