Measuring the interest rate risk of Belgium regulated savings deposits

thumbnail of fsr_2005_en_137_151 Original by K. Maes, T. Timmermans, 2005, 15 pages 

This summary note was Posted on

Saving deposits

  • Sight deposits can be withdrawn at any time and may be used as means of payments
  • Term deposits offer substantially higher market- consistent returns, but cannot be withdrawn until their defined contractual term expires.
  • Savings deposits are special, in the sense that they preserve a high degree of liquidity, while offering a relatively attractive rate of return.
  • In Belgium, savings deposits are also special because they are the subject of important regulation affecting their pricing, remuneration structure, and fiscal treatment.
  • Presence of the two embedded options
    • Depositors possess the right or option to withdraw all or a part of their deposited funds at any time.
    • The bank has the option to change the savings deposit rate in response to market rate changes


  • Savings deposits also account for a significant and increasing pro- portion of Belgian household assets : their share increased from 9.9 p.c. in December 1993 to 18.8 p.c. in September 2004.
  • Savings deposits have recently outstripped the combined total of bank bonds and all other deposits held by households.

Deposit rate dynamics

  • The spreads between long rates and savings deposit rates have been relatively stable, decreasing only slightly over time.
  • The decreased spreads between market and deposit rates may rflect a combination of structural changes in the market.
  • Smaller cross-subsidisation by savings deposits of other banking products,
  • Lower servicing costs of savings deposits thanks to advances in technology,
  • Changes in the competitive conditions.

Deposit balance dynamics

  • De-seasonalised savings deposit balances have grown
  • Growth has been relatively strong in the last 5 years
  • Deposit balances have some- times decreased in the past 1990-1994 and 2000-2002.
  • Deposit balance dynamics are driven by general market conditions.
  • Savings deposit balance growth rates are affected by depositors’ opportunity cost,
  • Savings deposit rates have been and still are rather sticky compared to market rates.
  • Approximate the opportunity cost as the difference between the 3m Treasury Certificate rate, net of withholding taxes, and the deposit rate.
  • Deposit rates move in the same direction as lagged market rates and typically in multiples of 1/8th percentage points.
  • Deposit rate dynamics may be further analysed following O’Brien (2000), who has estimated a partial adjustment model for U.S. retail deposit rates.
  • Deposit rate changes depend on whether deposit rates are above or below a possibly time-varying long-run equilibrium or target deposit rate

Measuring the interest rate risk of saving deposits

  • To measure the interest rate risk of savings deposits, two approaches can be adopted.
  • Banks’ profitability and net interest income at risk.
  • The term “core deposits” is sometimes used to reflect the fact that a substantial part of savings deposit balances is held by retail depositors who are not highly rate sensitive and are not expected to withdraw their balances over a short period of time.
  • Alternatively, the assessment can be based on the impact on banks’ solvency or market value of equity at risk.
  • Analyse the duration, i.e. market value sensitivity to interest rate changes, of savings deposits.
  • Simulate unexpected yield curve shocks on the market value of equity
  • Various models that are available to estimate the duration of savings deposits.
  • The shock tested is a 2 p.c. upward shift of the entire yield curve.
  • Extreme sensitivity to changes in market rates gives rise to a zero duration, whereas extreme insensitivity or sluggishness of deposit rates and balances gives rise to a much longer duration,
  • The risk weights are computed as proposed by the Basel Committee on Banking The risk weights are computed as proposed by the Basel Committee on Banking Supervision, i.e. as the approximate modified duration times the assumed interest rate shock (see BIS (2004)). The approximate modified duration calculation is based upon the midpoints of each time bucket, e.g. a time to maturity of 3.5 years is used

Static replication portfolio models

  • Calculate the return from investing the avail- able volume of deposits in a portfolio of fixed-income assets with various maturities such that a specific objective criterion is optimised
  • Constraint that the portfolio exactly replicates the dynamics of outstanding deposit balances over some historic sample period.
  • There is a clear monotonic relation between the impact of parallel yield curve shocks and the duration, with smaller duration resulting in a larger negative impact.
  • Maximise the risk-adjusted margin,
  • The duration of saving deposits is then estimated as the duration of the replicating portfolio, combining fixed-income assets of various maturities, that optimizes the criterion.
  • Internal model estimates of duration differ substantially across individual banks.
  • Most large Belgian banks rely on a particular variant of the static replicating portfolio model

Dynamic replication portfolio models

  • Some Belgian banks actually use or have been experimenting with more sophisticated modelling approaches, such as dynamic replicating portfolio models and net present value Monte Carlo simulation models.
  • The replicating portfolio approach basically boils down to an optimisation problem
  • All weights need to sum up to unity and short selling is often not allowed.
  • Banks, in practice, classify total deposits into interest-rate insensitive core deposits, volatile deposits, and remaining balances.
  • invested at a discretionary long horizon and volatile deposits at the interest rate risk free short horizon.
  • Static replicating portfolio models, maturing funds are always renewed at the same maturity and the replicating portfolio vector is assumed to be constant,
  • Differ through a focus on the valuation of deposit accounts, defining the value of the deposit liability as the discounted future cash flows that correspond to servicing outstanding balances.
  • Incorporate uncertainty in interest rate and balance dynamics by generating scenarios of their possible future outcomes.
  • Since the scenarios are based on current market circumstances, the resulting replicating portfolios are adjusted dynamically over time to the current situation.
  • Simulation is performed in 5 steps
    1. The dynamics of deposit rates and deposit balances are estimated as
    2. A large number of market rate paths, say 1000, are then simulated for the next, say, 30 years, from which 1000 simulated deposit rate and balances paths are then derived. The dynamics of economic rents depends on the dynamics of the spread between market and deposit rates, deposit balances, and servicing costs.
    3. The value of the saving deposit account, is then defined as the net present value of all future economic rents
    4. Steps two and three are repeated, but now based on the simulated market rate paths shocked
    5. the duration of the saving deposit account is then set equal to the change in the deposit liability value divided by the market interest rate.
  • There are two related modelling approaches to calculate the net present value of future economic rents,
    • Option Adjusted Spread (OAS)
    • Contingent claim or no-arbitrage approach.


  • The use of a longer time series may increase the risk of failing to detect changes in market or behavioural structure.
  • Model results are also quite sensitive to discretionary model parameter choices.
  • A reliable and robust measurement of the relationship between deposit balances and deposit rate dynamics is very difficult to obtain
  • While replicating portfolio (and alternative models) may be useful as risk management tools, the relatively large range of duration estimates that can be derived from these models may make supervisors reluctant to use a single model to make inferences about the interest rate risk of savings deposits.
  • The future is likely to be very different from the past specification of behavioural relationships
  • Sensitivity to discretionary model assumptions.
  • Moreover, it is unclear to what extent the duration estimated in normal times reflects savings deposits’ characteristics in stressful circumstances.
  • Portfolio models may fail to reflect the impact of stress events and are particularly vulnerable to model risk.
  • Monte Carlo and dynamic replicating portfolio models seem conceptually stronger and are able to capture uncertainty about future events, but more exposed to model risk


  • Rely heavily on discretionary model assumptions and the stability of the behavioural relations.
  • Favourable tax treatment and the liquidity services that regulated savings deposits
  • Account for the popularity of saving deposits in Belgium.
  • Interest rate risk management of non-maturity accounts remains an art as well as a science,
  • Complexities arise from the presence of two embedded options,
  • The withdrawal option and the deposit rate setting option, are clearly not independent of each other.