KRM-dc

Kamakura Risk Manager: Deposits and Charge Cards

Non-Maturity Deposits & Credit Card Loans

A substantial portion of the liabilities of major banks consists of non-maturity deposits. Similarly, credit card loans can be a significant part of a typical bank’s assets. Common characteristics among all such accounts include:

• No specific maturity
• Individual account holders can add or subtract balances as they wish
• The interest rate on these accounts is usually, but not always, a function of open market interest rates
• The balances in aggregate often move in response to changes in open market interest rates

With the strong trend in mark-to-market based risk management in banking, bankers face the difficult task of calculating the market value for non-maturity deposits and credit card loans.

As federal regulators have noted (PDF available: National Credit Union Administrations: Evaluation of Credit Union Non-Maturity Deposits), the treatment of non-maturity deposits will be, for many banks, the single most important assumption in measuring their exposure to interest rate movement. The regulators continue to rely on the bank’s internal modeling systems to determine the value and interest rate sensitivity of such accounts. This presents all bankers with the difficult task of accurately calculating the market value of deposits and credit card loans, as well as developing effective hedging strategies to protect this value against market rate movements.

Similarly, with the continued consolidation trend in the banking industry, accurate valuation of demand deposits, in particular, becomes critical in determining the value of an institution or a single branch. Acquiring and/or target banks will need to measure the deposit franchise value based on the unique characteristics of an institutions deposit portfolio.

The Proper Cash Flows

In the valuation of any security, total cash flow is the basic building block of valuation. For most securities, the maturity date is fixed and cash flow from principal stems from a pre-determined payment schedule associated with that security.

In the case of non-maturity deposits and credit card loans, however, the security is perpetual and aggregate principal is never returned in totality. Instead, changes in balances are simply another source or use of cash flow.

Hence, a crucial component in valuing non-maturity deposits and credit card loans is to isolate the total cash flows from these franchises. Total cash flow in a given time period for such accounts includes:

• Interest paid
• Non-interest expense of servicing
• Non-interest revenue
• Net change in balances
• Losses (credit cards only)

The Kamakura Approach

We have implemented an approach first proposed by Robert Jarrow and Donald van Deventer (to download these papers, please visit our free research signup page):

• Tibori Janosi, Robert Jarrow and Fedinando Zullo, “An Empirical Analysis of the Jarrow van Deventer Model for Valuing Non-Maturity Demand Deposits,” The Journal of Derivatives, (Fall 1999).
• Robert Jarrow and Donald van Deventer, "Power Swaps: Disease or Cure?," Risk Magazine, 9 (2), (February 1996). PDF
• Robert Jarrow and Donald van Deventer, “The Arbitrage-Free Valuation and Hedging of Demand Deposits and Credit Card Loans," Journal of Banking and Finance, 22 (3), (March 1998)
• Donald R. van Deventer and Kenji Imai, Financial Risk Analytics: "A Term Structure Model Approach for Banking, Insurance and Investment Management," Irwin Professional, 1997, Chapter 15, pp. 283-305.
• Three other papers are very consistent with the approach that Kamakura has taken in KRM-dc:
• D. Hutchinson and G. Pennachi, “Measuring Rents and Interest Risk in Imperfect Financial Markets: The Case of Retail Bank Deposits,” Journal of Financial and Quantitative Analysis, (1996), 399-417.
• James M. O’Brien, “Estimating the Value and Interest Rate Risk of Interest-Bearing Transactions Deposits,” Board of Governors, Federal Reserve System, November 2000,
• National Credit Union Administration, "Evaluation of Credit Union Non-Maturity Deposits" 
• The NCUA paper is a very important survey of various models and compares KRM-dc with products of other vendors.

The Jarrow-van Deventer approach relies on a no-arbitrage argument:

• Bankers constantly compare the cost of non-maturity deposits to other sources of funds. The present value of the non-maturity deposit is calculated by reference to these alternative sources of funds. The present value of the non-maturity deposit is the cost of replicating the cash flows of the deposit franchise from other funding sources.
• Similarly, bankers constantly compare the return on credit card loans to returns on alternative investments. The present value of the credit card loan is calculated by reference to these alternative sources of funding. The present value of the credit card loan is the return on replicating the cash flows of the credit card franchise from other investments.

This approach takes into account realistic movements in non-maturity deposit and credit card loan balances, as well as the impact of non-interest expense on the respective values. The result is a practical and realistic valuation that leads to accurate interest rate risk analysis.

Defining Balances and Rates

Jarrow and van Deventer [1998] assume balances to:

• Experience a decay rate for existing accounts
• Grow with an inflow of new accounts
• Grow at varying rates in response to changes in the market rates

Product rates are assumed to be sensitive to:

• The level of rates in previous periods
• The level of market rates in the current and past periods

Credit Card Losses

Credit card rates are decomposed into:

• Rates received
• Default rates

Both factors are assumed to be sensitive to the level of product and market rates in the current and past periods. The default rates can be further segregated into pools of different credit risks.

Term Structure Evolution

Jarrow and van Deventer [1998] use a one-factor Heath-Jarrow-Morton term structure model with:

• Deterministic volatilities
• Mean reversion of the spot rate to a long-run spot rate

Valuation Technique

Using no arbitrage and complete markets, Jarrow and van Deventer [1998] compute the net present value of demand deposits as the present value of investing the deposit balances at the market rate while incurring interest and non-interest expenses.

Given the stochastic evolution of the term structure of interest rates, demand deposit balances, and rates paid, the demand deposit valuation expression can be derived in closed form.

Jarrow and van Deventer [1996] show that a similar approach can be applied for the valuation of credit card loans. The portfolio value would be a function of the interest income received, the funding cost, non-interest expenses, and values for the separate pools of credit risk.

Kamakura Risk Manager-dc; What does it offer?

Kamakura Corporation has developed a stand-alone module that incorporates state-of-the-art analytics from Jarrow and van Deventer into an intuitive, simple to use module: Kamakura Risk Manager-dc (KRM-dc).

KRM-dc can be used with your existing analytical tools to enhance your analyses and improve your ability to properly manage the bank’s balance sheet.

KRM-dc uses many of the analytical capabilities common among all Kamakura Risk Manager modules including:

• Seven yield curve smoothing techniques
• Five term structure models
• Term structure parameter fitting functions
• Delta hedge calculations
• Various types of sensitivity analysis

KRM-dc allows you to forgo typical subjective analysis required with traditional core-volatile studies of non-maturity deposits and credit card loans. Using historical data, KRM-dc automatically calculates:

• Regression equations for balances and rates
• Value, delta, duration, and convexity
• Delta hedges

Regression Analysis

The data inputs for KRM-dc include:

• Historical portfolio balances
• Historical product rates
• Historical market rates

Using this information, KRM-dc will automatically derive the appropriate regression equations that best fit the observed historical patterns in balances and rates:

Term Structure Model

To properly define the evolution of market rates, product rates, and portfolio balances, you will use KRM-dc to select a term structure model and derive the proper parameters.

KRM-dc provides you with three distinct ways to derive the proper term structure parameter values for your analysis:

• Values implied in the current yield curve
• Values based on historical yield curves
• Values implied in observed option prices
• All these assumptions are captured in one comprehensive screen.

Valuation, Hedge, and Sensitivity

Using the closed-form solution pioneered by Robert Jarrow and Donald van Deventer, KRM-dc will:

• Value any non-maturity deposit or credit card loan portfolio
• Calculate the delta hedges using single maturity instruments
• Perform sensitivity analyses
• Real Time Web Video and Demo

For a real time web video and demo, please contact sales@kamakuraco.com.

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