style="font-size:15px;"> SifiBank makes an excellent case study for risk management since its far-flung businesses touch on every aspect of financial risk management that most banks would encounter. In fact, one could say that banks are in the business to take prudent risk. As will be seen shortly, banks that take zero risk are not going to be profitable enterprises. Similarly, banks taking excessive risk – that is, risk not well understood and outside the firm’s capabilities to price and manage that risk and its risk appetite – will eventually be doomed. That’s why the term prudent risk is critical to understanding the process of risk management.
Thinking of risk management as a process or system in itself is helpful since managing risk effectively entails establishing a feedback loop (Figure 1.1) in which risk tolerance is communicated across the organization; expectations are set in terms of how much risk is acceptable for businesses to take (usually expressed in terms of capital allocated to each line of business); there is ongoing measurement and reporting of risks, there are processes and controls for managing risk coming into the firm in the way of transactions, loans, and services; there are techniques and controls for mitigating risk on the books of the firm; and there are methods to adjust the level of risk on an ongoing basis consistent with the above process as well as market and environmental considerations.
Figure 1.1 Risk Management Feedback Loop
Unlike most products of nonfinancial companies, financial products are not physical in nature. Loans, deposits, and investment products for example provide customers with access to credit, enabling them to purchase physical products and services or compensate them for storing their financial assets with the institution. Risk management is an inextricable component of financial product development as a result. The features of financial products such as the term of the loan or deposit, the rate of interest, payment features, and eligibility criteria are effectively levers that the bank uses to manage the risk that the borrower defaults or the bank faces losses from interest rate risk exposure, among others. Consequently, effective risk management requires a deep understanding and appreciation for the business of the bank, the market, its competition, and the regulatory landscape it operates in as well as the structure and organizational dynamics of the firm itself.
FINANCIAL INTERMEDIATION AND PROFIT MAXIMIZATION
At its core, SifiBank, like other commercial banks, engages in profit-maximizing financial intermediation. Profit
(1.1)
where ri represents the rate on earning assets q for the ith product, and ii is the cost associated with the jth input x, either financial (e.g., deposits) or real (e.g., personnel).
Financial intermediation refers to the process by which banks take in a variety of liabilities such as deposits and debt and transform them into earning assets. Liabilities for banks are inputs into their production process that are used in creating loans, investments and services to bank customers.
Further, the bank is expected to maximize profit subject to technical conditions underlying a production function, P(q1… qn, x1, .. xm) = 0. In developing their strategic plans for the coming year, banks take into consideration a host of other information in setting their asset targets. These include such factors as relative peer profitability and other indicators of performance, and business structural issues such as product concentrations and competitive conditions, among others. Through the production function whereby the bank as a financial intermediary uses its financial inputs – including various forms of deposits including retail and wholesale sources as well as other funding sources – and nonfinancial inputs such as physical premises and personnel, the bank determines its level and combination of assets to produce, taking into account other external factors as described. As a result, the relationship between bank output and inputs could be described by the following first-order condition of the following simple constant elasticity of substitution (CES) production function2:
(1.2)
To illustrate the link between assets and deposits in this construct, assume the bank has a single asset denoted q in the model above that is produced using two types of deposits; x1 represents retail deposits and x2 describes brokered deposits.3 The relationship described by the CES production function shows that both inputs as factors of production define the level of assets for the firm. In equilibrium, the bank will select a target level of output q that maximizes the expected utility of profit formally described below. The input combinations of x1 and x2 are then optimized by their least cost combination in the profit function subject to any technical production constraint such as funding limitations. External factors driving target output for the bank such as peer performance or other metrics could be subsumed within the constant term C of the production function.
The profit model can be extended to include the production function as well as to introduce uncertainty (risk) into the decision making process.
(1.3)
where
(1.4)
where
(1.5)
(1.6)
The term
(1.7)
Setting the derivative of output q equal to zero yields:
(1.8)
Assuming that the bank utility function follows
Brokered deposits are a form of wholesale deposit that banks may use to augment their retail branch generated deposit base. They may be purchased in markets from brokers that buy and package these deposits from other institutions.
Lagrange multipliers are used in some types of constrained optimization problems where closed form solutions may be difficult to otherwise obtain.
