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# Chapter 13 - PowerPoint PPT Presentation

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

• 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

• = 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

• 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

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

Saunders & Allen Chapter 13

• 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%

• 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