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Chapter 13 Risk-Adjusted Return on Capital Models

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Saunders & Allen Chapter 132 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.

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Saunders & Allen Chapter 133 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.

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Saunders & Allen Chapter 134 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.

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Saunders & Allen Chapter 135 The Market-based Approach to Measuring Capital at Risk If D L =2.7, L=$1m, R=1.1%, R=10%, then: L = -$ 27,000

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Saunders & Allen Chapter 136

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7 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 x.5 x $1m = $27,000 (same as market-based approach)

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Saunders & Allen Chapter 138 Calculating the RAROC of the Loan Example 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.

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Saunders & Allen Chapter 139 The RAROC Denominator and Correlations

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Saunders & Allen Chapter 1310 Incorporating Unsystematic Risk 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.

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