GRADUATE SCHOOL OF BUSINESS
Global Risk Management: A Quantitative Guide
Capital
Ren-Raw ChenFordham University
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• The bank must maintain capital (Tier 1 Tier 2) equal to at least 8% of its RWA
– 0% - cash, any OECD government debt
– 0%, 10%, 20% or 50% - public sector debt
– 20% - development bank debt, OECD bank debt, OECD securities firm debt, non-OECD bank debt (under one year maturity) and non-OECD public sector debt, cash in collection
– 50% - residential mortgages
– 100% - private sector debt, non-OECD bank debt (maturity over a year), real estate, plant and equipment, capital instruments issued at other banks
Tier 1 Capital
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• Tier 1 capital is the core measure of a bank's financial strength. It is composed of
– common stock and
– disclosed reserves (or retained earnings), but may also include
– non-redeemable non-cumulative preferred stock.
Tier 1 Capital
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• The Basel Committee also observed that banks have used innovative instruments over the years to generate Tier 1 capital; these are subject to stringent conditions and are limited to a maximum of 15% of total Tier 1 capital.
Tier 1 Capital
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• Tier 2 is limited to 100% of Tier 1 capital
– Undisclosed reserves
– Revaluation reserves
– General provisions/general loan-loss reserves
– Hybrid debt capital instruments
– Subordinated term debt
Tier 2 (supplementary) Capital
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• Banks will be entitled to use Tier 3 capital solely to support market risks as defined in paragraphs 709 to 718(Lxix).
• Tier 3 capital will be limited to 250% of a bank’s Tier 1 capital that is required to support market risks.
• This means that a minimum of about 28½% of market risks needs to be supported by Tier 1 capital that is not required to support risks in the remainder of the book;
Tier 3 Capital
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• Either one:
– Fixed (8%)
– IRB
Regulatory Capital (RegCap)
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• Correlation
– It is the amount of risk capital which a firm requires to cover the risks that it is running or collecting as a going concern, such as market risk, credit risk, and operational risk.
– Firms and financial services regulators should then aim to hold risk capital of an amount equal at least to economic capital.
Economic Capital
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• EL (expected loss) = PD x LGD
• UL (unexpected loss) – awareness after the crisis
– E.g.
– UL=p(1-p), largest when p = ½.
Economic Capital
Default => 1 R−
No default => 0
p
1 p−
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Economic Capital
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• Risk-adjusted return on capital
= (Expected Return)/(Economic Capital)
= (Expected Return)/(Risk-based Capital)
= (Expected Return)/(Value at Risk)
• Risk-adjusted return on capital
= (Adjusted Income)/(Value at Risk)
• Taken from Saunders and Allen (Ch.13)
RAROC
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• Adjusted Income
= Spread (direct income on loan) + Fees (indirect income) – Expected Loss (PD * LGD) – Operating Costs (direct cost of loan)
• Multiply the above by (1 – tax rate)
RAROC
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• Value (or Capital) at Risk
– Market-based approach
• 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
• Calculate UL using a multiple x LGD x exposure x standard deviation of default rates
RAROC
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• Market-based Approach
– ∆L = - DL x L x ∆R/(1+RL)
– ∆L: Dollar capital risk the exposure or loss on the amount
– DL : Duration of the loan
– L: Risk amount or loan exposure
– ∆R: Expected discounted change in credit premium or risk factor loan
– RL: Return on the loan
RAROC
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• Market-based Approach
– If DL=2.7, L=$1m, ∆R=1.1%, R=10%, then: ∆L = -$ 27,000
RAROC
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• Experientially-based Approach
– 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. E.g. multiplier = 6.
– If LGD=0.5, Exposure=$1m, Loan σ=22.5 bps, then UL = 6 x .00225 x .5 x $1m = $27,000 (same as market-based approach)
RAROC
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• 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.
RAROC
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• CAPM
– Ri = Rf + βi (Rm – Rf)
– Ri – Rf = (ρσi/σm)(Rm – Rf)
– (Ri – Rf)/ρσi =(Rm – Rf)/σm
– RAROC <> hurdle rate
RAROC
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• Correlation!
– No correlation, then diversification works, 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.
RAROC
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• Correlation!
– 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).
RAROC
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• WACC
– Cost of equity
– Cost of debt (i) – is it right?
– Cost of asset = ROA
• M&M
– ROA = (E/A) rE + (D/E) (1–τ) i
– No bankruptcy
Costs of Capital
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• BSM
Costs of Capital
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• BSM
– ROA = (E/A) rE + (D/E) rD – τi
– N(d1) is delta of equity and N(-d1) is delta of debt
– Note that N(d1) + N(-d1) = 1
– A = D + E (all market value)
– rE is ROE
– E and rE given by stock market
– ROA is hard to estimate but doable
– Solve for rD
Costs of Capital
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• Tier 1 capital ratio = Tier 1 capital / Risk-adjusted assets >=6%
• Total capital (Tier 1 and Tier 2) ratio = Total capital (Tier 1 and Tier 2) / Risk-adjusted assets >=10%
• Leverage ratio = Tier 1 capital / Average total consolidated assets >=5%
Capital Ratios
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• Common stockholders’ equity ratio = Common stockholders’ equity / Balance sheet assets
Capital Ratios