Introduction to Loan Pricing and RAROC (Risk Adjusted Return on Capital)


Loan Pricing and RAROC or Risk Adjusted Return on Capital

Roopya Loan pricing models help financial institutions use to determine the cost to a borrower for providing a loan, encapsulating factors such as interest rates and fees. This pricing is closely tied to risk-based pricing, which adjusts the cost of credit based on the perceived risk of the borrower. A central concept within risk-based pricing is Risk-Adjusted Return on Capital (RAROC), a profitability metric that provides a standardized way to measure returns on capital while adjusting for the riskiness of the lending activities. RAROC enables banks to allocate capital more efficiently by pricing loans in a manner that seeks to optimize the return on capital, factoring in the credit risk, market risk, and operational risk associated with the loan. This approach ensures that riskier loans—those more likely to result in default—are priced higher to compensate for the increased risk, thereby aligning the pricing strategy directly with the underlying risk profile of the borrower.

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Introduction to Loan Pricing and RAROC (Risk Adjusted Return on Capital)

Formula for RAROC or Risk Adjusted Return on Capital

Risk-Adjusted Return on Capital (RAROC) is a key metric used in financial risk management and profitability analysis. Here is the formula for calculating RAROC:

RAROC = (Net Income – Expected Losses – Cost of Capital) / Economic Capital

Formula is explained as follows:

  • Net Income: This is the gross income from the lending business activity minus direct costs and operating expenses. It is the actual profit before considering the costs associated with risk. Net Income can be derived from financial statements as revenue minus operating expenses and other associated costs.
  • Expected Loss: This component includes expected losses from defaults and is typically calculated based on historical loss data, adjusted for current market conditions and borrower-specific risk factors. Expected Loss often uses models that consider the probability of default (PD) and loss given default (LGD). Expected Loss might be calculated using statistical models that incorporate PD and LGD, often derived from internal risk ratings and historical loss experience.
  • Cost of Capital: Represents the cost of funding the business activity. It is the rate of return required by investors to compensate them for the risk of investing capital. It can include the costs of both equity and debt financing, adjusted to reflect the specific risk profile and capital structure of the activity. Cost of Capital could be estimated using models like the Capital Asset Pricing Model (CAPM) for equity, and an appropriate interest rate for debt.
  • Economic Capital: Economic capital is the amount of capital required to cover potential unexpected losses at a certain confidence level over a specific time period. This calculation incorporates various risk types such as credit risk, market risk, and operational risk, and is typically modelled using techniques like Value at Risk (VaR) or its variants. Economic Capital is calculated using internal risk models that simulate the distribution of losses based on the firm’s risk profile and market conditions, ensuring it meets regulatory requirements and internal risk management policies.

Example of RAROC or Risk Based Loan Pricing

Suppose a bank issues a commercial loan of INR 10crore to a corporation. We will consider the following parameters:

Interest Rate on the Loan: 10% p.a.

Term of the Loan: 5 years

Operating Expenses Related to the Loan: INR 20 lakh p.a.

Probability of Default (PD): 3% p.a.

Loss Given Default (LGD): 50% of the exposure at default

Cost of Capital: 14% annually (reflecting the bank’s funding costs)

Economic Capital Requirement: Based on the bank’s internal models, let’s say it’s calculated as 12% of the loan amount to cover unexpected losses

Step 1: Calculate Expected Loss
Using the PD and LGD, we can calculate the Expected Loss (EL) for the loan annually:

EL = Loan Amount × PD × LGD

EL = INR 10,00,00,000 × 0.03 × 0.50 = INR 15,00,000 (INR 15 lakh p.a.)

Step 2: Calculate Net Income from the Loan
Annual Interest Income: INR 10,00,00,000 × 0.10 = INR 1,00,00,000

Annual Operating Expenses: INR 20 lakh

Annual Net Income before risk costs: INR 1,00,00,000 – INR 20,00,000 = INR 80,00,000 INR

Step 3: Adjust Net Income for Expected Loss
Adjusted Net Income = Annual Net Income − Expected Loss

Adjusted Net Income = INR 80,00,000 – INR 15,00,000 = INR 65,00,000 p.a.

Step 4: Calculate Economic Capital
Economic Capital is calculated to cover unexpected losses. For simplicity, if it’s set at 12% of the loan amount:

Economic Capital = INR 10,00,00,000 × 0.12 = INR 1,20,00,000

Step 6: Calculate RAROC
Now, let’s put all these components into the RAROC formula:

RAROC = (Adjusted Net Income − Cost of Capital × Economic Capital) / Economic Capital

First, calculate the cost component:

Cost of Capital Component = INR 1,20,00,000 × 0.14 = INR 16,80,000

Now, calculate RAROC:

RAROC = INR (65,00,000 − 16,80,000) / INR 1,20,00,000 = INR 48,20,000 / INR 1,20,00,000 = 0.40167 or 40.17%

This RAROC of 40.17% indicates that the return on capital, after adjusting for risk and cost of capital, is significantly higher than the required return by the bank’s capital providers (14%). This could mean the loan is a profitable venture for the bank, assuming all other risk assessments are correct and there are no significant changes in the economic or business environment.

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