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Chapter 13 . Risk-Adjusted Return on Capital Models. Definition of RAROC. RAROC = If RAROC > Hurdle rate then value adding. ROA = RORAC = EVA = economic value added = Adjusted income – ROE x K. Invest if 0. The Numerator: Adjusted Income. = Spread (direct income on loan) +

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### Chapter 13

Risk-Adjusted Return on Capital Models

Definition of RAROC

- RAROC =
- If RAROC > Hurdle rate then value adding.
- ROA =
- RORAC =
- EVA = economic value added = Adjusted income – ROE x K. Invest if 0.

Saunders & Allen Chapter 13

The Numerator: Adjusted Income

- = Spread (direct income on loan) +
- + Fees (directly attributable to loan) –
- - Expected Loss (EDF x LGD) –
- - Operating Costs (allocated to loan)
- Then multiply the entire amount by 1 – the marginal tax rate.

Saunders & Allen Chapter 13

The Denominator: Capital at Risk

- Market-based approach (BT model)
- Measure the maximum adverse change in the market value of the loan resulting from an increase in the credit spread
- Use duration model to measure price effects.

- Experientially-based approach (BA model)
- Calculate UL using a multiple x LGD x exposure x standard deviation of default rates.

Saunders & Allen Chapter 13

The Market-based Approach to Measuring Capital at Risk

- If DL=2.7, L=$1m, R=1.1%, R=10%, then: L = -$ 27,000

Saunders & Allen Chapter 13

The Experientially-based Approach to Capital at Risk Measurement

- If 99.97% VAR (AA rating) and normal distribution, then the multiplier is 3.4.
- But, most banks use a large multiplier because loan distributions are not normal.
- BA uses multiplier = 6.
- If LGD=.5, Exposure=$1m, Loan =.00225, then UL=6 x .00225 x .5 x $1m = $27,000 (same as market-based approach)

Saunders & Allen Chapter 13

Calculating the RAROC of the Loan Example Measurement

- Spread = .2% x $1m = $2,000
- Fees = .15% x $1m = $1,500
- EL = .1% x $.5m = ($500)
- Tax rate = 0%
- Adjusted Income = $3,000
- RAROC = $3,000/$27,000 = 11.1%
- If cost of capital < 11.1% then make loan.

Saunders & Allen Chapter 13

The RAROC Denominator and Correlations Measurement

Saunders & Allen Chapter 13

Incorporating Unsystematic Risk Measurement

- Equation (13.18) is the traditional Sharpe ratio for a loan. But, if all idiosyncratic risk is diversified away, then no need for RAROC. RAROC deals with untraded and unhedgeable assets (loans).
- Banks specialize in info-intensive relationship lending that cannot be hedged in capital markets. Risk of loan should be divided into: (1) liquid, hedgeable market risk component and (2) illiquid, unhedgeable component.
- The correlation of the unhedgeable component with the bank’s portfolio will determine the loan’s price. So different banks (with different portfolio correlations) will have different pricing (credit risk).
- Froot & Stein (1998): Loan’s hurdle rate =market price of the loan’s traded risk + bank shareholders’ cost of capital to cover nontradeable risk. The second term is idiosyncratic.

Saunders & Allen Chapter 13

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