Introduction

• Risk capital is the cushion that provides protection against the various risks inherent in the business of a corporation so that the firm can maintain its financial integrity and remain a going concern even in the event of a near-catastrophic worst-case scenario. Risk capital gives essential confidence to the corporation’s stakeholders, such as suppliers, clients, and lenders (for an industrial firm), or claimholders, such as depositors and counterparties in financial transactions (for a financial institution).
• Risk capital is often called economic capital, and in most instances, the generally accepted convention is that risk capital and economic capital are identical (although sometimes economic capital is defined as risk capital plus strategic capital).

Risk Capital Versus Regulatory Capital

• The concept of risk capital, which is intended to capture the economic realities of the risks a firm runs, should not be confused with regulatory capital.
  • First, regulatory capital only applies to a few regulated industries, such as banking and insurance companies, where regulators are trying to protect the interests of small depositors or policyholders.
  • Second, while regulatory capital performs something of the same function as risk capital in the regulators’ eyes, it is calculated according to a set of industry-wide rules and formulas and sets only a minimum required level of capital adequacy. It rarely succeeds in capturing the true level of risk in a firm, and the gap between a firm’s regulatory capital and its risk capital can be quite wide.
  • Furthermore, even if regulatory and risk capital are similar numbers at the level of the firm, they may not be similar for each constituent business line (i.e., regulatory capital may suggest that an activity is much riskier than management believes, or vice versa).
• The new regulatory capital requirements imposed by Basel III make it likely that for some activities, such as securitization, regulatory capital may end up much higher than economic capital. Still, economic capital calculation is essential for senior management as a benchmark to assess the economic viability of the activity for the financial institution. When regulatory capital is much larger than economic capital, it is likely that over time the activity will migrate to the shadow banking sector, which can price the transactions at a more attractive level.

Risk Capital Measurement

• Risk capital measurement is based on the same concepts as the value-at-risk (𝑉𝑎𝑅) calculation methodology. The choice of the confidence level and time horizon in the internal VaR models are key policy parameters that should be set by senior management (or the senior risk management committee) and endorsed by the board.
• Risk capital should be calculated in such a way that the institution can absorb unexpected losses up to a level of confidence in line with the requirements of the firm’s various stakeholders. No firm can offer its stakeholders a 100 percent guarantee (or confidence level) that it holds enough risk capital to ride out any eventuality. Instead, risk capital is calculated at a confidence level set at less than 100 percent—say, 99.9 percent for a firm with conservative stakeholders.
• The exact choice of confidence level is typically associated with some target credit rating from a rating agency such as Moody’s, Standard & Poor’s, and Fitch, as these ratings are themselves explicitly associated with a probability of default. It should also be in line with the firm’s stated risk appetite.

Emerging Uses Of Risk Capital Numbers

• Recently, risk capital numbers have been used to answer more and more questions, particularly in banks and other financial institutions. These include:
  • Performance measurement and incentive compensation at the firm, business unit, and individual levels. Risk capital can be plugged into risk-based capital attribution systems, often grouped together under the acronyms 𝑅𝐴𝑃𝑀 (risk-adjusted performance measurement) or 𝑅𝐴𝑅𝑂𝐶 (risk-adjusted return on capital). These can be used to compare the economic profitability, as opposed to the accounting profitability (such as return on book equity), of different activities. At the same time, 𝑅𝐴𝑅𝑂𝐶 numbers can be used as part of scorecards to compensate the senior management of particular business lines, as well as the infrastructure group, for their contribution to shareholder value.
  • Active portfolio management for entry/exit decisions – The decision to enter or exit a particular business should be based on both risk-adjusted performance measurement and the “risk diversification effect” of the business. For example, a firm focused on corporate lending in a particular region is likely to find that its returns fluctuate in accordance with that region’s business cycle. Ideally, the firm might diversify its business geographically or in terms of business activity. Capital management decisions seek an answer to the question, “How much value will be created if the decision is taken to allocate resources to a new or existing business, or alternatively to close down an activity?”
  • Pricing transactions – Risk capital numbers can be used to calculate risk-based pricing for individual transactions, ensuring that a firm is compensated for the economic risk generated by a transaction. For example, a loan to a non-investment-grade firm in relatively fragile financial condition must be priced higher than a loan to an investment-grade firm. However, the amount of the differential can be determined only by working out the amount of expected loss and the cost of the risk capital that must be set aside for each transaction. Trading and corporate loan desks in many banks rely on the “marginal economic capital requirement” component in the 𝑅𝐴𝑅𝑂𝐶 calculation to price deals in advance and to decide whether those deals will increase shareholder value rather than simply add to the volume of transactions.
• One problem is that a single measure of risk capital cannot accommodate all the different purposes at the same time.

Importance Of Economic Capital For Financial Institutions

1. Capital Usage in Financial Institutions – Capital is primarily used in a financial institution not only to provide funding for investments (as in a manufacturing corporation) but also to absorb risk. The fundamental reason for this is that financial institutions can leverage themselves to a much higher degree than other corporations at a much lower cost without raising equity, by taking retail deposits or issuing debt securities. Their debt-to-equity ratio might be as high as 20 to 1, compared to perhaps 2 to 1 for an industrial corporation.
2. Target Solvency as a Product – A bank’s target solvency is a vital part of the product it is selling. The primary customers of banks and other financial institutions are also their primary liability holders—e.g., depositors, derivatives counterparties, insurance policyholders, and so on. These customers are concerned about default risk on contractually promised payments. Customers make deposits with the expectation that the safety of their deposits does not depend on the economic performance of the bank. In over-the-counter markets, institutions are concerned about counterparty risk: a bank with a poor credit rating will find itself excluded from many markets. Maintaining good creditworthiness is, therefore, an ongoing cost of doing business for a bank.
3. Bank Opacity and Risk Management – Although bank creditworthiness is critical, banks are also highly opaque institutions. Banks use proprietary technology for pricing and hedging financial instruments, especially complex financial transactions. A typical bank’s balance sheet is relatively liquid and can change very quickly. Any outside assessment of the creditworthiness of a bank is, therefore, difficult to develop and rapidly becomes obsolete (as the risk profile of the bank keeps on changing). Maintaining enough risk capital and implementing a strong risk management culture allows the bank to reduce these “agency costs” by convincing external stakeholders, including rating agencies, of the bank’s financial integrity.
4. Competitive Markets and Capital Sensitivity – Banks operate in highly competitive financial markets, and their profitability is very sensitive to their cost of capital. Banks don’t want to carry too much risk capital because risk capital represents the money invested in the bank that does not have to be repaid under any fixed contractual agreement (e.g., equity capital). This flexibility, which allows risk capital to act as a safety buffer for the bank if times are hard, means that risk capital is relatively expensive to raise and hold (e.g., compared to debt capital). Therefore, understanding the dynamic balance between the capital the bank carries and the riskiness of its activities is very important.

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Risk Adjusted Performance Measures

• Traditional accounting-based measures of performance at the consolidated level and for individual business units, such as return on assets (𝑅𝑂𝐴) or return on book equity (𝑅𝑂𝐸), fail to capture the risk of the underlying activity.
• RAPM (risk-adjusted performance measurement) is a generic term describing all the techniques used to adjust returns for the risk incurred in generating those returns. It encompasses many different concepts, risk adjustments, and performance measures, with 𝑅𝐴𝑅𝑂𝐶 being the form most widely used in the banking sector. These 𝑅𝐴𝑃𝑀 measures are not fully consistent with one another.
  • RAROC (risk-adjusted capital) = risk-adjusted expected net income/economic capital. 𝑅𝐴𝑅𝑂𝐶 makes the risk adjustment to the numerator by subtracting a risk factor from the return (e.g., expected loss). It also makes the risk adjustment to the denominator by substituting economic capital for accounting capital.
  • RORAC (return on risk-adjusted capital) = net income/economic capital. 𝑅𝑂𝑅𝐴𝐶 makes the risk adjustment solely to the denominator. In practical applications:
    • 𝑅𝑂𝑅𝐴𝐶 = 𝑃&𝐿 (Profit and Loss) / 𝑉𝑎𝑅
  • ROC (return on capital) = 𝑅𝑂𝑅𝐴𝐶. It is also called 𝑅𝑂𝐶𝐴𝑅 (return on capital at risk).
  • RORAA (return on risk-adjusted assets) = net income/risk-adjusted assets.
  • ROROA (risk-adjusted return on risk-adjusted assets) = risk-adjusted expected net income/risk-adjusted assets.
  • S (Sharpe ratio) = (expected return – risk-free rate)/volatility. The ex-post Sharpe ratio—i.e., that based on actual returns rather than expected returns—can be shown to be a multiple of 𝑅𝑂𝐶.
  • NPV (net present value) = discounted value of future expected cash flows, using a risk-adjusted expected rate of return based on the beta derived from the 𝐶𝐴𝑃𝑀, where risk is defined in terms of the covariance of changes in the market value of the business with changes in the value of the market portfolio. In the 𝐶𝐴𝑃𝑀, the definition of risk is restricted to the systematic component of risk that cannot be diversified away. For 𝑅𝐴𝑅𝑂𝐶 calculations, the risk measure captures the full volatility of earnings, systematic and specific. 𝑁𝑃𝑉 is particularly well-suited for ventures in which the expected cash flows over the life of the project can be easily identified.
  • EVA (economic value added), or 𝑁𝐼𝐴𝐶𝐶 (net income after capital charge), is the after-tax adjusted net income less a capital charge equal to the amount of economic capital attributed to the activity, times the after-tax cost of equity capital. The activity is deemed to add shareholder value, or is said to be 𝐸𝑉𝐴 positive, when its 𝑁𝐼𝐴𝐶𝐶 is positive (and vice versa). An activity whose 𝑅𝐴𝑅𝑂𝐶 is above the hurdle rate is also 𝐸𝑉𝐴 positive.

RAROC: Risk-Adjusted Return On Capital

• 𝑅𝐴𝑅𝑂𝐶 is a conceptually simple approach used to allocate risk capital to business units and individual transactions for the purpose of measuring economic performance.
• The approach makes clear the trade-off between risk and reward for a unit of capital and, therefore, offers a uniform and comparable measure of risk-adjusted performance across all business activities. If a business unit’s 𝑅𝐴𝑅𝑂𝐶 is higher than the cost of the bank’s equity (the minimum rate of return on equity required by the shareholders), then the business unit adds value to shareholders. Senior management can use this measure to evaluate performance for capital budgeting purposes and as an input to the compensation for managers of business units.
• The following generic 𝑅𝐴𝑅𝑂𝐶 equation is a formalization of the trade-off between risk and reward:

\( \text{RAROC} = \frac{\text{after_tax expected risk_adjusted net income}}{\text{economic capital}} \)

• The 𝑅𝐴𝑅𝑂𝐶 equation employs economic capital as a proxy for risk and after-tax expected risk-adjusted net income as a proxy for reward.

For capital budgeting purposes, 𝑅𝐴𝑅𝑂𝐶 is calculated as:

\( \text{RAROC} = \frac{\text{expected revenues} – \text{costs} – \text{expected losses} – \text{taxes} + \text{return on risk capital} \pm \text{transfers}}{\text{economic capital}} \)

where:

• Expected revenues are the revenues that the activity is expected to generate (assuming no losses).
• Costs are the direct expenses associated with running the activity (e.g., salaries, bonuses, infrastructure expenses).
• Expected losses are primarily the expected losses from default, corresponding to the loan loss reserve the bank must set aside as the cost of doing business. This cost is priced into the transaction in the form of a spread over the funding cost, so there is no need for risk capital as a buffer to absorb this risk. Expected losses also include the expected loss from other risks, such as market and operational risks.
• Taxes are the expected amount of taxes imputed to the activity using the effective tax rate of the company.
• Return on risk capital is the return on the risk capital allocated to the activity, generally assumed to be invested in risk-free securities, such as government bonds.
• Transfers correspond to transfer pricing mechanisms between the business unit and the treasury group, including charges for funding costs, hedging interest rate, and currency risks, as well as overhead cost allocation from the head office.
• Economic capital is the sum of risk capital and strategic capital.

𝑠𝑡𝑟𝑎𝑡𝑒𝑔𝑖𝑐 𝑟𝑖𝑠𝑘 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 + 𝑏𝑢𝑟𝑛𝑒𝑑_𝑜𝑢𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙

• Risk capital is the capital cushion that the bank must set aside to cover the worst-case loss (minus the expected loss) from market, credit, operational, and other risks (e.g., business and reputation risks) at the required confidence threshold (e.g., 99%). It is directly related to the value-at-risk calculation at the one-year time horizon.
• Strategic risk capital refers to the risk of significant investments whose success and profitability are highly uncertain. If the venture is not successful, the firm will face a major write-off and potential reputation damage.
• Burned-out capital refers to capital spent on initiatives that ultimately may not be pursued due to inferior risk-adjusted returns. This capital is amortized over time as the risk of strategic failure dissipates.
• The goodwill element corresponds to the investment premium paid above the replacement value of the net assets when acquiring a company. Goodwill is depreciated over time.
• The figure illustrates the linkage between a risk loss distribution and the 𝑅𝐴𝑅𝑂𝐶 calculation. It displays an expected loss of 15 basis points (bps) and a worst-case loss of 165 bps at the 99% confidence level over a one-year horizon. The unexpected loss is the difference between the total loss and the expected loss, i.e., 150 bps, corresponding to the risk capital allocated to the activity.

RAROC For Capital Budgeting

• Consider a $1 billion corporate loan portfolio with a headline return of 9%. The bank has an operating direct cost of $9 million per annum and an effective tax rate of 30%. The portfolio is funded by $1 billion of retail deposits with a transfer-priced interest charge of 6%. Based on the risk analysis, economic capital is set at $75 million (7.5% of the loan amount) and is invested in risk-free securities at a 5% rate. The expected loss is 1% per annum ($10 million).

• If transfer price considerations are ignored, the after-tax 𝑅𝐴𝑅𝑂𝐶 for this loan is:

\( \text{RAROC} = \frac{(90 – 9 – 60 – 10 + 3.75)(1 – 0.3)}{75} = 0.14 \, \text{or} \, 14\% \)

This number represents the annual after-tax expected rate of return on equity needed to support this loan portfolio.

RAROC For Performance Measurement

• 𝑅𝐴𝑅𝑂𝐶 was first suggested as a tool for capital allocation on an anticipatory or ex-ante basis. Hence, expected revenues and losses should be used in the numerator of the 𝑅𝐴𝑅𝑂𝐶 equation for capital budgeting purposes. When 𝑅𝐴𝑅𝑂𝐶 is used for ex-post (after the fact) performance evaluation, the realized revenues and realized losses can replace the expected values in the calculation.

RAROC For Performance Measurement – Time Horizon

• All quantities plugged into the 𝑅𝐴𝑅𝑂𝐶 equation must be calculated based on a specific time horizon, such as one year or over the lifetime of a deal. Practitioners usually adopt a one-year time horizon as it corresponds to the business planning cycle and approximates the length of time needed to recapitalize the company in the event of a major unexpected loss.
• For credit risk, there is a straightforward equivalence between the one-year 𝑉𝑎𝑅 produced by credit portfolio models (e.g., CreditMetrics or 𝐾𝑀𝑉) and risk capital. The same applies to operational risk, as most internal models used by institutions adopt a one-year horizon. Thus, no adjustment in the one-year 𝑉𝑎𝑅 is needed to determine risk capital for credit and operational risks.
• However, this is not the case for market risk. For trading businesses, market risk is typically measured using short-term horizons—one day for risk monitoring on a daily basis and 10 days for regulatory capital. The challenge is to translate a one-day risk measure into a one-year risk capital attribution.
• The purpose of risk capital is to limit the risk of failure during a crisis when the bank suffers significant losses. If the “square root of time” rule is used—approximating the one-year 𝑉𝑎𝑅 by multiplying the one-day 𝑉𝑎𝑅 by the square root of the number of business days in a year (e.g., 252 or 250 days)—the point of risk capital would be missed entirely.
• This approach needs refinement by considering that even in a worst-case scenario, the firm might not be able to reduce its risk beyond a core risk level to remain financially viable for the rest of the year. To calculate a meaningful one-year economic capital allocation, the business in question should be analyzed to understand the time required to reduce the current risk position to the core risk level. This reflects the relative liquidity of positions during adverse market conditions.
• Estimations of the time to reduce risk should not assume a “fire sale” but instead assume a relatively orderly unwinding of positions. This process can take considerable time in some markets, as many firms discovered during the 2007-2009 financial crisis.
• The figure (not shown) provides an example of the calculation of risk capital when the core risk level is lower than the current risk position.

RAROC For Performance Measurement – Default Probabilities

• A point-in-time (𝑃𝐼𝑇) probability of default (𝑃𝐷), which is the approach used by 𝐾𝑀𝑉 and other economic/structural models, is reasonable for calculating near-term expected losses (𝐸𝐿) and for pricing financial instruments subject to credit risk. A through-the-cycle (𝑇𝑇𝐶) 𝑃𝐷, largely adopted by rating agencies, is more suitable for calculating economic capital, assessing current profitability, and making strategic decisions regarding products, geographies, and new business ventures.
• The probability of a firm maintaining the same rating when assessed using a 𝑃𝐼𝑇 approach is smaller than when using a 𝑇𝑇𝐶 approach. The 𝑇𝑇𝐶 approach, therefore, reduces the volatility of economic capital compared to 𝑃𝐼𝑇 approaches. It is useful to periodically compare the impact of using 𝑃𝐼𝑇 𝑃𝐷 versus 𝑇𝑇𝐶 𝑃𝐷 in the 𝑅𝐴𝑅𝑂𝐶 calculation, both during normal economic conditions and the worst parts of the economic cycle.

RAROC For Performance Measurement – Confidence Level

• As stated earlier, the confidence level in the economic capital calculation should align with the firm’s target credit rating. For example, most banks aim for an 𝐴𝐴 credit rating from rating agencies for their debt offerings, implying a one-year probability of default of 3 to 5 basis points. This corresponds to a confidence level ranging from 99.95% to 99.97%. This confidence level quantitatively expresses the firm’s risk appetite.
• Setting a lower confidence level may significantly reduce the amount of risk capital allocated to an activity, particularly when the institution’s risk profile is dominated by operational, credit, and settlement risks (where large losses are infrequent). Therefore, the choice of the confidence level can materially affect risk-adjusted performance measures and the resulting capital allocation decisions of the firm.

Hurdle Rate And Capital Budgeting

• The hurdle rate should be reset every six months or annually, or when it has changed by more than 10%. This hurdle rate is calculated as:

\( h_{AT} = \frac{[CE \times r_{CE}] + [PE \times r_{PE}]}{CE + PE} \)

• ​where 𝐶𝐸 and 𝑃𝐸 denote the market values of common equity and preferred equity, respectively, and \(𝑟_{CE}\) and \(𝑟_{PE}\) are the costs of common equity and preferred equity, respectively.
• The cost of preferred equity is simply the yield on the firm’s preferred shares. The cost of common equity is determined using a model such as the Capital Asset Pricing Model (CAPM):

\( r_{CE} = r_f + \beta_{CE}(\overline{R_M} – r_f) \)

• where \(𝑟_f\) is the risk-free rate, \(\overline{R_M}\) is the expected return on the market portfolio, and \(\beta\) is the firm’s common equity market beta.
• When a firm is considering investing in a business or closing down an activity, it computes the after-tax 𝑅𝐴𝑅𝑂𝐶 for the business or activity and compares it to the firm’s hurdle rate. In theory, the firm can then apply a simple decision rule:
  • If the 𝑅𝐴𝑅𝑂𝐶 ratio is greater than the hurdle rate, the activity is deemed to add value to the firm.
  • In the opposite case, the activity is deemed to destroy value for the firm and the activity should be closed down or the project rejected.
• However, applying this simple rule can sometimes lead to a firm accepting high-risk projects that lower the firm’s value and rejecting low-risk projects that could increase its value. High-risk projects, such as oil exploration, are characterized by very volatile returns, while low-risk projects, like properly risk-managed retail banking, produce steady revenues with low volatility.
• To overcome this, adjusted 𝑅𝐴𝑅𝑂𝐶 is calculated so that the systematic riskiness of the returns from a business activity is fully captured by the decision rule.

Adjusted RAROC

• Ideally, the traditional 𝑅𝐴𝑅𝑂𝐶 calculation should be adjusted to obtain a 𝑅𝐴𝑅𝑂𝐶 measure that takes into account the systemic riskiness of returns, and for which the hurdle rate (the critical benchmark above which a business adds value) is the same across all business lines. To correct the inherent limitations of the traditional 𝑅𝐴𝑅𝑂𝐶 measure, let’s adjust the 𝑅𝐴𝑅𝑂𝐶 ratio as follows:

\( \text{Adjusted RAROC} = \text{RAROC} – \beta_E (R_M – r_f) \)

where 𝑅 is the expected rate of return on the market portfolio, 𝑟 denotes the risk-free interest rate, and 𝛽 is the beta of the equity of the firm. The new decision rule is:

• Accept projects whose 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅𝐴𝑅𝑂𝐶 is greater than 𝑟.
• Reject projects whose 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅𝐴𝑅𝑂𝐶 is less than 𝑟.

• The risk adjustment, \( \beta_E (R_M – r_f) \) is the excess return above the risk-free rate required to compensate the shareholders of the firm for the non-diversifiable systematic risk they bear when investing in the activity, assuming that the shareholders hold a well-diversified portfolio. When the returns are thus adjusted for risk, the hurdle rate becomes the risk-free rate.

Diversification And Risk Capital

• The risk capital for a particular business unit within a larger firm is usually determined by viewing the business on a stand-alone basis, using the top-of-the-house hurdle rate that was discussed earlier. However, intuition suggests that the risk capital for the firm should be significantly less than the sum of the stand-alone risk capital of the individual business units, because the returns generated by the various businesses are unlikely to be perfectly correlated.
• Measuring the true level of this “diversification effect” is extremely problematic. As of today, there is no fully integrated 𝑉𝑎𝑅 model that can produce the overall risk capital for a firm, taking into account all the correlation effects between market risk, credit risk, and operational risk across all the business units of a company. Instead, banks tend to adopt a bottom-up decentralized approach, under which distinct risk models are run for each portfolio or business unit.
• For capital adequacy purposes, running these business-specific models at the confidence level targeted at the top of the house, for example, 99.97 percent, produces an unnecessarily large amount of overall risk capital, precisely because it neglects diversification effects (across both risk types and business activities). It is therefore common practice to adjust for the diversification effects by lowering the confidence level used at the business level to, say, 99.5 percent or lower—an adjustment that is necessarily more of an educated guess than a strict risk calculation.
• Let’s apply some boundaries around the problem. The aggregate 𝑉𝑎𝑅 figure obtained by this approach should fall in between the two extreme cases of perfect correlation and zero correlation between risk types and across businesses. For example, ignoring business risk, reputation risk, and strategic risk for illustrative purposes, suppose that the risk capital for each type of risk has been calculated as follows:
  • Market risk = $200
  • Credit risk = $700
  • Operational risk = $300

• Then the aggregate risk capital at the top of the house is:
  • Simple summation of the three risks (perfect correlation) = $1,200
  • Square root of the sum of squares of the three risks (zero correlation) = $787
• It can be said with some confidence, therefore, that any proposed approach for taking diversification effects into account should produce an overall 𝑉𝑎𝑅 figure in the range of $787 to $1,200.
• While the simple logic of the boundary setting makes sense, these boundaries are quite wide! They also lead to the reverse problem:
  • How should any diversification benefit that has been calculated for the business as a whole be allocated back to the business lines?
• The allocation of the diversification effect can be important for certain business decisions, such as determining the performance of each unit.
• Logically, a business whose operating cash flows are strongly correlated with the earnings of the other activities in the firm should require more risk capital than a business with the same volatility whose earnings move in a countercyclical fashion. Bringing together countercyclical business lines produces stable earnings for the firm as a whole; the firm can then operate to the same target credit rating with less risk capital.
• Institutions continue to struggle with the problem of attributing capital back to business lines, and there are diverging views as to the appropriate approach. For the moment, as a practical solution, most institutions allocate the portfolio effect pro rata with the stand-alone risk capital.
• Diversification effects also complicate matters within business units. Let’s look at this and other issues in relation to an example business unit, BU, which comprises two activities, X and Y.

• When calculating the risk capital of the business unit, let’s assume that the firm’s risk analysts have taken into account all the diversification effects created by combining activities X and Y and that the risk capital for BU is $100. The complication starts when trying to allocate risk capital at the activity level within the business unit. There are three different measures of risk capital:
  • Stand-alone capital
  • Fully diversified capital
  • Marginal capital

Diversification Within Business Units

• Stand-alone capital is the capital used by an activity taken independently of the other activities in the same business unit—that is, risk capital calculated without any diversification benefits. In the previous example, the stand-alone capital for 𝑋 is $60, and for 𝑌, it is $70. The sum of the stand-alone capitals of the individual constituents of the business unit is generally higher than the stand-alone risk capital of the business unit itself (it is equal only in the case of perfectly correlated activities 𝑋 and 𝑌).
• Fully diversified capital is the capital attributed to each activity 𝑋 and 𝑌, taking into account all diversification benefits from combining them under the same leadership. In the example, the overall portfolio effect is: \$30 \, (\$60 + \$70 – \$100)\. The portfolio diversification effect is allocated pro rata with the stand-alone risk capital, \$30 \times \frac{60}{130} = \$14\ for X and \$30 \times \frac{70}{130} = \$16\ for Y, so that the fully diversified risk capital becomes $46 for 𝑋 and $54 for 𝑌.
• Marginal capital is the additional capital required by an incremental deal, activity, or business, taking into account the full benefit of diversification. In the example, the marginal risk capital for 𝑋 (assuming that 𝑌 already exists) is $30($100 – $70) and the marginal risk capital for 𝑌 (assuming that 𝑋 already exists) is $40($100 – $60). In the case where more than two activities are included in the business unit 𝐵𝑈, marginal capital is calculated by subtracting the risk capital required for the 𝐵𝑈 without this business from the risk capital required for the full portfolio of businesses. Note that the summation of the marginal risk capital, $70 in the example, is less than the full risk capital of the BU.
• As this example shows, the choice of capital measure depends on the desired objective:
  • Fully diversified measures should be used for assessing the solvency of the firm and minimum risk pricing.
  • Active portfolio management or business mix decisions should be based on marginal risk capital, taking into account the benefit of full diversification.
  • Performance measurement should involve both perspectives: stand-alone risk capital for incentive compensation, and fully diversified risk capital to assess the extra performance generated by diversification effects.
• However, it is important to be cautious about the generosity of attributing diversification benefits. Correlations between risk factors drive the extent of the portfolio effect, and these correlations tend to vary over time. During market crises, in particular, correlations sometimes shift dramatically toward either 1 or -1, reducing or totally eliminating portfolio effects for a period of time.

RAROC Best Practices

• Economic capital is a key element in the assessment of business line performance, in the decision to exit or enter a business, and in the pricing of transactions. It also plays a critical role in the incentive compensation plan of the firm.
• In firms where 𝑅𝐴𝑅𝑂𝐶 has been implemented, business units challenge the risk management function about the fairness of the amount of economic capital attributed to them. The usual complaint is that their economic capital attribution is too high (never that it is too low!). Another complaint is that economic capital attribution is sometimes too unstable for purposes of trying to hit a target.
• The best way to defuse this debate is to be transparent about the methodology used to assess risk and to institute forums where the issues related to the determination of economic capital can be debated and analyzed. The VaR methodologies for measuring market risk and credit risk that underpin 𝑅𝐴𝑅𝑂𝐶 calculations are generally well accepted by business units. The disagreement stems from the setting of parameters that feed into these models and the consequent sizing of economic capital.

RAROC Best Practices – Recommendations

1. Senior management commitment – Given the strategic nature of the decisions steered by a 𝑅𝐴𝑅𝑂𝐶 system, the marching orders must come from the top management of the firm. The CEO and their executive team should sponsor the implementation of a 𝑅𝐴𝑅𝑂𝐶 system and actively promote a new culture within the firm where performance is measured in terms of contribution to shareholder value. The message to push down to the business lines is: What counts is not how much income is generated, but how well the firm is compensated for the risks it is taking on.
2. Communication and education – The 𝑅𝐴𝑅𝑂𝐶 group should be transparent and explain the 𝑅𝐴𝑅𝑂𝐶 methodology to all stakeholders, including business heads, business line managers, and the CFO’s office, to gain acceptance of the methodology throughout all management layers of the firm.
3. Ongoing consultation – The firm should establish a “parameter review group” composed of key representatives from the business units and the risk management function. This group periodically reviews the key parameters that drive risk and economic capital to promote fairness in the capital allocation process.
   • For credit risk, the parameters to review include probabilities of default, credit migration frequencies, loss given default, and credit line usage given default. These parameters evolve over the business cycle and should be adjusted as more data becomes available. An important issue is the choice of a historical period over which these parameters are calibrated—whether it should cover the whole credit cycle for stable risk capital numbers or a shorter period to make capital more procyclical (capital decreases when the credit environment improves and increases when it deteriorates).
   • For market risk, volatility and correlation parameters should be updated at least monthly using standard statistical techniques. Other key factors, such as the core risk level and “time to reduce,” should be reviewed annually.
   • For operational risk, the risk measurement approach is currently more judgmental and, therefore, more open to heated discussions.
4. Maintaining the integrity of the process – As with other risk calculations, the validity of 𝑅𝐴𝑅𝑂𝐶 numbers depends critically on the quality of the data about risk exposures and positions collected from management systems (e.g., in a trading business, the front and back-office systems). Only a rigorous process of data collection and centralization can ensure accurate risk and capital assessment. The same rigor should be applied to the financial information needed to estimate the adjusted-return element of the 𝑅𝐴𝑅𝑂𝐶 equation.
   • Data collection is probably the most daunting task in risk management. The 𝑅𝐴𝑅𝑂𝐶 group should be accountable for the integrity of the data collection process, calculations, and reporting process. Business units and the finance group should be accountable for the integrity of the specific data they produce and feed into the 𝑅𝐴𝑅𝑂𝐶 system.
5. Combine RAROC with qualitative factors – A simple decision rule for project selection and capital attribution was described earlier: accept projects where the 𝑅𝐴𝑅𝑂𝐶 is greater than the hurdle rate. In practice, other qualitative factors should be considered. All business units should be assessed using a two-dimensional strategic grid (not shown).
   • The horizontal axis of this figure corresponds to the RAROC return calculated on an ex-ante basis. The vertical axis is a qualitative assessment of the quality of the earnings produced by the business units. This measure considers the strategic importance of the activity for the firm, the growth potential of the business, the sustainability and volatility of earnings in the long run, and any synergies with other critical businesses in the firm.
   • Priority in the allocation of balance sheet resources should be given to businesses in the upper right quadrant. At the other extreme, the firm should try to exit, scale down, or fix activities of businesses in the lower left quadrant. Businesses in the “managed growth” category (lower right quadrant) are high-return activities with low strategic importance. Conversely, businesses in the “investment” category (upper left quadrant) are currently low-return activities with high growth potential and strategic value.
6. Put an active capital management process in place – Balance sheet requests from the business units such as economic capital, leverage ratio, liquidity ratios, and risk-weighted assets should be channeled to the 𝑅𝐴𝑅𝑂𝐶 group every quarter. Limits are set for economic capital, leverage ratio, liquidity ratios, and risk-weighted assets based on the analysis discussed in this chapter. The treasury group often reviews these limits to ensure they are consistent with funding limits. This limit-setting process is a collaborative effort, with any disagreements about balance sheet resource allocation put to arbitration by the senior executive team. Leverage ratios may restrain management from growing the bank beyond a certain level, making it more important for banks to work every dollar of capital hard—𝑅𝐴𝑅𝑂𝐶 analysis is one way to achieve this.

• Wherever risk capital is an important concern, 𝑅𝐴𝑅𝑂𝐶 balances the divergent desires of various external stakeholders while aligning them with the incentives of internal decision-makers. When business units (or transactions) earn returns in excess of the hurdle rate, shareholder value is created, and the allocated risk capital indicates the amount of capital required to preserve the desired credit rating.
• 𝑅𝐴𝑅𝑂𝐶 information allows senior managers to better understand where shareholder value is being created or destroyed. It promotes strategic planning, risk-adjusted profitability reporting and incentive compensation schemes, proactive resource allocation, better management of concentration risk, and improved product pricing.
• Because 𝑅𝐴𝑅𝑂𝐶 is not just a common language of risk but also a quantitative technique, a 𝑅𝐴𝑅𝑂𝐶-based capital budgeting process can be likened to an internal capital market in which businesses compete for scarce balance sheet resources—all with the objective of maximizing shareholder value. This makes 𝑅𝐴𝑅𝑂𝐶 a useful tool for capital allocation, both for banks and nonbank corporations.