Credit Portfolio Management phần 8 ppsx

from capital. Second-loss enhancements should be risk-weighted based on their external ratings. If they are not externally rated or if the assets are in multiple buckets, they should be risk-weighted according to the highest weighting of the underlying assets for which they are providing loss protection. Other commitments (i.e., liquidity facilities) usually are short term and, therefore, effectively are currently not assessed a capital charge since they are converted at 0% to an on-balance-sheet credit equivalent amount as required by the 1988 Basle Accord. Under certain conditions, liquidity facilities provided by the sponsor may be converted at 20% and risk-weighted at 100%. Otherwise these facilities will be treated as credit exposures. IRB Approach—Treatment for Issuing Banks For banks issuing securitiza- tion tranches, the Basle Committee proposed that the full amount of re- tained first-loss positions would be deducted from capital, regardless of the IRB capital requirement that would otherwise be assessed against the un- derlying pool of securitized assets. The Basle Committee indicated that it is considering whether issuing banks that retain tranches with an explicit rating from a recognized exter- nal credit assessment institution could apply an IRB capital requirement tied to that rating by mapping this assessment into the PD/LGD frame- work. However, the Basle Committee indicated that internal ratings will not be acceptable. IRB Approach—Treatment for Investing Banks The Basle Committee pro- posed to rely primarily on ratings for such tranches provided by external credit assessment institutions. Specifically, the bank would treat the tranche as a single credit exposure like other exposures, and apply a capital requirement on the basis of the PD and LGD appropriate to the tranche. The appropriate PD would be that associated with the external rating on the tranche in question. Treatment of Explicit Risks Associated with Synthetic Securitization Reacting to the fact that banks had used synthetic CDOs to reduce regula- tory capital, the Basle Committee stated that the new rules will reduce the incentive for banks to engage in a synthetic securitization in order to mini- mize their capital requirements. The Basle Committee indicated that a number of issues need to be re- solved in order to develop a consistent and comprehensive treatment of synthetic securitizations (both standardized and IRB approaches). A key Securitization 239 issue the committee raised is the amount of credit risk that is transferred to third parties and whether a large degree of risk transference is neces- sary in order to obtain regulatory capital relief. NOTE 1. This subsection relies heavily on Merritt, Gerity, Irving, and Lench (2001). 240 TOOLS TO MANAGE A PORTFOLIO OF CREDIT ASSETS PART Three Capital Attribution and Allocation CHAPTER 8 Capital Attribution and Allocation A ttribution is a measurement problem. Given the current portfolio and the corresponding amount of economic capital needed to support that portfolio, how would the capital be assigned currently to individual busi- ness units or to individual transactions? It has implications for how the in- stitution prices its services internally and externally, how it compensates employees, and how much it would pay to acquire a business (or how much it would accept from a buyer for one of its businesses). Allocation is the optimization problem. The allocation decision re- quires me to determine if some rearrangement of my capital would result in a higher value for the firm. However, before we can deal with either of these, we need to consider how the total economic capital for the firm—not just economic capital for credit risk—would be measured. MEASURING TOTAL ECONOMIC CAPITAL So far, we have been looking at one slice of economic capital—that associ- ated with credit risk. We now need to broaden our scope and think about the capital associated with all risks (i.e., including market risk and opera- tional risk, as well as credit risk). Economic capital is associated with the volatility of the economic value of the bank or its business units. Unfortunately, this volatility in value fre- quently cannot be observed, so it is calculated via proxy measures, such as the volatility of earnings or of the value of individual transactions. Banks may measure volatility (unexpected losses) with a “top-down” measure, a “bottom-up” measure, or more likely, a combination of the two. Top-Down Approach The top-down measures employ earnings (or cash flow) volatility to esti- mate the volatility of the unit’s asset value. These models use historical data 243 on earnings, or a model, to project volatility into the foreseeable future. The volatility of market value can easily be implied from these proxy mea- sures. [See Matten (2000) for a full discussion of this approach.] Top-down measures are most appropriate for high volume businesses (e.g., consumer lending), where transaction level detail is unavailable and the allocation of capital to specific transactions is not required. In the top-down approach, we consider the whole firm and examine earnings volatility. We collect data on period-to-period earnings and then create a distribution of historical profit volatility. This kind of approach is applicable to firms in which the businesses remain stable over time (i.e., when we look at one period to the next, the business hasn’t changed). Furthermore, it requires a lot of data—hope- fully high frequency data. (I would like daily observations of earnings, but it’s likely that monthly or quarterly is the best I can get.) In the styl- ized example in Exhibit 8.1, we’ve collected the data and used them to create a histogram. In order to obtain a measure of economic capital, we must specify the confidence level. Note that this confidence level is in terms of earnings (a flow), rather than in terms of value. If we want a 99% confidence level, we need to select the value of earnings that will isolate 1%, the area of the dis- tribution in the left-hand tail. (Note that we look at the left-hand tail, be- cause we are looking at a distribution of earnings, rather than a distribution of losses.) Suppose that the board has specified the target insolvency rate to be 1 / 10 of 1% (i.e., a 99.9% confidence level). We would use a histogram like 244 CAPITAL ATTRIBUTION AND ALLOCATION EXHIBIT 8.1 Top-Down Approach to Measuring Total Economic Capital— Earnings at Risk –240 –180 –120 –60 0 60 120 180 240 300 Historical Earnings Distribution Losses at Target Confidence Level One could also use standard deviation. 0% 2% 4% 6% 8% 10% 12% 14% 16% that in Exhibit 8.1 to find the earnings number that will put 1 / 10 of 1% of the area of the histogram in this left-hand tail. We call this number “earn- ings at risk” (EAR). Given that we have identified a critical earnings number, how do we convert that earnings number into a capital number? We need to convert this flow number into a stock—into a capital number. The question is: “How much capital is needed to provide the necessary support to earn- ings?” That is, how much capital is needed to ensure that earnings will be at least the specified level (EAR) per period? And since we need that amount every period, we solve for the required capital by treating this as a perpetual annuity: The advantage of a top-down approach is that it provides an estimate of total economic capital. By looking at earnings for the business unit or for the entire firm, we are picking up credit risk, market risk, and opera- tional risk. The problem is that there are very few businesses for which you could do a top-down approach. Again, you need the business to be stable and you need to have high frequency data in order to do this. Bottom-Up Approach The “bottom-up” designation derives from the fact that individual transac- tions are modeled and then aggregated to arrive at portfolio or business unit capital. The financial institutions that use this approach obtain sepa- rate measures of credit risk capital, market risk capital, and operational risk capital: ■ The financial institution could use one of the credit portfolio models we described in Chapter 4 to determine credit risk capital. ■ A Value at Risk (VaR) model could be used to estimate market risk capital. For an overview of VaR, I would point you first to Chapter 19 in my book on market risk management, Managing Financial Risk (McGraw-Hill, 1998). ■ In the case of operational risk capital, there is no generally accepted model. We have provided an overview of the various approaches to measuring operational risk capital in the appendix to this chapter. As illustrated in Exhibit 8.2, to date, most firms are simply summing credit risk capital, market risk capital, and operational risk capital to get Capital EAR = r Capital Attribution and Allocation 245 their estimate of total economic capital. By summing them, the firm is making a conservative estimate (i.e., the estimate of total economic capital will be too big). By summing the three risk capital numbers, we have as- sumed that the risks are perfectly positively correlated. If the risks are less than perfectly positively correlated, total economic capital will be less than the sum. While the more common approach is simply to sum the risk capital numbers, some firms are beginning to devote research to identifying the de- gree of correlation. The following excerpt from JP Morgan Chase’s 2001 Annual Report indicates that they have measured the correlations between credit risk, market risk, operating risk, and private equity risk: Comparison of Top-Down and Bottom-Up Approaches Exhibit 8.3 provides a comparison of top-down and bottom-up ap- proaches to measuring economic capital. 246 CAPITAL ATTRIBUTION AND ALLOCATION EXHIBIT 8.2 Bottom-Up Approach to Measuring Total Economic Capital—Sum Credit, Market, and Operational Risk Capital Credit Risk Capital Market Risk Capital Operational Risk Capital Economic Capital = + + Obtained from a Credit Portfolio Model `` Obtained from some type of operational risk model Obtained from a VaR Model Credit Risk 13.6 Market Risk 3.9 Operating Risk 6.8 Private Equity Risk 5.3 Goodwill 8.8 Asset Capital Tax 3.7 Diversification Effect (9.0) Total Economic Capital $33.1 ATTRIBUTING CAPITAL TO BUSINESS UNITS Without question, banks and other financial institutions are interested in measuring the capital consumed by various activities. The conundrum of capital attribution is that there is no single way to accomplish it. In fact, Nobel laureate Robert Merton and his colleague at the Harvard Business School, Professor Andre Perold, make the following observation regarding the capital attribution process. Full [attribution] of risk capital across the individual businesses of the firm . . . is generally not feasible. Attempts at such a full [attribu- tion] can significantly distort the true profitability of individual busi- nesses.—Merton and Perold, p. 241 However, you should not take this to mean that attribution is im- possible. Rather, we think Professors Merton and Perold’s warning rein- forces a two-part message about attributing capital to individual business activities: (1) there are different ways of measuring the capital consumed by a particular activity, and (2) these different measures have different uses. Perhaps a third message is that the user should be aware of the limitations of each measure, as no one measure is suitable for every application. The problem in attributing capital is whether (and, if so, how) to as- sign a portfolio benefit—namely diversification—to the elements of the portfolio. Practitioners speak about three commonly employed measures of capital—stand-alone, marginal, and diversified. Different firms will cal- culate these capital numbers differently, but they tend to agree on the idea behind the measures. Capital Attribution and Allocation 247 EXHIBIT 8.3 Comparison of Top-Down and Bottom-Up Approaches to Measuring Total Economic Capital Top Down Bottom Up • Historical earnings data are • Models intensive available. Credit VARs are still It is “clean.” relatively new concepts. It reflects current business. Operational VARs pose a challenge. • Better suited to evaluating business • Suited to both business unit and unit than transaction level returns. transactional capital calculations. Does not give a capital figure May be used in pricing of for individual transactions. transactions, e.g., loans. Stand-Alone Capital Stand-alone capital is the amount of capital that the business unit would require, if it were viewed in isolation. Consequently, stand-alone capital would be determined by the volatility of each unit’s earnings. Because it does not include diversification effects, stand-alone capital is most often used to evaluate the performance of the managers of the busi- nesses. The business unit managers should not be given credit for portfolio effects, because they were not under the control of that manager. The weakness of that argument is that the unit is part of a group of businesses and the bank should be careful about encouraging its managers to ignore the interrelationships. It is possible to construct scenarios where businesses that are not profitable on a stand-alone basis add shareholder value within a diversified firm. Marginal Capital Marginal capital measures the amount of capital that the business unit adds to the entire firm’s capital (or, conversely, the amount of capital that would be released if the business unit were sold). It is generally agreed that marginal capital is most appropriate in evaluating acquisitions or divestitures. Marginal capital would not be an appropriate tool for performance evaluation, because it always underal- locates total bank capital. And even if the marginal capital numbers were scaled up, 1 the signals sent about profitability are potentially very misleading. Diversified Capital Diversified capital (also referred to as allocated capital) measures the amount of the firm’s total capital that would be associated with a particu- lar business unit. Diversified measures are sometimes referred to as portfolio beta measures because the apportionment of risk is based on the covariance of each business unit with the entire organization in the same way that stock’s beta is calculated from its covariance with the market. At- tributing business capital in this way has intuitive appeal and it is fairly widespread. Obtaining the correlations required is a challenge. Estimates can be based on historical performance data within the institution and manage- ment’s judgment. Conceptually it is possible to derive estimates for broad classes of activity (e.g., retail lending versus commercial lending) 248 CAPITAL ATTRIBUTION AND ALLOCATION [...]... from the risk-free rate to the portfolio in question Exhibit 8. 11 shows two portfolios I know that the Sharpe Ratio for Portfolio 2 is higher than that for Portfolio 1, because the slope of the line to Portfolio 2 is higher than the slope of the line to Portfolio 1 Finally, let’s look at the relation between the Sharpe Ratio and the efficient frontier In Exhibit 8. 12, Portfolios 1 and 2 have the same... insight into what financial institutions are actually doing, we provide some results from the 2002 Survey of Credit Portfolio Management Practices that we described in Chapter 1 2002 SURVEY OF CREDIT PORTFOLIO MANAGEMENT PRACTICES Do you explicitly evaluate the performance of your portfolio( s) of credit assets? Yes No 90% 10% If yes, Return on Assets or Return on Equity Return on Regulatory Capital RAROC... conclusions (in Exhibit 8. 9) To provide some insight into what financial institutions are actually doing, we conclude this section with some results from the 2002 Survey of Credit Portfolio Management Practices that we described in Chapter 1 2 58 CAPITAL ATTRIBUTION AND ALLOCATION EXHIBIT 8. 9 Evaluation of Risk Contribution Measures • Most risk contribution measures are additive and sensitive to credit quality... risk.) Exhibit 8A.2 illustrates a stylized loss distribution, which combines both the frequency of the loss events and their severity Exhibit 8A.3 categorizes the various operational risk models that have been publicly discussed.4 20 Frequency (Number of Occurrences) 18 16 14 12 10 8 6 4 2 0 123 276 623 1,406 3 ,88 5 10,737 36,365 123,163 Loss Severity (Thousands of Dollars, Log Scale) EXHIBIT 8. A2 Stylized... you will likely hear about Today, most equity portfolio managers are measured against some benchmark portfolio (e.g., the S&P 500) The Information Ratio (also attributed to Professor Sharpe) is the portfolio s excess return relative to the benchmark portfolio divided by the increase in risk for the portfolio in question relative to the risk of the benchmark portfolio 262 CAPITAL ATTRIBUTION AND ALLOCATION... any information Region in which loss data are captured 98 100 Percentile Expected Loss 99.97th Percentile EXHIBIT 8. 7 Logic Behind a Tail-Based Risk Contribution Measure 257 Capital Attribution and Allocation Highest Risk 100 Standard Deviation Rank 90 80 70 60 50 40 30 20 10 0 0 10 20 30 Lowest Risk 40 50 60 70 80 90 100 Tail-Based Rank EXHIBIT 8. 8 Comparison of Standard Deviation–Based and Tail-Based... follows that if you have the maximum Sharpe Ratio, you will be on the efficient frontier 261 Capital Attribution and Allocation Return Portfolio 2 Portfolio 1 Rf 0 Risk EXHIBIT 8. 11 Sharpe Ratio = Slope of Ray from Risk-Free Rate Return Portfolio 2 Portfolio 1 Rf 0 Risk EXHIBIT 8. 12 Efficient Frontier = Maximum Sharpe Ratio for Given Levels of Risk Other Performance Measures for Equities While the Sharpe Ratio... sum to total portfolio risk (see the Statistics Appendix for a proof): N σp = ∑ RC i i =1 For example, RiskMetrics Group’s CreditManager (described in Chapter 4) starts by recognizing that portfolio variance is the sum over all covariances of the positions; so the portfolio standard deviation can be allocated on the basis of the sums of columns in the covariance matrix Consequently, in CreditManager,... prices send the correct signal 2 68 CAPITAL ATTRIBUTION AND ALLOCATION about where the most value can be created for an additional unit of capital or any other resource To provide some insight into what financial institutions are actually doing, we provide some results from the 2002 Survey of Credit Portfolio Management Practices that we described in Chapter 1 In an optimal portfolio the marginal return... marginal capital business is exited? for the businesses In the jargon of credit portfolio management, the measure of the amount of capital attributed to a transaction is commonly expressed in the form of a “risk contribution” measure In this section, we look at some of the risk measures that have been proposed and are available in the credit portfolio models As Chris Finger of the RiskMetrics Group points . 24% 189 Business 1 = 222 – 189 = 33 Businesses 1 and 3 2,000 23% 186 Business 1 = 222 – 186 = 36 Businesses 1 and 2 2,000 18% 146 Business 1 = 222 – 146 = 77 In the jargon of credit portfolio management, . a Credit Portfolio Model `` Obtained from some type of operational risk model Obtained from a VaR Model Credit Risk 13.6 Market Risk 3.9 Operating Risk 6 .8 Private Equity Risk 5.3 Goodwill 8. 8 Asset. MANAGE A PORTFOLIO OF CREDIT ASSETS PART Three Capital Attribution and Allocation CHAPTER 8 Capital Attribution and Allocation A ttribution is a measurement problem. Given the current portfolio