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A Critique of Revised Basel II Outline 1. Conclusions 2. XYZ Theory of Regulatory Capital 3. Revised Basel II Capital Rule Robert Jarrow 1 1. Conclusions 1. Revised Basel II framework provides a (very) rough approximation to an ideal capital rule. 2. Due to (1) and XYZ Theory, revised Basel II should only be used in conjunction with other rules for determining minimal capital levels: - FDICIA leverage based rules - Parallel run and transitional floor periods are prudent. 3. Due to (1) and XYZ Theory, maintaining aggregate industry capital at pre-revised Basel II framework levels is prudent. Robert Jarrow 2 2. XYZ Theory of Regulatory Capital Randomness in the economy determined by the evolution of a set of state variables. t State variables include individual bank characteristics and business cycle characteristics (macro-variables). Robert Jarrow 3 The Bank’s Optimal Capital The bank’s optimal capital level is defined to be that capital which maximizes shareholders’ wealth, independently of regulatory rules. Xt f (t,t) Banks may or may not know f( . , . ). Larger (international) banks – yes Smaller (regional banks) – ??? Robert Jarrow 4 Ideal Regulatory Capital Regulatory capital is needed due to costly externalities associated with bank failures. The ideal regulatory capital is defined to be that (hypothetical) capital determined as if regulatory authorities had perfect knowledge (information). Zt h(t,t) Hypothesis 1 (Costly Externalities): Zt Xt Robert Jarrow 5 Ideal Regulatory Capital Hypothesis 2 (Unknown Zt): h( . , . ) unknown to regulators Due to: (i) uncertainty over the exact form of the appropriate risk measure (Value at Risk, Coherent, …) (ii) insufficient data to compute risk measure Robert Jarrow 6 Required Regulatory Capital Regulatory authorities specify a rule to approximate the ideal capital. This is the required regulatory capital. Yt g(t,t) Hypothesis 3 ( Approximate Ideal Capital from Below): Yt Zt Robert Jarrow 7 Required Regulatory Capital Justification: 1. Believed that many banks choose Xt > Yt for competitive reasons. Then, under hypothesis 1, Zt > Xt > Yt. 2. Rule chosen (shown later) is based on asymptotic theory where idiosyncratic risks are infinitesimal and diversified away, implies Zt > Yt. 3. Rule chosen (shown later) so that ideally, probability of failure is less than .001. Implies A credit rating or better (Moody’s). In practice, required capital does not achieve this level for many banks, so that for these banks Zt > Yt. Robert Jarrow 8 Required Regulatory Capital Example: In revised Basel II, the rule for required capital is (for illustrative purposes) g (t,t) 0.08 j risk weighted asset values j Will discuss later in more detail. Robert Jarrow 9 Theorem 1 Given hypotheses 1 and 2. Let g j (t,t) for j=1,…,N represent a collection of regulatory capital rules. Let hypothesis 3 hold. Then, Yt max{ g j (t,t):all j} is a better approximation to Zt than any single rule. If hypothesis 3 does not hold, then no simple ordering of regulatory capital rules is possible without additional structure. Robert Jarrow 10 Theorem 1 - implications 1. New rules should be implemented without discarding existing rules. Implies retention of leverage based rules (FDICIA) is prudent. 2. Four year parallel run period with yearly transitional floors (95%, 90%,85%) within Basel II revised framework is prudent. Robert Jarrow 11 Theorem 2 Let hypotheses 1 – 3 hold. Let g i (t,t) for i = 1,…,m be the regulatory capital for bank i, Then when considering a new rule gnew(t,t) g i (t,t). i m m i 1 i 1 Robert Jarrow 12 Theorem 2 - implications 1. Scaling individual bank capital so that in aggregate, industry capital does not decline, is prudent. Current scale is 1.06 based on the 3rd Quantitative Impact Study. Tentative magnitude. 2. Requiring that the regulations be restudied/modified if a 10% reduction in aggregate capital results after implementation is prudent. Robert Jarrow 13 3. The Revised Basel II Capital Rule The following analysis is independent of XYZ theory. Revised Basel II rule illustrated on a previous slide. In revised Basel II, the risk weightings are explicitly adjusted for credit risk, operational risk, and market risk. Liquidity risk is only an implicit adjustment. Robert Jarrow 14 The Revised Basel II Capital Rule Two approaches: 1. Standard (based on tables and rules given in revised Basel II framework). 2. Internal ratings/ Advanced approach (based on internal models). For my analysis, concentrate on internal ratings/advanced approach. Robert Jarrow 15 Credit Risk Risk weights determined based on bank’s internal estimates of PD, LGD and EAD. These estimates input into a formula for capital (K) held for each asset. Capital K based on: 1. Value at Risk (VaR) measure over a 1-year horizon with a 0.999 confidence level. 2. Asymptotic single-factor model, with constant correlation assumption. 3. An adjustment for an asset’s maturity. Discuss each in turn… Robert Jarrow 16 PD, LGD, EAD PD is 1-year long term average default probability – not state dependent. LGD is computed based on an economic downturn – quasi-state dependent. EAD is computed based on an economic downturn – quasi-state dependent. These do not change with business cycle. Robert Jarrow 17 PD, LGD, EAD Ideal regulatory capital should be state dependent. Pro: Makes bank failures counter-cyclic. Con: Makes bank capital pro-cyclic. Could adversely effect interest rates (investment). But, monetary authorities have market based tools to reduce this negative impact. Robert Jarrow 18 Problems with VaR Problems with the VaR measure for loss L. VaR(L) inf{x 0: P(L x) 0.999} Well-known that VaR: ignores distribution of losses beyond 0.999 level, and penalizes diversification of assets (provides an incentive to concentrate risk). Robert Jarrow 19 Example: Concentrating Risk Loss P(LA) P(LB) P(L(A+B)/2) $0 0.9991 0.9991 0.9982 $.50 0 0 0.0018 $1 0.0009 0.0009 0.0000 VaR(LA) = 0 and VaR(L(A+B)/2) = $.50 Robert Jarrow 20 Given VaR – Portfolio Invariance Capital K formulated to have portfolio invariance, i.e. the required capital for a portfolio is the sum of the required capital for component assets. Done for simplicity of implementation. But, it ignores benefits of diversification, provides an incentive toward concentrating risk. Robert Jarrow 21 Given VaR – Single Risk Factor The asymptotic model (to get portfolio invariance) has a single risk factor. The single risk factor drives the state variables vector. Inconsistent with evidence, e.g. Duffee [1999] needed 3 factors to fit corporate bond prices. Robert Jarrow 22 Given VaR – Common Correlation When implementing the ASRF model, revised Basel II assumes that all assets are correlated by a simple function of PD, correlation bounded between 0.12 and 0.24. No evidence to support this simplifying assumption??? Robert Jarrow 23 Given VaR – Normal Distribution for Losses Formula for K implies that losses (returns) are normally distributed. Inconsistent with evidence: Ignores limited liability (should be lognormal) Ignores fat tails (stochastic volatility and jumps) Robert Jarrow 24 Given VaR – Maturity Adjustment Capital determination based on book values of assets. This ignores capital gains/losses on assets over the 1- year horizon. Gordy [2003] argues that a maturity adjustment is necessary to capture downgrades of credit rating in long-dated assets. Do not understand. Asset pricing theory has downgrade independent of maturity. Maturity (duration) adjustment only (roughly) captures interest rate risk. Robert Jarrow 25 Significance of Error P. Kupiec constructs a model – Black/Scholes/Merton economy, correlated geometric B.M.’s for assets. Considers a portfolio of zero-coupon bonds. Computes ideal capital, compares to revised Basel II framework capital. Finds significant differences. Conclusion: revised Basel II capital rule is a (very) rough approximation to the ideal rule. Robert Jarrow 26 Operational Risk Basic indicator and standard approach: capital is proportional to income flow. Advanced measurement approach: internal models approach based on VaR, 1-year horizon, 0.999 confidence level. Jarrow [2005] argues operational risk is of two types: system or agency based. Income flow captures system type risk. Agency risk is not captured by income flow. More important of the two types. Only possibly captured in advanced measurement approach. Robert Jarrow 27 Market Risk Standardized and internal models approach. Concentrate on internal models approach. Internal models approach is VaR based with 10-day holding period and 0.99 confidence level with a scale factor of 3. Why the difference from credit risk? Could lead to regulatory arbitrage if an asset could be classified as either. Robert Jarrow 28 Liquidity Risk Liquidity risk only included implicitly in credit risk (via the LGD, EAD being for an economic downturn) market risk (via the scale factor of 3). Better and more direct ways of doing this are available, see Jarrow and Protter [2005]. Robert Jarrow 29

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default probabilities, Credit Risk, default probability, equity prices, probability of default, credit spreads, Yildiray Yildirim, Tibor Janosi, recovery rate, Robert Jarrow

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posted: | 2/15/2010 |

language: | English |

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