The Merrill Lynch Banking Group includes two U.S. domestic banks with combined assets of over $80 billion, which places it among the top 15 depository institutions in the United States. Merrill Lynch Bank USA (ML Bank USA) is our bank with assets in excess of $60 billion.

Liquidity and Revolving Credit Lines


Banks typically act as intermediaries, accepting deposits from some customers and using those deposits to fund loans to other clients and to make investments. ML Bank USA is no different. In our case, the Bank takes deposits through investment accounts of an affiliate's retail investors, and uses them to finance revolving credit lines to institutional clients.

Liquidity is the ability to meet all financial obligations when due. Liquidity risk is the potential inability to meet these obligations. The Merrill Lynch Banking Group seeks to assure liquidity at all times, across market cycles and through periods of financial stress. As an institution it takes a very conservative stance to managing liquidity risk.

Revolving credit lines give borrowers access to a specified amount of cash on demand for short-term funding needs. These credit lines function for corporations in much the same way credit cards or home equity lines of credit work for individuals. They establish a credit limit and allow the corporation to borrow, on demand, up to that limit. Revolving credit lines offered by banks are rarely a primary source of short-term borrowing, but serve mainly as backup to commercial paper, which is the cheapest source of short-term borrowing for corporations. Each credit line has an associated dollar amount, expiration date and renewal options. Once a credit line is in use, the borrower can choose to continue to use the line up to its expiration date or pay it off.

Merrill Lynch Management Science Group


The two primary divisions in Merrill Lynch's organization are Global Private Client (GPC) and Global Markets & Investment Banking (GMI). GPC is the retail brokerage division of Merrill Lynch, providing investment and other financial services to individual clients. Investment services are delivered to these clients through a sales force of about 14,000 financial advisors (FAs) in more than 500 offices around the world. Assets in GPC accounts totaled $1.4 trillion as of year-end 2004. GMI is one of the world's top global investment banks, providing institutional sales and trading, investment banking advisory and capital raising services to corporations, governments and institutions worldwide.

Merrill Lynch established its Management Science Group in 1986. The mission of the group is to support strategic decision-making in complex business situations through the use of quantitative modeling and analysis. The group provides analytical and business consulting using a broad set of operations research and management science techniques, including optimization, simulation and multivariate statistics.

The Management Science Group is comprised of 12 professionals. Being organizationally a part of GPC Marketing, the group's efforts are roughly evenly distributed between supporting Marketing and other GPC business units. Over the years we developed expertise in application areas including compensation analysis, pricing analysis, mutual fund portfolio optimization, quantifying the impact of business strategies, evaluating effectiveness of marketing efforts, and developing prospecting and cross-selling models. We successfully built up a strong reputation within Private Client, resulting in significant demand for our services.

Merrill Lynch and its Management Science Group have been recognized by INFORMS several times for their use of operations research. In 1997 Merrill Lynch received the INFORMS Prize for the effective integration, application and impact of management 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 Integrated Choice, a new product offering at Merrill Lynch, which gathered $83 billion of client assets during its first 18 months of introduction. Most recently, in 2004, we won the Wagner Prize for the liquidity modeling described here.

Timeline and Business Objectives


In 2000, ML Bank USA began to establish revolving credit lines for corporations that are clients of GMI. The business was expected to grow rapidly over the next several years. Initially the Bank developed its own model to assess liquidity risk. Consistent with its conservative and prudent approach to risk management, the Bank initially assumed a contingent draw rate of 50 percent, i.e., kept 50 cents of liquidity for each dollar of credit line commitments to meet potential draws in the contingent scenario. The key business question was: Could this be safely lowered without taking on significant risk, thereby freeing up additional liquidity?

As the credit line portfolio grew, the Bank soon recognized the need for a more comprehensive and rigorous modeling approach to assess liquidity risk, so it came to the Management Science Group in 2002 and asked for help in developing such a model. The Bank's Treasury Group already had a strong working relationship with Management Science through a series of joint projects focused on managing the liquidity risk associated with client deposits and withdrawals.

In the case of the revolving credit model, the Bank had several specific business objectives. It wanted to estimate expected usage rates of the credit portfolio over a five-year time horizon; to understand how usage would vary under stress; to identify potential sources of risk, such as concentrations of commitments by industry or credit rating; and to help support its long-term planning process.

A team was established to support the effort, including nine members from the Banking Group and Management Science. Members of the team from Management Science were Manos Hatzakis, Russ Labe, Bonnie Liao, Je Oh and Lihua Yang, while Tom Duffy, Wenyue Hsu, Sheldon Luo and Adeesh Setya participated from the Banking Group. The model was developed over a period of about four months, and the initial version was implemented in late 2002.

Model Description


To help ML Bank USA understand credit usage patterns in order to set adequate liquidity margin levels for its portfolio of revolving credit lines (revolvers), we built a Monte Carlo simulation that estimates aggregate monthly borrower usage. We selected the Monte Carlo framework as the most suitable for modeling the complexities of a revolver portfolio. Within the simulation, we embedded three OR/MS techniques that capture the stochastic dynamics driving the two types of uncertainty associated with the portfolio: timing and amount of credit usage by each borrower. The three techniques are a Markov process, the generation and use of correlated stochastic variables and expert systems.

A borrower's revolver usage is primarily a function of its credit rating. We modeled the month-to-month stochastic changes in borrowers' credit ratings as a Markov transition process. The underlying assumption, that the process is memory-less, is accepted industry-wide. A matrix of migration probabilities across Markovian states, i.e., credit ratings, can be constructed from historical data. In our model, we used more than two decades of credit history from the Moody's Corporation credit rating service database.

Credit rating migrations are correlated within and across industries. To capture credit migration correlations in our model, we generate and use correlated stochastic variables.

Revolver usage is affected by business decisions made about expiring credit lines by borrowers or the lender. We model such decisions in the course of the simulation as expert system rules, based on industry practice and managerial judgment. One set of rules models a borrower's decision to extend repayment over time. A second set of expert system rules deals with the lender's decision to renew an expiring credit line.

We estimate a borrower's credit usage through empirical probability distributions of whether the borrower will start using a previously unused relvolver, or continue using an already drawn-upon revolver; the amount of usage; and, for multiple-tranche revolvers, the sequence in which they will be used.

Ease of use and flexibility are paramount for a production model. An Excel-based Visual Basic Controller drives the revolver model. Through a simple interface, the Controller enables the user to input revolver data and set parameters, run the simulation and view outputs. The time horizon of the simulation is typically 60 months, in line with the Bank's five-year planning horizon. The Bank usually runs 10,000 replications, which take about two hours of elapsed time in today's PC speeds. We wrote the Monte Carlo simulation in Arena 7.01.

The Management Science Group supports and maintains the model in a continual process of improvement and enhancement. In collaboration with the Bank we refine model parameters, such as expert system rules and tranche usage sequence, by analyzing historical data of Merrill Lynch's revolver portfolio. Jointly with Moody's Corporation credit rating service, we update the credit rating migration matrix to make sure it incorporates the most recent rating migration history.

Additional details of this work will be published in the September/October 2005 issue of Interfaces, which will also include all of the finalists from the 2004 Wagner Prize competition.

Application, Benefits and Business Impact


The revolver model has been well received by both the Bank's internal and external constituents. The model provided, for the first time, a scientific and robust measurement of liquidity risk for commercial paper backstops, and thus greatly increased confidence in its usage at the Bank.

In terms of process benefits, the model is now run on a regular basis, and its results form an important part of the Bank's overall stress liquidity analysis, focusing on confidence levels at two standard deviations. The model is a valuable planning tool that helps us evaluate the impact of portfolio growth on future liquidity risk.

The model also generated a substantial financial impact. Before the model was implemented, the Bank's assumption of a 50 percent contingent draw rate was conservative and prudent. Simulation model results indicated that usage did not exceed 20 percent of outstanding commitments at a 97.5 percent confidence level. In addition, we evaluated high-stress sensitivity scenarios by running the model with adjusted inputs — such as increasing correlation within and across industries or increasing the draw probabilities. Even in these cases, usage rates were still far less than the assumed 50 percent of outstanding commitments. The difference between a 20 percent and 50 percent usage rate, applied to a portfolio of $14 billion, translates into freed up liquidity of $4 billion. These assets can now be allocated to more profitable uses such as loans, instead of being kept in low-yielding cash equivalents. Furthermore, since the model was implemented, the Bank grew its portfolio of commitments from $8 billion and 80 companies to more than $14 billion and about 200 companies.



Russ Labe is director of the Analytics and Management Science Group at Merrill Lynch, where he has practiced OR/MS for the last 18 years. Manos Hatzakis is vice president of Management Science at Merrill Lynch.

Editor's Note: A full version of this Wagner Prize-winning application is scheduled for publication in Interfaces, Vol. 35, No. 5, September-October 2005.

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