Risk adjusted return on capital raroc

Risk Adjusted Return on Capital (RAROC)

Risk Adjusted Return on Capital (RAROC) is a financial metric that evaluates the profitability of a project, business unit, or customer relationship in relation to the amount of risk taken. As a core component within financial institutions' risk management frameworks, RAROC provides a consistent approach to performance measurement and capital allocation by adjusting returns for the level of risk incurred.

History and Origin

The concept of Risk Adjusted Return on Capital (RAROC) was pioneered by Bankers Trust in the late 1970s, primarily driven by the need for a more comprehensive method to analyze risk and return, especially as the derivatives market grew in complexity.¹³ At the time, conventional methods of evaluating risk proved insufficient for the intricate financial markets. Bankers Trust developed RAROC to provide a consistent framework for comparing the profitability of various transactions, sections, or even entire business lines by relating their returns to the capital placed at risk.¹² This innovation was crucial in enabling the bank to assess the economic value added by different business units and strategic choices, moving beyond nominal profits to consider the inherent risk level associated with activities.¹¹ Its success led to its widespread adoption across the financial services sector, becoming a fundamental tool for risk management and financial analysis.⁹, ¹⁰

Key Takeaways

RAROC is a financial metric used by financial institutions to measure the profitability of an endeavor relative to its associated risk.
It aids in strategic capital allocation and performance measurement by providing a risk-adjusted view of returns.
RAROC considers various types of risk, including credit risk, market risk, and operational risk.
A higher RAROC generally indicates a more efficient use of economic capital for a given level of risk.
The metric is crucial for banks and other financial entities in making informed decisions about lending, investing, and structuring business units.

Formula and Calculation

The basic formula for Risk Adjusted Return on Capital (RAROC) is:

\text{RAROC} = \frac{\text{Risk-Adjusted Return}}{\text{Economic Capital}}

Where:

Risk-Adjusted Return typically represents the expected revenue from a project or business unit, minus all costs, including expected loss, funding costs, and operating expenses. It is the net profit adjusted for the probability of loss.
Economic Capital is the amount of capital a firm needs to absorb potential unexpected losses from its risks (e.g., credit risk, market risk, operational risk) over a specific time horizon and at a specified confidence level. It often correlates with Value at Risk (VaR).

More granularly, the Risk-Adjusted Return can be expressed as:

\text{Risk-Adjusted Return} = \text{Revenue} - \text{Operating Costs} - \text{Funding Costs} - \text{Expected Loss}

And Economic Capital is calculated to cover unexpected loss (the variability around the expected loss).

Interpreting RAROC

Interpreting RAROC involves comparing the calculated ratio to a firm's predetermined hurdle rate or cost of economic capital. A project or business unit is generally considered acceptable if its RAROC exceeds this hurdle rate, indicating that the risk-adjusted returns justify the capital consumed. Conversely, a RAROC below the hurdle rate suggests that the endeavor does not generate sufficient returns for the amount of risk taken.

For example, a RAROC of 15% means that for every dollar of economic capital employed, the project is generating a 15% risk-adjusted return. Banking institutions use RAROC to ensure that capital is deployed efficiently across different activities, incentivizing business lines to manage their risks effectively and allocate capital optimally to maximize shareholder value.

Hypothetical Example

Consider a banking institution, Diversified Bank, evaluating two potential lending projects, Project A and Project B, both requiring $10 million in economic capital and expected to generate $2 million in revenue after operating and funding costs. Diversified Bank's hurdle rate for risk-adjusted returns is 12%.

Project A:

Expected Revenue (after costs): $2,000,000
Expected Loss: $500,000
Economic Capital: $10,000,000

Risk-Adjusted Return (Project A) = $2,000,000 - $500,000 = $1,500,000
RAROC (Project A) = $\frac{$1,500,000}{$10,000,000} = 0.15 = 15%$

Project B:

Expected Revenue (after costs): $2,000,000
Expected Loss: $1,000,000
Economic Capital: $10,000,000

Risk-Adjusted Return (Project B) = $2,000,000 - $1,000,000 = $1,000,000
RAROC (Project B) = $\frac{$1,000,000}{$10,000,000} = 0.10 = 10%$

In this scenario, Project A, with a RAROC of 15%, exceeds Diversified Bank's 12% hurdle rate, making it an attractive investment. Project B, however, with a RAROC of 10%, falls below the hurdle rate, indicating that its risk-adjusted return does not adequately compensate for the economic capital required. Diversified Bank would likely pursue Project A and reject Project B, or seek ways to improve Project B's risk-adjusted return.

Practical Applications

RAROC is widely applied in financial institutions for several key purposes:

Lending Decisions: Banks use RAROC to price loans and evaluate the profitability of individual credit exposures, ensuring that the interest rate charged compensates for the borrower's credit risk and the economic capital consumed.
Business Unit Performance Evaluation: It provides a standardized metric for assessing the performance of different departments, such as corporate banking, investment banking, or trading desks. This allows for fair comparisons across diverse activities with varying risk profiles.
Strategic Capital Allocation: RAROC guides management in allocating scarce regulatory capital and economic capital to the most profitable and risk-efficient business lines or projects. This helps maximize overall firm value.
Risk-Based Pricing: For complex financial products, RAROC helps in setting prices that explicitly account for the underlying risks.
Enterprise Risk Management: It integrates various risk types (market risk, credit risk, operational risk) into a single performance measure, providing a holistic view of risk-adjusted returns across the organization. Financial entities, particularly banks, use such frameworks to gauge their return on capital, ensuring they adequately compensate for the risks undertaken. [Risk.net, 2]

Limitations and Criticisms

Despite its widespread adoption, RAROC has several limitations and criticisms:

Model Dependence: The accuracy of RAROC heavily relies on the underlying risk models used to calculate expected loss and economic capital (often derived from Value at Risk (VaR) models). These models can be complex, and their assumptions may not always hold true, especially during periods of market stress or for "tail events" (rare, extreme events).
Data Quality and Availability: Accurate calculation of RAROC requires extensive and high-quality historical data for risk parameters. Data limitations, particularly for less liquid assets or new products, can undermine the reliability of the metric.
Complexity and Implementation Cost: Developing and maintaining robust systems for calculating RAROC can be resource-intensive, requiring significant investment in technology and expertise.
Gaming the Metric: There is a potential for business units to manipulate inputs or assumptions to inflate their RAROC figures, emphasizing the need for strong governance and oversight.
Focus on Quantifiable Risks: RAROC primarily focuses on quantifiable financial risks (credit risk, market risk, operational risk) and may not fully capture qualitative risks like reputational risk or strategic risk. Challenges in incorporating all material risks, including emerging ones like climate-related risks, into internal models can affect the comprehensiveness of such metrics.⁶, ⁷, ⁸ Regulators, such as the European Central Bank, continuously refine their guidance on internal models, highlighting the ongoing challenges in ensuring their accuracy and integrity.⁴, ⁵ Effective risk data aggregation and reporting, as emphasized by the Basel Committee on Banking Supervision, are foundational but often challenging for banks to fully achieve.¹, ², ³

RAROC vs. Return on Capital (RoC)

While both RAROC and Return on Capital (RoC) are financial metrics that measure the efficiency with which a company generates profits from its capital, the key distinction lies in their treatment of risk.

Return on Capital (RoC) is a straightforward profitability metric that measures the returns generated from capital invested, without explicitly adjusting for the level of risk undertaken. It typically calculates net operating profit after tax as a percentage of capital employed. RoC is useful for general profitability comparisons among projects or business units of similar risk profiles.

RAROC, on the other hand, explicitly incorporates a risk adjustment into its calculation. It measures the return generated per unit of economic capital or Value at Risk (VaR), making it suitable for comparing the performance of activities with diverse risk characteristics. RAROC ensures that projects with higher inherent risks are evaluated against the greater capital required to support those risks. This risk-adjusted perspective is crucial for effective capital allocation in financial institutions, allowing for a more equitable comparison of performance across different risk-taking ventures.

FAQs

What is the primary purpose of RAROC?

The primary purpose of RAROC is to measure the profitability of a financial activity or business unit in relation to the amount of risk it entails. It helps financial institutions make informed decisions about where to allocate their economic capital.

How is economic capital determined in RAROC?

Economic capital in RAROC is typically determined by quantifying the amount of capital needed to cover potential unexpected loss over a specific time horizon and at a certain confidence level. This often involves statistical models like Value at Risk (VaR), which consider various types of risk such as credit risk, market risk, and operational risk.

Who primarily uses RAROC?

RAROC is primarily used by financial institutions, particularly banks and insurance companies. It's a key tool for risk management, capital allocation, and performance measurement across different business lines and products.

Can RAROC be used by non-financial companies?

While RAROC was developed within the financial sector, its underlying principle of adjusting returns for risk can be theoretically applied to any company making capital investment decisions. However, the specific methodologies for calculating economic capital and various risk types are most refined and prevalent within financial institutions.