PROFITABILITY MEASURES
Category: Risk Management in Banking
Classical profitability measures include the Return On Equity (ROE) and the Return On Assets (ROA). Risk-based profitability measures embed risk adjustment combining expected loss and economic capital.
Economic Capital
Risk-based measures require quantified risk measures. For credit risk, the risk measures are economic capital and expected loss. Both serve for the banking transactions, at the portfolio level, for any subportfolio, using the risk contribution as the capital base, and for any facility, using also the risk contribution as the capital base. For market risk, capital only is relevant, globally, or allocated to subportfolios or facilities through risk contributions. Both market risk capital and credit risk capital for market transactions serve to adjust Profit and Loss (P&L) for risk.
Using regulatory capital for risk-adjusting measures also makes sense. However, as long as regulatory forfeits do not sufficiently differentiate the risk and are not in line with economic capital, using the regulatory capital results in mispricing risks, which is a competitive disadvantage. Regulatory forfeits are progressively enriched, step-by-step, by regulators. The old forfeits (before the January 2001 guidelines) consider private small business risk as equivalent to the risk of AAA large corporations, which falls short of the essential requirements of RAPM and RBP. However, whatever the regulatory scheme, banks have to meet regulatory capital definitions. Therefore, they still have to obtain a sufficient return on this capital and keep monitoring its cost for transactions and portfolios.
We focus on economic capital as a prerequisite for risk-adjusted measures. Technically, however, the regulatory capital-adjusted measures RaRoC and SVA are easy to obtain by simply substituting regulatory capital for economic capital in the same formulas, so that there is no difficulty in calculating both.
RaRoC Measures
The two basic variants for risk-adjusted ratios are the Return on Risk-adjusted Capital (RoRaC) or RaRoC. The RoRaC is a profitability calculated on risk-based capital. RaRoC adjusts first the return for risk by netting expected loss from income for banking transactions. Both adjustments are necessary for banking transactions, and adjustment for capital only suffices for market transactions. In the following, RaRoC is the generic name for the return on risk-based capital.
We discuss the credit risk case, given that only capital without Expected Loss (EL) adjustment suffices for market risk. The RaRoC ratio adjusts the earnings with EL and uses risk contributions as economic capital. The revenues are the All-In Spread (AIS), which averages all interest revenues and fees into an annualized average. The formula applies both pre-operating costs and post-operating costs:
Economic capital is the portfolio capital for the entire portfolio and is the capital allocation, or risk contribution, for subportfolios or facilities. There are two risk contributions, absolute and marginal, each corresponding respectively to ex post measures and ex ante measures. At this stage, we simply use risk contributions, given that we have to use the right one depending on the purpose of the measure:
where RC(K) is the risk contribution of a facility or subportfolio to the capital K.When considering that the capital allocation RC(K) provides a risk-free return yf x RC(K),it should be included in the revenues.
The usage of RaRoC implies the definition of a hurdle rate, k%, which is the minimum risk-adjusted return on a transaction. The EL netted from revenues has different interpretations depending on whether it applies to individual transactions or to portfolios of transactions. For an individual transaction, the EL concept looks theoretical since the loss will either occur or not. In any case, the loss is never equal to the EL, since the actual loss is either zero or the loss given default. For portfolios, EL has a statistical meaning because setting aside a fraction of revenues of all transactions will, after consolidation, result in a sufficient provision for meeting the overall EL requirement (estimated on an ex ante basis).
The fully developed analytical formulas use the following notation:
• Exposure A.
• Asset all-in return r (%).
• Cost of debt i. This cost includes any credit spread applicable to the bank.
• Allocated debt D.
• Operating costs oc (%).
• Expected loss el (%).
• Allocated capital RC(K) = K.
The Hurdle Rate
The hurdle rate k% is the minimum required return as a percentage. There are two important benchmarks for setting this hurdle rate:
• The required return on capital, since this is a shareholder target that indicates whether a particular transaction creates or destroys value.
• The mean return of the bank portfolio, because it is important to know whether a transaction of a subportfolio improves or deteriorates this average.
The first benchmark derives from the price of risk in the capital market from well-known equity return models. It is the return k% required by shareholders given the risk of the stock as measured by the beta of the banks stocks, following the CAPM framework or the Arbitrage Pricing Theory (APT) framework. An order of magnitude of such a return is 20-25% before tax. This benchmark applies to revenues net of all operating costs. If revenues are pre-operating costs, the benchmark is higher since it should provide the revenues required to absorb all unallocated costs in addition to providing the required pretax income to shareholders. The next section illustrates the simple adjustment required to determine revenues, given the post-operating cost hurdle rate and the non-allocated costs.
RaRoC and SVA
For decision-making purposes and to compare performance to a hurdle rate, RaRoC and SVA are equivalent. By definition, RaRoC > k% is equivalent to SVA at k% > 0. However, they provide different pictures of business volume, risk-free and low-profitability transactions.
Business Volume
A drawback of ratios is that they do not account for size. It is nice to have a RaRoC of 50% with a transaction of 1 million euros. However, it is even nicer if the transaction size is 10 million euros. In order to improve an overall profitability rate, it is always possible to eliminate those transactions that are less profitable and to keep only the rest. In such cases, the portfolio profitability increases at the expense of the volume of business. Since both business volume and profitability are desirable, SVA measures might look appropriate, but they do not provide the percentage profitability, so we cannot tell whether a high SVA results from a large size or from a large percentage profitability.
This is a business issue. If there is a permissible trade-off between percentage profitability and volume, it makes sense to aggregate transactions. For instance, we can have a low RaRoC loan to a customer because it attracts new business later on. Each individual transaction with a customer might not be profitable, once it is risk-adjusted. But all of them might. Client-driven revenues are more relevant than transaction-driven revenues. Therefore client-based profitability is as necessary as transaction-based profitability. This applies also for any business policy aimed at gaining market share. However, this shows that improper usage of risk-adjusted measures could lead to rejecting profitable transactions because of a pure transaction-based reporting.
Risk-free Transactions
A well-known drawback of RaRoC is that the ratio can take very high values for close to zero risk, such as with Aaa counterparties. In addition, it increases to infinity with risk-free transactions. This is more a reporting drawback than a conceptual flaw. It is normal for non-risky borrowers not to consume any capital. RaRoC has no value added in this case. This does not mean that a relevant target pricing is undefined. When capital drops to zero, the risk premium is zero, and the target revenues should still absorb the operating costs, plus the cost of debt, plus any mark-up. Nevertheless, very high RaRoC, infinite ratios or negative ratios appearing in reports create confusion. SVA does not have this flaw. If risk is zero, the SVA equals revenues, pre- or post-operating costs, without deduction of any cost of risk, and remains meaningful. In addition, a negative SVA is also meaningful, while a negative RaRoC is not. The negative SVA means that the business destroys value for shareholders and tells us how much.
Netting EL from Revenues and RaRoC
RaRoC ratios can be negative when revenues do not absorb costs plus expected loss EL. A partial remedy would be to include EL in capital, instead of using capital in excess of EL. This means that capital should absorb both expected and unexpected losses. SVA does not have these drawbacks and is always meaningful. If capital drops to zero because the transaction is risk-free, both EL and cost of capital in the SVA calculations drop to zero, but the other terms remain relevant.