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Capital Structure in Banks 177 and hence UL would also be equal to zero, indicating that there would be no credit risk. For simplicity, we have ignored the time index in this derivation. But all parameters are estimated, as was done previously, at time H. Note that, since default is a Bernoulli variable with a binomial B(1;PD)- distribution: 203 σ 2 PD = PD ⋅ (1 – PD) (5.6) Since it is typically difficult in practice to measure the variance of the loss rate σ 2 LR due to the lack of sufficient historical data, we will have to assume in most cases a reasonable distribution for the variations in the loss rate. Unfortunately, unlike the distribution for PD, the loss rate distribution can take a number of shapes, which result in different equations for the variance of LR. Possible candidates are the binomial, the uniform, or the normal distribution. Whereas the binomial distribution overstates the variance of LR (when a customer defaults, either all of the exposure amount is lost or nothing), the uniform distribution assumes that all defaulted borrowers would have the same probability of losing anywhere between 0% and 100%. Therefore, the most reasonable assumption is the normal distribution, because of the lack of better knowledge in most cases. 204 The shape of this assumed normal distribution should take into account the empirical fact that some customers lose almost nothing, that is, almost fully recover, and it is very unlikely that all of the money is lost during the work-out process. 205 Like EL, UL can also be calculated for various time periods and for rolling time windows across time. By convention, almost always one-year intervals are used. 206 Hence, all measures of volatility need to be annualized to allow comparisons among different products and business units. 207 Again, the same methodology can be applied to derive the UL resulting from country risk using the three components of country EL. 203 See Bamberg and Baur (1991), p. 123. 204 Also see Ong (1999), p. 132. 205 As mentioned above, even unsecured loans almost always recover some amount in the bankruptcy court, see, for example, Eales and Bosworth (1998), p. 62, or Carty and Lieberman (1996), p. 5. 206 See Ong (199), p. 121. 207 For convenience and again due to lack of data, the volatility of LR is assumed to be constant over time (intervals).
178 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS Unexpected Loss Contribution (ULC) Credit risk cannot be completely eliminated by hedging it through the securities markets like market risk. 208 Even credit derivatives and asset securitizations can only shift credit risk to other market players. These actions will not eliminate the downside risk associated with lending. However, they can transfer credit risk to the market participant best suited to bear it, because the only way to reduce credit risk is by holding it in a well-diversified portfolio (of other credit risks). 209 Therefore, we need to change our perspective of looking at credit risk from the single, standalone credit to credit risk in a portfolio context. The expected loss of a portfolio of credits is straightforward to calculate because EL is linear and additive. 210 Therefore: EL = EL = EA ⋅PD ⋅LR P n ∑ n ∑ i i= 1 i= 1 i i i where EL P = Expected loss of a portfolio of n credits. (5.7) However, when measuring unexpected loss at the portfolio level, we need to consider the effects of diversification because—as always in portfolio theory—only the contribution of an asset to the overall portfolio risk matters in a portfolio context. In its most general form, we can define the unexpected loss of a portfolio UL P as: UL = n n ∑∑ ωω ρ UL UL P i j ij i j i= 1 j= 1 (5.8) where n ∑ i= 1 ω = 1 and ω = i i n ∑ i= 1 EA i EA i (5.9) ω i = Portfolio weight of the i-th credit asset ρ ij = Correlation that default or a credit migration (in the same direction) of asset i and asset j will occur over the same 208 Credit risk only has a downside potential (i.e., to lose money), but no upside potential (the maximum return on a credit is limited because the best possible outcome is that all promised payments will be made according to schedule). 209 See Mason (1995), pp. 14–24, and Ong (1999), p. 119. As Mason shows, the same argument can be applied to the management of insurance risk. 210 See Ong (1999), p. 123.
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isk management and value creation i
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Copyright © 2002 by John Wiley & S
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preface From an empirical as well a
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acknowledgments No book is solely t
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x CONTENTS Goals of Risk Management
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xii CONTENTS Definition of RAROC 24
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xiv FIGURES Figure 5.5 Figure 5.6 F
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symbols ↑ ↓ α β i xvi Increas
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xviii SYMBOLS ln Natural logarithm
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abbreviations APT BIS bn bps CAPM C
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2 RISK MANAGEMENT AND VALUE CREATIO
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CHAPTER 2 Foundations for Determini
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Foundations for Determining the Lin
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eferences Aguais, Scott D., and Ant
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References 295 Blanden, Michael (19
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References 297 and Abuses,” Journ
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References 299 Froot, Kenneth A., a
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References 301 risiken aus Handelsg
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References 303 Investments in Stock
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References 305 Institute of Technol
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References 307 Sharpe, William F. (
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References 309 Wall, L.D., and John
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312 INDEX Approach (continued) top-
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314 INDEX Capital: Tier-1, 139, 146
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316 INDEX Credit: derivatives, 178,
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318 INDEX Expectations: homogeneous
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320 INDEX Incentive(s), 22, 33, 45,
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322 INDEX Managers, poorly diversif
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324 INDEX Overinvestment, 75, 79, 8
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326 INDEX Reserve(s) (continued) lo
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328 INDEX Risk, liquidity, 3, 165 R
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330 INDEX Sharpe ratio, 244, 252 Sh
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332 INDEX Value at risk (VaR) (cont
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