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http://pubsonline.informs.org Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines Tom Duffy, Manos Hatzakis, Wenyue Hsu, Russ Labe, Bonnie Liao, Xiangdong (Sheldon) Luo, Je Oh, Adeesh Setya, Lihua Yang, To cite this article:

Tom Duffy, Manos Hatzakis, Wenyue Hsu, Russ Labe, Bonnie Liao, Xiangdong (Sheldon) Luo, Je Oh, Adeesh Setya, Lihua Yang, (2005) Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines. Interfaces 35(5):353-369. http:// dx.doi.org/10.1287/inte.1050.0157 Full terms and conditions of use: http://pubsonline.informs.org/page/terms-and-conditions This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact [email protected]. The Publisher does not warrant or guarantee the article’s accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. © 2005 INFORMS Please scroll down for article—it is on subsequent pages INFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics.

For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org Vol. 35, No. 5, September–October 2005, pp. 353–369 issn0092-2102 eissn1526-551X 05 3505 0353 inf orms ® doi10.1287/inte.1050.0157 © 2005 INFORMS Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines Tom Duffy Merrill Lynch Global Bank Group, 34th Floor, 250 Vesey Street, New York, New York 10080, [email protected] Manos Hatzakis Merrill Lynch Management Science Group, PO Box 9065, Princeton, New Jersey 08543-9065, [email protected] Wenyue Hsu Merrill Lynch Bank USA, PO Box 9018, Princeton, New Jersey 08543-9018, [email protected] Russ Labe, Bonnie Liao Merrill Lynch Management Science Group, PO Box 9065, Princeton, New Jersey 08543-9065 {[email protected], [email protected]} Xiangdong (Sheldon) Luo Merrill Lynch Bank USA, PO Box 9018, Princeton, New Jersey 08543-9018, [email protected] Je Oh Merrill Lynch Management Science Group, PO Box 9065, Princeton, New Jersey 08543-9065, [email protected] Adeesh Setya Merrill Lynch Bank USA, PO Box 9018, Princeton, New Jersey 08543-9018, [email protected] Lihua Yang Merrill Lynch Management Science Group, PO Box 9065, Princeton, New Jersey 08543-9065, [email protected] Merrill Lynch Bank USA has a multibillion dollar portfolio of revolving credit-line commitments with over 100 institutions. These credit lines give corporations access to a speciﬁed amount of cash for short-term funding needs. A key risk associated with credit lines is liquidity risk, or the risk that the bank will need to provide signiﬁcant assets to the borrowers on short notice. We developed a Monte Carlo simulation to analyze liquidity risk of a revolving credit portfolio. The model incorporates a mix of OR/MS techniques, including a Markov transition process, expert-system rules, and correlated random variables to capture the impact of industry cor- relations among the borrowers. Results from the model enabled the bank to free up about $4 billion of liquidity.

Over the 21 months since the bank implemented the model, the portfolio has expanded by 60 percent to over $13 billion. The model has become part of the bank’s tool kit for managing liquidity risk and continues to be used every month.

Key words: ﬁnancial institutions: banks; probability: Markov processes. M errill Lynch was founded in 1914 by Charles E. Merrill, with the vision of bringing Wall Street to Main Street. Merrill Lynch has two major business divisions, the Global Private Client Group (GPC) and Global Markets and Investment Banking (GMI).

GPC is the retail part of the business, provid- ing brokerage, investment, and banking services toindividual retail clients and small to midsize busi- nesses. Merrill Lynch provides investment services to these clients through a sales force of 14,000 ﬁnancial advisors (FAs) in 500 ofﬁces around the world. GPC supports trading in a wide range of securities, includ- ing stocks, bonds, mutual funds, and other ﬁnancial instruments. It also offers such products as mortgages, home equity loans, annuities, and insurance and such 353Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines 354 Interfaces 35(5), pp. 353–369, © 2005 INFORMS services as trust and estate-planning services, and 401(k) employee-beneﬁts administration. GPC serves about 3 million households and has $1.3 trillion of assets under management.

GMIserves major corporations and institutions around the world. It helps companies raise capital through new issues of equity and debt, and it acts as a market maker in a wide range of securities. GMIalso provides advice and guidance to companies in such areas as mergers and acquisitions.

Merrill Lynch established its management science group in 1986, and the group has been part of the GPC organization since 1990. It helped Merrill Lynch win the INFORMS Prize in 1997 for the effec- tive integration, application, and impact of manage- ment science on the decision making and success of the ﬁrm. In 2001, the group won the Edelman Prize in recognition of the pricing analysis for Inte- grated Choice, a new product at Merrill Lynch, which gathered $83 billion of client assets during its ﬁrst 18 months.

The mission of the management science group is to use quantitative modeling and analysis to support strategic decision making in complex business situ- ations. The group provides analytical and business consulting to many GPC business units using a broad range of operations research and management sci- ence techniques, including optimization, simulation, and multivariate statistics. Application areas include compensation analysis, pricing analysis, mutual-fund- portfolio optimization, quantifying the impact of business strategies, evaluating the effectiveness of marketing efforts, and developing prospecting and cross-selling models.

The Merrill Lynch banking group supports both GPC and GMI. It comprises several Merrill Lynch afﬁliates, including Merrill Lynch Bank USA (ML Bank USA) and Merrill Lynch Bank and Trust Co. (MLB&T). ML Bank USA has assets of over $60 billion. The bank acts as an intermediary, accepting deposits from Merrill Lynch retail cus- tomers and using the deposits to fund loans and make investments. Uninvested cash in Merrill Lynch investment accounts can be automatically swept into ML Bank USA deposits. One of the ways ML Bank USA deploys these assets is by providing revolving credit lines to institutional borrowers. CurrentlyML Bank USA has a portfolio of about $13 billion in credit-line commitments with over 100 institutions.

In the context of this work, liquidity is the ability to meet all cash obligations when due. For a bank, such obligations are caused by the demand for funds made by its borrowers or by its depositors. This concept of liquidity is distinct and unrelated to liquidity in the trading markets (Schomburg 2001). Consequently, liq- uidity risk is a bank’s potential inability to meet its cash obligations. The Merrill Lynch Banking Group seeks to ensure liquidity at all times, across market cycles, and through periods of ﬁnancial stress. It does so by maintaining positive cash ﬂow gaps over mul- tiple years in a simulated contingency scenario. It periodically tests the availability, under stress con- ditions, of alternative sources of funding, including the Federal Reserve, Federal Home Loan Banks, and repurchase agreements (a repurchase agreement is a contract in which the seller of securities agrees to buy them back at a speciﬁed time and price). Background: Revolving Credit Lines Revolving credit lines, or credit facilities, give borrow- ers access to a speciﬁed amount of cash on demand for short-term funding needs. These credit lines func- tion for corporations in the same way credit cards or home equity lines of credit work for individuals.

The bank establishes credit limits and allows the cor- porations to borrow, on demand, up to these limits (Figure 1). The borrowers are institutional clients who need short-term funding. On the other side are the individual clients with investment accounts at Merrill Lynch. ML Bank USA acts as an intermediary, using the cash deposits to fund the revolving credit lines.

The credit lines banks offer are not a primary source of short-term borrowing but serve mainly as backup liquidity for issuers of commercial paper, which is the cheapest source of short-term borrowing for corpo- rations and foreign governments. They typically use these lines to retire maturing commercial paper dur- ing the process of rolling it over, or when they cannot roll it over because of a credit downgrade or general adverse market conditions. Rating agencies require evidence of short-term backup liquidity before assign- ing a commercial paper rating to an issuer. They typ- ically require liquidity backup of about 50 percent of commercial paper outstanding for the highest-ratedDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 355 ML Bank USA – liquidity provider Liquidity supply Cash Deposits Investor A Investor B Investor C Borrower 1 Borrower 2 Borrower 3 Institutiona l cl ients Revolving credit line portfolio De mand for short-term fun ds Retail clients Figure 1: This ﬁgure shows the structure and funding of a revolving credit portfolio. The bank acts as an inter- mediary, accepting deposits from retail investors and using these deposits to provide the necessary liquidity for the portfolio. issuers and typically 100 percent for those with less than the highest A1-P1 rating. (Ratings for short-term debt are issued by all four US credit-rating agen- cies. Standard and Poor ’s short-term ratings range from A-1 (highest) to D (default); Moody’s range from P-1 (highest) to P-3 (lowest); they also issue sub- grades, for example, A-1+) (Hahn 1993). So, in addi- tion to serving as liquidity backup, revolvers play a credit-enhancing role (Federal Reserve System Board of Governors 2003).

Each credit line has an associated dollar amount, an expiration date, and renewal options. Some borrowers have multiple lines, or tranches, with different dollar amounts and expirations. When companies have mul- tiple lines, they can choose to use any one tranche or Facility Facility Commitment Facility borrower Facility name effective date maturity date amount Diversiﬁed/Conglomerate Revolver 5 year 7/8/2002 7/8/2007 60 000 000 services 1 Diversiﬁed/Conglomerate Revolver 364D-1year term out 2003 7/7/2003 7/6/2004 25 000 000 services 1 Insurance 1 Revolver 3 year-2 year term out 3/31/2003 3/31/2006 55 000 000 Insurance 2 Revolver 364D-1 year term out 2003 7/17/2003 7/15/2004 50 000 000 Insurance 2 Revolver 5 year 7/18/2002 7/18/2007 65 000 000 Utilities 1Revolver 364D-1year term out 3/7/2003 3/5/2004 10 000 000 Utilities 2 Term 364D-1year term out 4/9/2003 4/7/2004 350 000 000 Retail 1Revolver 4 year 3/7/2002 6/22/2006 50 000 000 Retail 1Revolver 364D-1year to 2003 6/20/2003 6/18/2004 31 818 182 Table 1: These sample credit facilities range in duration from one to ﬁve years and represent commitment amounts of $10 to 350 million. A number of borrowers have multiple facilities (Diversiﬁed/Conglomerate 1, Insurance 2, and Retail 1). a combination of tranches. Once a credit line is in use, the borrower can choose to continue to use the line up to its limit or pay it off. The borrower must immedi- ately repay any amounts outstanding when the credit line expires (Table 1).

Regulatory treatment of revolvers depends on their original term to maturity. Regulatory capital is needed (at a 50 percent risk weight) only if the revolving credit facility has a maturity of a year or more. For this reason, banks typically offer facilities consisting of two tranches: a low-priced 364-day tranche and a higher-priced one maturing in three to ﬁve years or more.

Credit lines are often funded through a consortium (syndicate) of banks, which helps spread the liquidityDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines 356 Interfaces 35(5), pp. 353–369, © 2005 INFORMS Global facility Commitment commitment Facility name amount amount Revolver 5 year 60 000 000 6 000 000 000 Revolver 364D-1year term out 2003 25 000 000 2 000 000 000 Revolver 3 year-2 year term out 55 000 000 500 000 000 Revolver 364D-1year term out 2003 50 000 000 1 375 000 000 Revolver 5 year 65 000 000 1 375 000 000 Revolver 364D-1year term out 10 000 000 225 000 000 Term 364D-1year term out 350 000 000 350 000 000 Revolver 4 year 50 000 000 2 250 000 000 Revolver 364D-1year to 2003 31 818 182 1 750 000 000 Table 2: These examples show credit amounts committed by one bank ver- sus the total commitment by the syndicate of banks for each facility in our sample set.

risk across multiple institutions (Table 2). The bank generally determines the lending rate on these loans as a ﬂoating base rate tied to the prime rate or to the London Interbank Offered Rate (LIBOR). It typically negotiates the spread over the base rate when it estab- lishes the credit line (Hahn 1993).

Some revolving credit lines have a term-out option, which allows the borrower to use the funds for an additional period after expiration, typically for one year. The bank negotiates this feature with the bor- rower when it establishes the credit line, typically for lines that expire in less than one year. If the borrower chooses to invoke a term-out option, the bank can- not refuse the request. At the end of the additional period, the company must fully repay any outstand- ing amount (Table 3). Facility Facility Final Facility borrower Facility name effective date maturity date term-out date Diversiﬁed/Conglomerate Revolver 5 year 7/8/2002 7/8/2007 Null services 1 Diversiﬁed/Conglomerate Revolver 364 days-1year term out 2003 7/7/2003 7/6/2004 7/6/2005 services 1 Insurance 1 Revolver 3 year-2 year term out 3/31/2003 3/31/2006 3/31/2008 Insurance 2 Revolver 364 days-1 year term out 2003 7/17/2003 7/15/2004 7/15/2005 Insurance 2 Revolver 5 year 7/18/2002 7/18/2007 Null Utilities 1Revolver 364 days-1year term out 3/7/2003 3/5/2004 3/5/2005 Utilities 2 Term 364 days-1year term out 4/9/2003 4/7/2004 10/7/2004 Retail 1Revolver 4 year 3/7/2002 6/22/2006 Null Retail 1 Revolver 364 days-1 year to 2003 6/20/2003 6/18/2004 6/18/2005 Table 3: In these examples of term-out conditions in our sample facilities, three of the facilities have no term-out option, and all but one (Insurance 1) are associated with facility durations of less than one year.Ratings Ratings current current Facility borrower Facility name S&P Moody’s Diversiﬁed/Conglomerate Revolver 5 year BBB+Baa1 services 1 Diversiﬁed/Conglomerate Revolver 364 days-1year BBB+Baa1 services 1term out 2003 Insurance 1Revolver 3 year-2 year AAA Aaa term out Insurance 2 Revolver 364 days-1year AAA Aaa term out 2003 Insurance 2 Revolver 5 year AAA Aaa Utilities 1Revolver 364 days-1year BBB−Baa2 term out Utilities 2 Term 364 days-1year BBB−Ba1 term out Retail 1Revolver 4 year AA Aa2 Retail 1Revolver 364 days-1year AA Aa2 to 2003 Table 4: This table shows the current credit ratings for sample facilities provided by two rating agencies with their different scales.

The bank can renew credit lines, typically basing its decisions on the credit rating of the borrower when the line expires, the history of the borrower ’s use of the credit line, and other revolving credit-line com- mitments at that time (Table 4).

Banks’ ability to offer revolving credit facilities and other forms of backup liquidity to commercial-paper issuers becomes most crucial in times of systemwide liquidity shocks (Gatev and Strahan 2005, Kanatas 1987, Kashyap et al. 2002). Gatev and Strahan con- tend that banks’ deposit inﬂows provide a naturalDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 357 hedge against increases in loan demand that fol- low declines in market liquidity, for example, dur- ing the recent Enron crisis (Zuckerman 2002), and thus banks can provide backup liquidity at a lower cost than other ﬁnancial institutions. Empirical evi- dence supports the argument that when market liq- uidity dries up and commercial paper rates rise, the increased deposit inﬂows associated with the ﬂight to cash safety that banks experience helps them to meet increased demand for loans from borrowers draw- ing down their preexisting commercial paper backup lines without having to tap into their holdings of liq- uid assets.

Two key drivers of credit-line usage could affect liq- uidity risk: (1) low-level ongoing use by the various borrowers for short periods and (2) default by com- panies to whom a bank has extended credit, a greater threat. The bank considers a borrower to be in default when the borrower fails to make an interest or prin- cipal payment on any debt obligation on time. That failure signals severe ﬁnancial distress and causes an immediate downgrade to the lowest credit rating.

As a borrower ’s credit rating worsens, it tends to increase the use of its revolving credit facilities.

Because a credit rating of A or better is required to gain access to the commercial paper market, bor- rowers rated below A (Table 5) use revolving credit as a substitute to commercial paper for short-term funding. A downgrade to a rating below investment grade typically triggers debt covenants that call for Description S&P Moody’s Investment Grade Highest AAA Aaa High AA Aa Upper medium A A Medium BBB Baa Speculative Grade (“Junk”) Lower medium BB Ba Speculative B B Poor CCC Caa Highly speculative CC Ca Lowest C C Default D Subgrade examples AA+, AA, AA−Baa1, Baa2, Baa3 Table 5: We compare the long-term debt-rating scales of the two major credit-rating agencies, Standard and Poor’s and Moody’s.Average revolver Debt rating utilization (%) UUIED (%) AAA 0 169 0 AA 1 673 4 A4 672 3 BBB 20 072 0 BB 46 874 5 B63 781 1 CCC 75 086 0 Table 6: We show revolver utilization by Standard and Poor’s senior debt rating based on monthly Citibank portfolio data from 1987 through 1993.

UUIED is usage of the normally unused commitment in the event of default. Utilization increases as debt rating quality decreases. the accelerated repayment of certain types of a bor- rower ’s debt obligations. In this case, a borrower increases revolver use to obtain the funds to meet such obligations. Usage jumps in the event of default, as borrowers tap into every source of liquidity avail- able (Marker 1997). A summary of revolver usage statistics compiled by Asarnow and Marker (1995) based on monthly Citibank portfolio data from 1987 through 1993 (Table 6) gives evidence of these trends.

Furthermore, a number of companies or industries may experience ﬁnancial weakness simultaneously and invoke the use of their credit lines, creating a drain on liquid funds. In these situations, the compa- nies are unlikely ever to repay the loans. The bank must manage deposits to meet these liquidity risks as well as the overall likelihood of defaults in the revolv- ing credit portfolios.

Revolving credit facilities generate revenues in the form of interest and fees. Borrowers pay facility fees regardless of usage. The bank assesses a commitment fee ranging from ﬁve to more than 50 basis points annually on the unused portion of a facility. It charges borrowers that use their facilities heavily a usage fee.

The cash committed to funding the facility amounts to a fraction of the facility size except during occurrences of extreme company-speciﬁc or marketwide liquidity stress.

Business Objectives In 2000, ML Bank USA began establishing revolving credit lines for client companies to use excess liquid- ity proﬁtably. Although the business began slowly, the bank expected it to grow rapidly over the next severalDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines 358 Interfaces 35(5), pp. 353–369, © 2005 INFORMS years. Initially the bank developed its own spread- sheet model to assess the liquidity risk, but it soon recognized that it needed a more comprehensive and sophisticated model to help it to manage the growing portfolio. It wanted a model that would —Assess the liquidity risk associated with its cur- rent credit-line commitments; —Evaluate contingency and stress scenarios to esti- mate liquidity needs in extreme situations; —Identify sources of potential risk exposure, such as concentrations in speciﬁc industries; and —Evaluate the potential growth of its revolving- credit-line commitments and their use over three to ﬁve years for hypothetical portfolios.

The results of these analyses would directly affect management’s decision on liquidity risk and there- fore the deployment of bank assets and the bank’s proﬁtability.

The Modeling Approach Modeling revolving credit facilities is complex largely because the borrowers can vary their usage. While some of the elements, such as rating transition proba- bilities are typically used in credit-risk models (Hirtle et al. 2001), we believe our work is the ﬁrst compre- hensive Monte-Carlo-based modeling of the liquidity behavior of a revolving-credit-facility portfolio that incorporates a Markovian rating-transition process, expert-system rules, and various degrees of correla- tion within and across industry sectors. Marker (1997) sketches a modeling methodology Citibank uses to value facilities rather than to evaluate the joint liquid- ity behavior of a portfolio of revolvers.

The underlying framework of our liquidity risk model is a Monte Carlo simulation (Figure 2).

The model simulates monthly credit-line usage for each company and each tranche over a ﬁve-year (60-month) time horizon. During this time, credit ratings of companies change, tranches expire, some get renewed, some are terminated, and companies exercise term-out options. We took a Monte Carlo simulation approach because many of the key param- eters are stochastic by nature. The simulation allows us to evaluate a wide range of scenarios and estab- lish probability levels for the key outcomes the bank needs. The model incorporates the following OR/MS techniques:—A Markov transition process to model the monthly stochastic changes in credit ratings for each company; —The generation of correlated stochastic variables to capture correlations in credit-rating migrations aris- ing from economic conditions that affect companies in a single industry or in different industries; and —Expert-system business rules to determine when companies will exercise term-out options and whether the bank will renew or terminate expiring lines of credit.

The innovative combination of these OR/MS tech- niques to address the needs of ML Bank USA is what sets this work apart.

Stochastic variables in the model include:

—The monthly credit rating for each company; —The probability that a company will start using a credit line; —The probability that a company will continue using an already drawn credit line; —The amount of the credit line used; and —The sequence in which the company uses the dif- ferent tranches.

We provide a process ﬂow diagram of the model in Figure 2. Monte Carlo Simulation The simulation model projects the monthly liquidity requirements of the total existing portfolio of revolv- ing credit facilities at Merrill Lynch by modeling each borrower ’s timing and amount of credit use as a func- tion of its credit rating and previous month’s use.

Credit ratings are updated every month. A borrower ratedain montht−1 will be rateda in monthtif the following holds: a −1 b=1 pab

A borrower ’s probability of nonzero credit use in a given month is much higher if the borrower hasDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 359 1. Get next company 2. Set new credit rating 3. Get next tranche 8. Another tranche? 5. In use? 11.

Company term out? 13. ML renews? 7. Set usage to 0 6.

Continue to use? 10.Start to use credit? 9. Set credit usage 12. Set usage to 100% 14. Set available credit to 0 D Yes No A Yes BNoFYes No Yes C C No No Yes No E No Yes4. Tranche expires? Yes Figure 2: This process-ﬂow diagram shows the simulation logic for each company for each month. The simulation processes are A: Cumulative draw probability distribution (function of credit rating), B: Draw probability conditional on currently using credit, C: Distribution of percent drawn on available credit line (function of credit rating), D: Credit rating transition matrix, E: (Expert system) Term-out exercise rules (when a term out is exercised, usage is set to 100 percent for all tranches), and F: (Expert system) ML tranche renewal rules.Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

The amount of use can vary randomly based on a user-deﬁned distribution that takes into account a borrower ’s right to draw deeper in its facility or prepay all or part of the loan balance without penalty.

We modeled default as an absorbing state, that is, it is impossible for borrowers to migrate out of the default status. The model assumes a borrower will increase use of its facility to 100 percent upon default and remain fully drawn throughout that particular simulation run. This is a conservative treatment of borrowers in default, because it implies total loss on a defaulted facility, even though expected loss is often less than 100 percent in reality, especially given the absolute priority of claims on bank loans over all other forms of the borrower ’s debt and against its equity in the event of bankruptcy.

For borrowers that have facilities with term-out options, the business rules that govern whether they will invoke their term-out options depend on their credit rating the month the facility expires and the path it followed to get there. Because invoking a term- out option is a sign that the borrower ’s credit qual- ity is deteriorating, the bank usually refuses to renew the borrower ’s credit line. Consequently, the model sets all the borrower ’s facilities to full usage when the borrower exercises a term-out option on any one of them. The termed-out facility remains 100 percent drawn until the term-out period expires. At that time, it gets paid in full. The borrower ’s other facilities remain 100 percent drawn until their expiration, at which time they get paid off. None of the affected facilities are renewed throughout that particular sim- ulation run.

The bank reserves the right to not renew a facility of a borrower whose credit rating is below a certain threshold in the month the facility expires. The simu- lation assumes that a facility will be paid off if it is not renewed, except in the event that the borrower exer- cises a term-out option. If the borrower does not exer- cise a term-out option and has additional unexpired facilities, the bank may renew them if the borrower ’s credit rating improves during subsequent months and is above the renewal threshold when they expire.

We developed the simulation model on version 7.01 of the Arena simulation software. A Visual Basic controller embedded in an Excel spreadsheet drivesthe model. The controller enables the user to input borrower data and revolving-credit-line data, to set parameters, to run the simulation, and to create reports. The simulation’s time horizon is typically 60 months, in line with the bank’s ﬁve-year planning horizon. To get reliable projections for the total liq- uidity needs of the portfolio over a multiyear time horizon, we tested the model extensively, and we determined that we needed at least 5,000 replications to obtain stable distribution results. Random Number Generation and Industry Correlations The random numbers assigned to stochastic variables in the model are generated by internal functions of the Arena software package. For most of the stochas- tic variables, we used the uniform distribution ran- dom number function in Arena, which generates a random value uniformly distributed between 0 and 1.

We then compared the generated random number to the cumulative density function (speciﬁed as an input to the model) to classify the variable into a speciﬁc outcome. We used this approach for the fol- lowing stochastic variables: credit-line use, amount of credit used, continued line use, and multiple tranche selection.

In the case of credit-rating transitions, we used a more complicated approach so that we could take industry correlations into account. That is, compa- nies in the same industry are more likely to move up or down the credit-rating scale at the same time than companies in different industries. In this case, we need to generate stochastic variables that are cor- related at a higher level for companies in the same industry and at a lower level for companies in dif- ferent industries. We used a ﬁve-step decomposition process (Appendix). The decomposition process is complex and involves calculating eigenvalues, matrix transpositions, and square roots. But we can easily use the result to generate random values with the desired correlation properties. In Step 1, we generate a vectorX= x 1 x 2 x C T, whereCis the num- ber of companies with credit lines andXis a vector of independent, identically distributed standard nor- mal stochastic variables X∼N 0 I , whereIis the identity matrix). In Step 5, we obtain a vectorY=Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 361 y1 y 2 y C T of correlated standard normal vari- ables Y∼N 0 R , whereRis the industry correlation matrix) through special transformations of matrixR in Steps 2 through 4. We then compare the adjusted random numbers to the credit-rating transition matrix to determine the new credit rating for each com- pany. An additional complication is that, to make this comparison, we need to transform the credit-rating transition matrix to a normally distributedN 0 1 cumulative density function. We do this in Excel, using the inverse normal distribution function (as a preprocessing step), which then feeds into Arena.

The model uses the SAS IML library of matrix alge- bra functions to decompose the industry-correlation matrix (Appendix). We developed the default correla- tions for companies in the same industry and in dif- ferent industries through proprietary research as part of a separate study. The Credit-Migration Matrix The credit-migration matrix is the most important input to the model because it drives the borrowers’ frequency and amount of facility use. The rows and columns of this square matrix correspond to credit ratings at monthst−1 andt, respectively. An ele- mentp ab of the matrix represents the probability that a borrower with a credit rating ofain montht−1 will have a credit rating ofbin montht. Because they are probabilities, the elements of the matrix are non- negative and sum to 1 across rows. We assume that the credit-transition process is a discrete-time Markov From/To Aaa Aa1Aa2 Aa3 A1···B1B2 B3 Caa2-C3 Default Aaa 95% 4% 1% 0% 0%··· Aa13% 92% 4% 1% 0%··· Aa2 1% 3% 90% 4% 1%··· Aa3 A1 ···Probability (credit rating changes fromatoa ) B1 B2 B3 Caa2-C3 Default 0% 0% 0% 0% 0%···0% 0% 0% 0% 100% Table 7: This sample transition matrix provides monthly credit-migration probabilities. The rows correspond to the current credit rating. The probabilities that an AA2-rated borrower will be upgraded or downgraded one notch are three percent and four percent, respectively. Default is the absorbing state. chain, that a borrower ’s credit rating in montht depends only on the rating in montht−1 and not on the path it followed to get there, and that the credit-migration matrix is constant throughout the simulation’s time horizon. Ross (1995) gives more information on Markov processes.

Credit ratings in the US are issued by four major agencies, of which the largest and best known are Standard and Poor ’s (S&P) and Moody’s (Table 5), and the two smaller ones are Fitch, and Duff and Phelps. The credit rating measures the two major agencies use are somewhat different. S&P measures a borrower ’s overall capacity to meet its debt obli- gation and hence its probability of default. Moody is believed to also incorporate in its ratings a judg- ment on borrowers’ expected recovery in the event of default, hence expected loss. Schuermann (2004) sum- marizes the extensive literature on expected loss, or loss given default.

A substantial body of work has accumulated on the measurement and estimation of credit-migration matrices (Jafry and Schuermann 2004). In our model, we use a one-month credit-migration matrix based on Moody’s ratings (Table 7). As customary, Caa includes all ratings below it (for example, Ca/CC, C and their subgrades) and above D, which represents a borrower in default.

Expert System Rules One of the unique components of the simulation model is the expert-system rules we incorporated toDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines 362 Interfaces 35(5), pp. 353–369, © 2005 INFORMS determine actions that Merrill Lynch and the bor- rower would take when speciﬁc events occur. These speciﬁc events are the bank’s decision to renew a credit line and the borrower ’s decision to invoke a term-out option when credit lines expire.

Management Science and the ML Bank USA staff worked together to develop these business rules. We based the rules on industry practice and managerial judgment. They do not affect any of the stochastic variables used in the simulation model. The decision rules are a function of the credit rating of the bor- rower when the credit line expires and the number of downgrades in the borrower ’s credit rating in the pre- vious 12 months. We coded the expert-system rules into the Arena simulation, and the model invokes them each month for each company as needed.

We deﬁned some parameters in the expert-system rules as variables that users can change. We designate these parameters in the rules below with ∗ and show illustrative parameter values in italics.

The following rules (Figure 3) govern borrowers’ decisions to invoke the term-out option:

—When a term out is available, the company will exercise the option if (1) Its credit rating at expiration is CCC ∗ or lower, AND (2) Its credit rating was loweredtwo ∗ or more times during the previous 12 months. Aaa Aaa Aa1 Aa1 Aa2 Aa2 Aa3 Aa3 A1 A1 A2 A2 A3 A3 Baa1 Baa1 Baa2 Baa2 Baa3 Baa3 Ba1 Ba1 Ba2 Ba2 Ba3 Ba3 B1 B1 B2 B2 B3 B3 Caa-C Caa-C Default Default 7 notches 4 notches 4 notches 2 notches Term-out exercise threshold rating Term-out option exercised Term-out option not e xercised Term-out op tion exercised Term-o ut o ption not exercised Montht–12 MonthtTime Figure 3: In this example of expert-system rules for term-out options, the decision to exercise a term-out option is a function of the borrower’s cur- rent (montht) credit rating and the steepness of the downgrade path to it.

Below a certain rating threshold, term-out option exercises can be trig- gered by less steep downgrade paths. Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa-C Default Do not renew If no term-out exercise: Renew Else, Do not renew Aa123B .- )r oeaf B-nEcxB lI B-cB3o f,foBE 32xBf Il3 3Bwao xarB 3BrBtnx oeB wB afalr ol 3BrBt n 3Bwao xarB wBcBrwf lr n sl33ltB33f 233Bro 3Bwao 3noar1 nrw teBoeB3 ao enf B-B3 afBw nr, oB3ERl2o lcoalrfi =Bxlt n B3R onar oe3Bfelxw 3noar1 oB3ERl2o B-B3 afBf n3B aEEnoB3anx ol oeB 3BrBtnx wB afalri OR (1) Its credit rating at expiration is higher than CCC ∗ , AND (2) Its credit rating was downgradedfour ∗ or more levels during the last 12 months.

—When companies exercise their term-out options, credit-line use is set to 100 percent across all tranches.

The following rules (Figure 4) govern the deci- sion by Merrill Lynch to renew a credit line when it expires:

—If a company is in default when a tranche expires, ML does not get paid and the line remains fully utilized.

—If a company exercises its term-out option, ML does not renew any tranches with that borrower when they expire.

—If a company does not exercise a term-out option, or it does not have a term-out option, then (1) If the credit rating is CCC- ∗ or lower, ML will not renew the line, and if the line is in use, assume it is paid off and the borrower is no longer in the portfolio; OR (2) If the credit rating is higher than CCC- ∗ ,ML will renew the tranche.Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 363 Implementation In implementing the model, we made it easy and ﬂex- ible for nontechnical users to operate. We installed run-time versions of the model on several worksta- tions at ML Bank USA, where the staff runs it as needed. The model is driven through a Visual Basic controller embedded in an Excel spreadsheet. The controller allows the user to invoke all of the neces- sary steps to run the model and generate output. The process is simple and user friendly; it does not require knowledge of Arena or SAS. The system invokes and executes the software programs behind the scenes.

The user enters data into the three cells in Step 1 and then clicks on each of the three remaining cells in sequence (Figure 5).

The input ﬁles required for the simulation model are extracted from the bank’s loan record database and processed into the formats Arena requires. Dur- ing the input-ﬁle preparation (Step 2), the SAS IML matrix algebra function library is automatically called to decompose the industry correlation matrix and cal- culate arrayB. The input ﬁles passed to Arena include detailed facility data on each borrower (Tables 1 and 2), the rating-transition matrix, industry adjust- ments (arrayB), expert-system rules, and simulation controls. The user can change many of the parameters (for example, transition-matrix values, business-rule cutoffs and time limits, industry correlations, credit- usage rules and probabilities) passed to the simula- tion to further customize the scenario.

Step 1Enter data into blue fields Tracking file name comml_loans.xls in the data input folder Number of replications 10,000 Final result file name jan31norenewals.xls in the results folder Step 2Double-click this button to prepare data for simulation Step 3Run the simulation model Step 4Double-click this button to process the simulation output Prep for model Process model output Run simulation Figure 5: We use this Visual Basic control screen to enter data and simu- lation parameters and run the software modules. In Step 3, the Visual Basic program invokes the Arena software to run the simulation. For a typical scenario, it takes approximately two hours to com- plete and generate the output ﬁles. Upon completion of the simulation, the Visual Basic program processes the model output into a user-friendly summary report in Step 4. The main outputs of the simulation are the following usage charts:

—The usage chart (Figure 6) shows projected liq- uidity requirements for the total portfolio over a 60-month time horizon. Usage at the 97.5th percentile and at the 99.95th percentile, which correspond to two and three standard deviations are the inputs to the bank’s planning process.

—The percent usage chart (Figure 7) shows the same statistics as the usage chart as a percent of the total commitment by month.

A wide range of additional outputs reﬂects the underlying richness of the simulation and helps users to analyze other projected characteristics of the revolver portfolio. For example, —The usage-rating-default table (Table 8) tracks statistics on defaulted borrowers, such as the average, median, and percentiles of the number of borrowers in default and their credit use for each month in the simulation.

Another set of outputs shows average revolver uti- lization (Table 9) and number of borrowers (Table 10) for each credit rating across time.

Ongoing Improvements and Enhancements The management science group supports and main- tains the model and continually improves and enhances it in three main areas. We work with the bank to reﬁne model parameters, such as expert- system rules and the tranche-usage sequence, by ana- lyzing historical data on Merrill Lynch’s revolver portfolio. Jointly with the Moody’s rating agency, we update the credit-rating-migration matrix to incorpo- rate the most recent rating-migration history. Finally, we work with Merrill Lynch’s risk-management group to obtain the most accurate industry-correlation estimates.

Business Impact The liquidity risk model helps ML Bank USA manage the revolving credit lines. It provides a scientiﬁc andDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines 364 Interfaces 35(5), pp. 353–369, © 2005 INFORMS 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 Months from present time Liquidity requirement ($B) Usage at 99.95% of observationsUsage at 97.5% of observationsMedian usageAverage usage Figure 6: In this projection of the ﬁve-year liquidity requirement of the revolving credit-line portfolio, revolving credit usage remains at or below the 97.5th percentile line in 975 out of 1,000 replications. Conversely, it exceeds the 97.5th percentile line in only 25 out of 1,000 replications. The 97.5th percentile line represents usage under “normal” conditions. The 99.95th percentile line is typically used in conjunction with extreme stress test scenarios.

0% 5% 10% 15% 20% 25% 1 3 5 7 9 1113151719 212325 2729 313335373941434547 49 5153 5557 59 Months from present time Liquidity requirement (% of commitment) Percent Usage at 99.95% of observationsPercent Usage at 97.5% of observationsMedian Percent usageAverage Percent usage 0%5123 99 )r sM%o 52fLM tp sM3 L2t03 s%tr tp sM3 ne3yc3f2 i%P1%m%sc 23P1%23(3rs tp sM3 23etie%r5 23m%syi%r3 Lt2spti%t) h3 oMth 23m%s i%r3 1of53 fo f L32 3rs tp sM3 stsfi Lt2spti%t t((%s(3rsqDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 365 Month 1Month 2 Month 3···Month 60 Maximum number of 5 5 5···20 defaults Number of defaults at 3 3 3···13 99.95% of observations Number of defaults at 111···6 97.5% of observations Median number of 0 0 0···1 defaults Average number of 0 0 0···2 defaults Maximum default usage 25 3% 31 7% 31 7%···48 3% Default usage at 99.95% 9 6% 10 9% 13 7%···37 5% of observations Default usage at 97.5% 2 0% 2 1%2 1%···17 3% of observations Median default usage 0 0% 0 0% 0 0%···0 0% Average default usage 0 1%0 1%0 2%···2 5% Table 8: The usage-rating-default table tracks statistics on defaulted bor- rowers, such as the average, median, and percentiles of number of bor- rowers in default and their credit usage for each month of the simulation.

robust measure of liquidity risk. The bank has conﬁ- dence in its new liquidity measure because it is based on the model’s output.

The bank realized the following ﬁnancial beneﬁts:

—The model reduced the bank’s requirement for liquidity reserves from 50 percent of outstanding commitments to about 20 percent, freeing up about $4 billion of liquidity for other uses.

—During the ﬁrst 21 months after we implemented the model, the portfolio expanded by over 60 percent from $8 billion in commitments and 80 companies to $13 billion and over 100 companies.

In addition, the bank obtained the following bene- ﬁts in processing:

Rating Month 1(%) Month 2 (%) Month 3 (%)···Month 60 (%) Baa1 12 12 13···16 Baa2 8 10 12···24 Baa3 23 25 26···29 Ba137 36 35···26 Ba2 35 36 36···21 Ba3 11 15 19···16 Table 9: In this display of average revolver utilization for all borrowers in a credit rating, the boldface row indicates a sharp increase in utilization for borrowers rated Baa3 or lower, because access to less expensive funding sources is lost at those ratings. —The bank uses the model to evaluate extreme- risk scenarios by changing model assumptions.

—The bank uses the model in long-range planning.

The bank continues to use the model monthly to evaluate liquidity and to manage its $13 billion portfolio of credit lines. To analyze basic liquidity, the bank typically runs the model once a month.

The key outputs are the maximum credit-line use at the 99.95th and 97.5th percentile. The bank uses the vectors of monthly draw rates generated by the model at these percentiles as inputs into a separate stress- analysis model that it runs weekly. The results from the stress scenario analysis provide the bank with its overall stress liquidity measure.

Before ML Bank USA had the liquidity model, its assumptions about the liquidity reserves it needed for its revolving credit lines were very conservative. It assumed that borrowers could draw 50 percent of its outstanding credit commitments. Based on the model, this ﬁgure is now between 15 and 20 percent, a reduc- tion of 30 percent or more. This change in its assump- tions had the effect of releasing about $4 billion in additional liquidity that the bank can now deploy for other uses with higher returns.

ML Bank USA also uses the model to evaluate extreme risk scenarios, such as systemic ﬁnancial- market problems that could affect the entire portfo- lio of borrowers. It evaluates such stress situations by changing all the industry correlations in the model to 1.0, greatly increasing the likelihood that compa- nies will migrate towards lower credit ratings and potential defaults. Under this scenario, the model indicates that credit-line draws could double, but they would still be well below the old assumption of 50 percent of outstanding commitments.

The bank also uses the model to enhance its long- range planning. Semiannually the bank develops a four-year forecast of its balance sheet based on input from various business units. It uses the model results to project funded revolving credit facilities in the future. The projections improve its management of the balance sheet and the funding planning process.

In addition, the bank occasionally uses the model to evaluate the impact of signiﬁcant growth in revolv- ing commitments over a three- or four-year time hori- zon. It does so by running the liquidity model with a hypothetical portfolio of increasing credit lines.Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines 366 Interfaces 35(5), pp. 353–369, © 2005 INFORMS Rating Month 1Month 2 Month 3···Month 60 Baa120 20 20 11 Baa2 16 16 16 12 Baa3 5 5 5 6 Ba13 3 3 4 Ba2 3 3 3 3 Ba3 0 11 2 Table 10: In this display of the number of borrowers in each credit rat- ing, the boldface row shows a sharp decrease in the number of borrowers below a minimum credit rating, reﬂecting the lender’s policies of credit extension and renewal.

Conclusion The revolving-credit-liquidity model enabled ML Bank USA to improve its management of the liquid- ity risk associated with its $13 billion revolving-credit portfolio and freed up $4 billion of liquidity. The bank implemented and uses the model as part of its stan- dard operating process. The model is a mix of sev- eral operations research techniques, including Monte Carlo simulation, Markov transition processes, and expert-system rules. In addition, it generates corre- lated stochastic variables to capture industry corre- lations in credit ratings. The model is an excellent example of the practice of management science yield- ing signiﬁcant business beneﬁts.

Appendix The Mathematical Process for Generating Correlated Random Variables Problem: Generate random vectorYwith covariance matrixR, whereRreﬂects the correlations associated with companies in the same or different industries.

Solution:Step1. Generate a vectorXof indepen- dent random variables fromN 0 1 , whereX= x 1 x 2 x c T andC=number of companies with credit lines.

Step2. DecomposeR.R=ADA T, whereDis a diagonal matrix of eigenvalues.

Step3. DecomposeD.D=EE, whereE=D 1/2 .

Step4. CalculateB=AE.

Step5. CalculateY=BX, whereY= y 1 y 2 y c T and is distributed asN O R , andC=number of companies with credit lines.VectorYwill have covariance matrixR, as shown in the following proof:

Va r Y =Va r BX =Va r AEX = AE Va r X E TAT =A EE T A T =ADA T =R Note thatRmust be a positive deﬁnite matrix.

An Example of Industry Correlation Calculations This example is for illustrative purposes, and we have changed the actual numbers.

Sample List of Companies • Retail 1 • Retail 2 • Communications 1 • Communications 2 • Energy 1 • Energy 2 • Finance 1 • Finance 2 • Manufacturing 1 • Manufacturing 2 Step0. Assume that correlation in the same indus- try isr 1; correlation in different industry isr 2 1>r 1> r 2>0 .

Step1. Construct the correlation matrix for the above 10 companies:

R=                                      1r 1 r2 r2 r2 r2 r2 r2 r2 r2 r1 1r 2 r2 r2 r2 r2 r2 r2 r2 r2 r2 1r 1 r2 r2 r2 r2 r2 r2 r2 r2 r1 1r 2 r2 r2 r2 r2 r2 r2 r2 r2 r2 1r 1 r2 r2 r2 r2 r2 r2 r2 r2 r1 1r 2 r2 r2 r2 r2 r2 r2 r2 r2 r2 1r 1 r2 r2 r2 r2 r2 r2 r2 r2 r1 1r 2 r2 r2 r2 r2 r2 r2 r2 r2 r2 1r 1 r2 r2 r2 r2 r2 r2 r2 r2 r1 1                                       wherer 1=correlation among companies in the same industry, andr 2=correlation among companies in different industries.Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 367 Step2. DecomposeRintoR=ADA T, whereDis a diagonal matrix of eigenvalues. A=                                      0 3162278−0 3133050 0 5087871−0 0495650−0 2012930 0 3536361 0 2052221−0 3286600−0 0235670 0 4735532 0 3162278−0 3133050 0 5087871−0 0495650−0 2012930−0 3536360−0 2052220 0 3286600 0 0235666−0 4735530 0 3162278 0 0889365−0 3255660−0 3869770−0 3692510−0 1130970 0 4541310 0 2868519 0 4324016 0 1082546 0 3162278 0 0889365−0 3255660−0 3869770−0 3692510 0 1130966−0 4541310−0 2868520−0 4324020−0 1082550 0 3162278−0 3172100−0 3348780 0 4310395 0 0379438−0 2648710−0 3850590−0 2201990 0 4229035 0 2328912 0 3162278−0 3172100−0 3348780 0 4310395 0 0379438 0 2648706 0 3850591 0 2201986−0 4229030−0 2328910 0 3162278 0 5415790 0 1516563 0 2873404−0 0335870 0 4825545−0 3056310 0 3666516 0 1948923 0 0362582 0 3162278 0 5415790 0 1516563 0 2873404−0 0335870−0 4825540 0 3056306−0 3666520−0 1948920−0 0362580 0 3162278 0 0000000 0 0000000−0 2818380 0 5661867 0 2431777 0 0998419−0 3560590 0 3092622−0 4565910 0 3162278 0 0000000 0 0000000−0 2818380 0 5661867−0 2431780−0 0998420 0 3560586−0 3092620 0 4565910                                       D=                                3 77 0 87 0 87 0 87 0 87 0 55 0 55 0 55 0 55 0 55                                 Step3. ConstructE=D 1/2 as a diagonal matrix with values as the square root of the corresponding eigen- values inD: E=                                    1 9416488000000000 00 932737900000000 000 93273790000000 0000 9327379000000 00000 932737900000 000000 74161980000 0000000 7416198 0 0 0 00000000 7416198 0 0 000000000 7416198 0 0000000000 7416198                                     Step4. Construct matrixBso thatB=A∗E:

B=                                      0 6140033−0 2223200 0 4745650−0 0462310−0 1877530 0 2622635 0 1521968−0 2437410−0 0174770 0 3511964 0 6140033−0 2223200 0 4745650−0 0462310−0 1877530−0 2622640−0 1521970 0 2437408 0 0174775−0 3511960 0 6140033 0 0829545−0 3036680−0 3609480−0 3444140−0 0838750 0 3367925 0 2127351 0 3206776 0 0802838 0 6140033 0 0829545−0 3036680−0 3609480−0 3444140 0 0838747−0 3367930−0 2127350−0 3206780−0 0802840 0 6140033−0 2587400−0 3123530 0 4020468 0 0353916−0 1964330−0 2855670−0 1633040 0 3136336 0 1727167 0 6140033−0 2587400−0 3123530 0 4020468 0 0353916 0 1964333 0 2855674 0 1633037−0 3136340−0 1727170 0 6140033 0 5051512 0 1414556 0 2680133−0 0313280 0 3578720−0 2266620 0 2719161 0 1445360 0 0268898 0 6140033 0 5051512 0 1414556 0 2680133−0 0313280−0 3578720 0 2266617−0 2719160−0 1445360−0 0268900 0 6140033 0 0000000 0 0000000−0 2628810 0 5281038 0 1803454 0 0740447−0 2640600 0 2293550−0 3386170 0 6140033 0 0000000 0 0000000−0 2628810 0 5281038−0 1803450−0 0740450 0 2640601−0 2293550 0 3386170                                       Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit Lines 368 Interfaces 35(5), pp. 353–369, © 2005 INFORMS Step5. Generate the random independent vec- torXfrom Normal 0 I with covariance=I(identity matrix). LetY=B∗X. Then,Yis a random sample that incorporates industry correlations (with covari- ance matrixR):

X=                                          0 23441 −0 49978 −0 17211 −0 07346 −0 62066 1 03902 0 54514 0 94261 0 89600 −0 73138                                           Y=                                          0 1814252 0 4750346 0 4812961 −0 747548 −0 064951 0 6530688 0 9206000 −0 130574 0 2674681 −0 596534                                           Acknowledgments Several people contributed to the success of this effort and deserve special recognition. We thank Andy Saperstein, chief operating ofﬁcer and ﬁrst vice president of Merrill Lynch’s ﬁnancial advisory center, and Allen Braithwaite, ﬁrst vice president of Merrill Lynch’s treasury, for their leadership and support throughout the project. We thank Bill Creager, director of marketing analytics, Gail Eisenkraft, ﬁrst vice president of marketing strategy, and Paula Polito, senior vice president of GPC marketing, for their ongo- ing support of our analytical work. We extend our sincere thanks to Raj Nigam, retired chief scientist and director of the Merrill Lynch management science department for his leadership, friendship, and inspiration through many years. We thank Nenad Marinovich, head of credit-risk ana- lytics at Merrill Lynch’s corporate risk-management group,for his help and contributions on the industry correla- tions. Last but not least, we thank the team in the Merrill Lynch analytics and management science department— Stuart Altschuler, Janet Chen, Mark Goldstein, Jukti Kalita, Gretchen Marsh-Ferino, Deepak Singh, Lonn Vreeland, and Zhaoping Wang—for their hard work and constant insis- tence on excellence. References Asarnow, Elliot, James Marker. 1995. Historical performance of the U.S. corporate loan market: 1988–1993.Commercial Lending Rev.

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Allen G. Braithwaite III, ﬁrst vice president of ML & Co. Treasury, 4 World Financial Center, New York, NY 10080, made the following comments in a written memo dated August 23, 2004: “The revolving credit liquidity risk management model, which was devel- oped and implemented in 2002, provided the ﬁrst sci- entiﬁc measurement of liquidity risk in the Bank’s portfolio. The model increased Bank Treasury’sDownloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.

Duffy et al.:Merrill Lynch Improves Liquidity Risk Management for Revolving Credit LinesInterfaces 35(5), pp. 353–369, © 2005 INFORMS 369 conﬁdence in measuring the liquidity required for the portfolio, which in turn resulted in freeing up approx- imately $4 billion of term liquidity. As management became comfortable with the model, the revolving line of credit portfolio increased substantially to about$13 billion. Over the last several years Management Science and Bank Treasury have collaborated on a number of innovative modeling projects, all of which are used regularly by Bank Treasury in measuring liquidity.”Downloaded from informs.org by [132.174.254.97] on 25 February 2017, at 11:18 . For personal use only, all rights reserved.