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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 l.jpg

Chapter 13

Risk-Adjusted Return on Capital Models


Definition of raroc l.jpg
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


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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


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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


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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



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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


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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


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The RAROC Denominator and Correlations Measurement

Saunders & Allen Chapter 13


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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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