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Capital Budgeting in Banks 253 The model presented above shows how RAROC has to be constructed so that it can be compared to the cost of equity capital as determined for example, by the CAPM. RAROC therefore assumes that economic capital is compensated by the market and that it is the correct risk measure. Only then are decisions based on RAROC versus R E h consistent with maximizing value. However, this assumes that the riskiness of the economic capital is the same as that of the bank’s equity capital 64 and that hence economic capital has to earn the same returns as the equity capital. Given the discussion in the previous chapter and that economic capital is assumed to be invested in a reserve pool to guarantee a certain default probability, this seems unlikely to be the case. Additionally, and as pointed out for instance by Johanning, economic capital determined on a VaR basis is incompatible with the maximization of expected utility in the neoclassical world. Therefore, RAROC is not a suitable internal performance measure in all circumstances. 65 Deficiencies of RAROC In this section, we will discuss the deficiencies and fundamental problems of RAROC. Deficiencies of the Generic RAROC Model One of the advantages of RAROC mentioned previously, is that it adjusts the risk of any transaction to that of the bank’s equity by changing the leverage of the transaction via a different economic capital requirement. Therefore, RAROC avoids the need to estimate the external beta of the transaction. 66 There are two problems associated with this approach. First, the allocated capital is a cushion to absorb losses up to a prespecified confidence level and, therefore, a total risk measure. 67 The risk contributions of single transactions are based on internal betas that are calculated vis-à-vis the existing bank portfolio. Since these results are compared to externally driven hurdle rates, one has to assume that the bank portfolio is a good proxy for the market portfolio. 68 This might actually be correct, because typically we find bank betas to be around 1.0, 69 in which case one could show that the internal betas are similar (if not identical) to external 64 See Crouhy et al. (1999), p. 6. 65 See Johanning (1998), pp. 73–86. We will address this problem below. 66 See Crouhy et al. (1999), p. 7. 67 See Grübel et al. (1995), p. 618. 68 As claimed by Zaik et al. (1996), p. 87. 69 See Schmittmann et al. (1996), p. 648, for large German universal banks (not niche players).
254 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS betas. 70 However, one should keep in mind that the chosen total risk measure is different from the priced and systematic market risk. Since RAROC does not use any valuation model to derive the relative ordering of expected returns, 71 it is not able to provide a consistent relative ranking of transactions. 72 Second, we have already shown that you can either fix the default probability or the hurdle rate, but not both at the same time. 73 Thus, the following assumption is not justified: that due to changes in the leverage, which fix the default probability, we can use a single hurdle rate across all bank transactions. 74 In order to prove that the RAROC analysis generates reliable results with regard to value creation, one could formulate the following fundamental hypotheses: ■ ■ If we consider a zero NPV project, RAROC should always equal the (bankwide) hurdle rate R h E and should, thus, indicate that the bank is indifferent vis-à-vis this transaction. If we consider a transaction with positive (negative) NPV, RAROC should always be larger (smaller) than the (bankwide) hurdle rate R h E . However, given the above analysis, we can show that these fundamental premises do not necessarily hold true. Let us first consider zero NPV transactions. In the above-defined model, RAROC changes even for NPV = 0 transactions with a change in the riskiness of the transactions and with changes in the correlation of the transactions to the broad market portfolio (as defined in a CAPM world). Figure 6.2 depicts the effects that are derived applying the analysis conducted by Crouhy et al. (1999). As can be seen, RAROC increases with increases in the riskiness of a transaction. RAROC is also higher, the higher the correlation of the transaction is to the broad market portfolio. Banks applying RAROC as defined previously, therefore, tend to choose high-risk, high-correlation projects, be- 70 However, this is not true in general. 71 See Crouhy et al. (1999), p. 16. 72 See James (1996), p. 14, and which we will see in more detail below. 73 When the leverage is set so that it matches a fixed equity return, the prespecified default level will change with changes in the asset risk—or fixing the capital structure for the default probability results in a change of the equity return with a change in the asset risk. The same holds true for changes in the correlation. See above and Crouhy et al. (1999), p. 12. 74 See Crouhy et al. (1999), p. 8.
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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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Page 316 and 317: eferences Aguais, Scott D., and Ant
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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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