GRADUATE SCHOOL OF BUSINESS

Global Risk Management: A Quantitative Guide

Capital

Ren-Raw ChenFordham University

2

• 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−

10

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