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Capital Budgeting in Banks 249 However, as can be easily seen, in order to do so, we will need to change the capital structure (i.e., V A,T /F and hence D/E) as σ A (the riskiness of the transaction) changes. However, as we change the capital structure (D/E as plotted on the x- axis in Figure 6.1), we also change the return on equity (here denoted as R_E). Note that D/E = 11.5 represents an equity percentage of 8%, 15.67 represents 6%, and 24.0 represents 4%. So, in the typical areas of bank and transaction leverage ratios, we experience significant variations in the expected equity return for relatively small changes in the capital structure. This may seem to be at odds with the intuition of the M&M propositions at first sight. 54 However, we are not trying to demonstrate the irrelevance of the financing decision on the firm value here, but rather the effects when a firm is trying to fix its default probability. 55 Because the same holds true when the correlation of the asset with the market portfolio (ρ A,M ) increases, we can plot the following table that summarizes the results (see Table 6.1) where E(R A ) = Expected return on asset (which is determined via the CAPM) E(R E ) = E(V E,T )/V E,0 – 1 = The expected return on equity (which is also determined via the CAPM) ↑ (↓) = Indicate an increase (decrease) in the respective measure. So, we can conclude from the above discussion that one can either fix the default probability or R E h (the hurdle rate), but not both at the same time. 56 Before we turn to the consequences of this conclusion in the next section, we will now define RAROC—using the same modeling context— so that it can be compared to a CAPM-based hurdle rate. Let us consider a single one-year investment A of the bank. Let I be the cost of the investment for asset A, which is an NPV = 0 transaction, and V A,t be the market value of the investment at time t. It follows that therefore V A,0 = I. Let us further assume that economic capital EC is necessary to set up a reserve pool that is invested in risk-free bonds to fix the probability of default at the predetermined confidence level, which is a common assumption for calculating RAROC in practice. 54 Note that we are using the same assumptions as they do. 55 And hence the effects on R E rather than on WACC, the weighted average cost of capital, or on value. Note that R D is labeled R_D in Figure 6.1. 56 Fixing the default probability (i.e., d 2 ) has an effect on the required rate of return that is of an order of magnitude less than the effect of fixing the required rate of return on the change in the default probability. See Crouhy et al. (1999), pp. 11–13.
250 RISK MANAGEMENT AND VALUE CREATION IN FINANCIAL INSTITUTIONS 10.11 11.50 13.29 15.67 19.00 24.00 32.33 49.00 99.00 D/E 60% 60% 50% 50% R_E WACC R_D 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% 4.26 4.56 4.88 5.25 5.67 6.14 6.69 7.33 8.09 9.00 Figure 6.1 Return on equity and changing capital structure.
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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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100 RISK MANAGEMENT AND VALUE CREAT
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Page 316 and 317: eferences Aguais, Scott D., and Ant
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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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