Based on the joint agency policy statement issued by federal bank regulators in August, which proposed a framework for measuring interest rate risk and assessing capital adequacy, valuation of nonmaturity deposits continues to present significant difficulty.

This concern is important for two reasons.

First, the foundation for this proposed risk measurement framework is "the exposure to a bank's underlying economic value from movements in market interest rates," that is, market value of portfolio equity. Much of this underlying economic value is based on the value of nonmaturity deposits, which is highly dependent on market rate movements.

Interest rates on these deposits are often a complex function of open market interest rates. And the level of deposit balances in aggregate often moves in conjunction with open market rates.

Because these deposits have no specific maturity, individual depositors can freely add or subtract balances as they wish, and they often do so based on alternative market rate returns.

Second, as the regulators explicitly note, the treatment of nonmaturity deposits will be, for many banks, the "single most important assumption" in measuring their exposure to interest rate movement.

Although the regulators present the banking community with some supervisory guidelines, they continue to rely on the banks' internal modeling systems to determine the value and interest rate sensitivity of these liabilities. This presents all bankers with the difficult task of accurately calculating the mark-to-market value of nonmaturity deposits, as well as developing effective hedging strategies to protect this value from market rate movements.

Measuring the value of deposits depends primarily on the present value of all future cash flows associated with these deposits. Because total cash flow is the basic building block for valuing nonmaturity deposits, the net increase or decrease in deposit balances must be included in determining deposit cash flows.

For securities with a fixed maturity date, cash flow from principal stems from a predetermined payment schedule associated with that security. In the case of the nonmaturity deposit, however, the security is a perpetual one, and principal is never "returned." Rather, changes in deposit balances are simply another source of cash flow.

The fact that deposit balances move when open market interest rates move is a critical determinant of deposit value that is often overlooked.

Consider a deposit whose interest rate is constant at 2%. Traditionally, bankers would calculate the present-value cost of this deposit in one of two ways: by assuming the liquidation value of the deposit is its par value or by valuing the deposit as a perpetual bond with a 2% coupon.

The first assumption leads one to the conclusion that, because the value of deposits won't change when rates change, nonmaturity deposits should only be invested in very short-term assets where the market value doesn't change when rates change.

The second assumption leads one to the opposite conclusion: The assumed perpetual nature of the deposit indicates that the right investment for zero interest rate risk is a security with a long maturity and a fixed rate.

Since these two conclusions are at odds with one another, a more realistic approach is needed.

Here is an outline to an approach that offers more realism. First, historical data provide a useful benchmark for specifying how responsive management will be in moving nonmaturity deposit rates as market rates rise and fall.

Modifying historical behavior with good judgment about the future, management specifies the links between open market rates - for example, Libor, the London interbank offered rate - and nonmaturity deposit rates.

Second, historical analysis will show the degree to which deposit balances have either increased (in response to the greater "money supply" that comes with inflation) or decreased (because of disintermediation) when open market rates have risen in the past.

Since the competitive environment each bank faces is different, deposit balance behavior of each will be different. Once this response is known for a given deposit category, our approach produces a mark-to-market valuation and interest rate sensitivity that reflects movements in nonmaturity rates and balances.

At the heart of this valuation approach is the recognition that nonmaturity deposits are expensive to collect. Our approach takes noninterest expense into account in measuring the present-value cost and rate sensitivity of nonmaturity deposits.

The present-value calculation is done using recent advances in the arbitrage-free pricing of interest rate derivatives. This process was illustrated in recent work for a major U.S. regional bank.

In recent years, nonmaturity deposit rates at the bank averaged about half the three-month Libor, and the adjustment of deposit rates was very slow in response to moves in open market rates. Looking only at rate and balance movements would lead one to the misleading conclusion that deposits had a present-value cost of only about half their book or par value.

In reality, most auctions of deposit franchises by the Resolution Trust Corp. produced premiums of 2% to 20% of the amount of deposits, indicating that the present-value cost of deposits auctioned were in the range of 80% to 98% of par value.

The difference is due to the high noninterest expense of collecting nonmaturity deposits. This expense changes with interest rates as bankers spend more on marketing and technology to attract nonmaturity deposits when the rate environment makes them attractive.

In the regional bank's case, we used historical market values for the bank (figured as stock price times number of shares outstanding) to calculate the implied present-value cost of nonmaturity deposits quarterly over three years.

We calculated the value of assets and subtracted the cost of all other liabilities and the market value of common stock to get the implied deposit values.

The implied market values of nonmaturity deposits ranged between 93% and 103% of the book value of deposits. The present-value cost of deposits was and should be above par in a low interest rate environment when bankers face an effective "floor" on both the noninterest expense of collecting deposits and on the interest rate paid on those deposits.

We then adjusted our model to fit these implied deposit values. The most important adjustment was the estimated noninterest costs of collecting nonmaturity deposits.

Having firmly grounded the model in reality, we could then do detailed stress testing and interest rate risk analysis on a mark-to-market basis. Of course, if we believed the implied market value of deposits historically was incorrect, we could have overridden those values with values we felt were more appropriate and fit the model to those overridden values for stress-testing purposes.

This approach takes into account realistic movements in nonmaturity deposits and balances, as well as the impact of noninterest expense on deposit values. The result is a practical and realistic valuation of deposits that leads to accurate interest rate risk analysis, fully validated by back-testing on true movements in bank market values.

This averts the need for bankers to base risk management programs on arbitrary assumptions about their most important liabilities.

Mr. Jarrow is a professor at Cornell University's Johnson Graduate School of Management and managing director of research at Kamakura Corp., a risk management company based in Chigasaki, Japan. Mr. Levin, based in New York, is Kamakura's director of U.S. operations.

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