Building a Replicating Portfolio for Bank Deposits
Summary
The document explains a replicating portfolio approach for modelling bank deposits, particularly non-maturing deposits whose interest rates and withdrawal behavior do not match a fixed contractual maturity. It describes allocating the deposit balance across maturity buckets, then choosing portfolio weights by optimizing a criterion such as a regression that relates market rates to deposit interest income, excluding margin.
The instruments can be bonds or similar assets with periodic or maturity payments. As tranches mature, they are reinvested at prevailing rates; a suitable portfolio aims to track the deposit’s interest income. This representation can support balance-sheet risk measures, including repricing gaps and BPV or DV01, and inform hedging. The exchange gives a conceptual outline rather than a worked allocation: it does not specify the optimization objective, instruments, calibration data, or evidence that the replication will be accurate. Results depend on those choices and on how deposit behavior is modelled.
Key ideas
- Portfolio weights can be estimated by optimizing a criterion that links market rates to deposit interest income.
- A replicating portfolio may use bonds or similar instruments with selected maturities and payment schedules.
- Matured tranches are reinvested at prevailing market rates.
- A well-calibrated portfolio approximates deposit interest income and provides a repricing profile for risk measurement and hedging.
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Full text
# Modelling Bank deposit with replicating portfolio
# Modelling Bank deposit with replicating portfolio
I am trying to understand how deposits in bank are modelled, and one such modelling approach is replicating portfolio approach as provided in http://www.diva-portal.org/smash/get/diva2:1208749/FULLTEXT01.pdf
Below is the excerpt on how to construct a replicating portfolio
However I failed to understand how exactly Author wants to build the replicating portfolio. Let say I have a deposit amount $N_t$ at time $t$. And as a process of building replicating portfolio, I consider $2$ time buckets i.e. $6M, 12M$, allocation of total deposit amount into these $2$ buckets are $N_{1,t}, N_{2,t}, \left(N_{1,t} + N_{2,t} = N_t\right)$. And 1st time bucket consists of $6$ instruments with $1M$ maturities and similarly second bucket consist of $12$ instruments with $1M$ maturities. Therefore there are $18$ such instruments.
I failed to understand,
- How exactly the principal amounts $N_{1,t}, N_{2,t}$ are allocated into those $18$ instruments?
- What those $18$ instrument each with $1M$ maturities are?
- How exactly they are mimicking my original deposit?
Any insight on above pointers will be very helpful.
## Answer by emot (score 1)
https://quant.stackexchange.com/a/69446
> How exactly the principal amounts $N_{1,t}, N_{2,t}$ are allocated into those $18$ instruments?
Weights are found by optimizing some criterion (there are a few) which is described in chapters 2.2.1 in the paper you mention. Basically you run linear regression and find the weights of market rates that explain your NMD interest income without margin.
> What those $18$ instrument each with $1M$ maturities are?
They are bonds like instruments paying coupon at maturity or at some time interval. You choose what you want them to be.
> How exactly they are mimicking my original deposit?
As you move forward in time, tranches mature and are reinvested at new prevailing market rates. If your replicating portfolio is correctly set-up then interest income on it should be close to your factual portfolio. This helps in balance sheet management i.e. you know repricing periods of NMD therefore you know how to represent those principal amounts in risk measures such as repricing gap or BPV/DV01 and you can easily hedge those risks.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.