Abstract
A bank provides a so-called maturity transformation
service: it gathers liquidity from its customers' demand deposits and
trades this amount on the financial market, particularly to issue loans to
individuals, to corporates or to other financial institutions. This unique role
of financial middleman exposes the bank to a major risk, known as liquidity
risk : indeed, it invests in long-term financial assets the liquidity held
on «non-maturity» deposits, which have no stated maturity and where
individual depositors have the right to add or substract balances without
restriction. Therefore, an unexpected and massive withdrawal can result in a
sudden mismatch between assets and liabilities of the retail bank. In fact, the
latter becomes incapable of raising enough liquidity and is forced to borrow on
the money market and /or to sell part of its long-term financial assets in
order to face its customers' demand. If the market conditions are quite poor at
this very moment, with very high interest rates, the institution can
potentially carry a significant loss in the event of such a scenario.
In order to minimize its liquidity risk exposure, it has to
invest in short-term assets an important enough proportion of its demand
deposit liability. Nevertheless, it is more interesting to trade long-terme
assets since they generally offer higher return rates and enable the bank to
smooth its margin over time. Thus, the bank has to reach a relevant compromise
between the two kinds of assets. It has to define its risk-appetite internal
policy that will drive its investment strategies on the financial markets. This
management is closely dependent on the statistical models used for predicting
both the interest rates and the demand deposit liability : it is known as
Asset-Liability Management (ALM). It requires a frequent analysis of
assets and liabilities and of their probable evolution. Within this context,
the estimation of both future liquidity needs and excess is of the utmost
importance.
This paper explores the subject of asset-liability management
for a retail bank by proposing first a theoretical evolution model, and then a
hedging, of the demand deposit liability of the financial institution.
The first part of the study consists in proposing scenarios
for the future evolution of the «non-maturity» deposit liability. The
latter is defined as the total amount held by customers on their demand
deposits.
The existing literature on the subject we have read only
proposed macroecomic-oriented models, which appeared to be irrelevant from our
point of view. Indeed, we believe that the stochastic evolution of the deposit
liability is a complex process driven by various effects, ranging from economic
ones (the Gross Domestic Product, the inflation rate) to demographical ones
(the age structure of the customer base) or behavioral ones (the attrition
rate). None of the papers we have consulted wak taking these different aspects
into account.
Therefore, we have built a far more accurate
microeconomic-oriented theoretical framework. This stochastic model relies on
an apportionment, that is to say a breakdown, of the customer base both by
strata (on a financial criterium) and by age and reproduces the random moves on
individuals' demand deposits while integrating various exogenous factors such
as inflation or mortality rates. Then we have implemented this innovative
mathematical model on computer. The purpose of the conducted simulations was to
analyze both the relevance of the results implied by our model and their
sensibility to the different parameters.
We have notably proved that the underlying model used for
inflation strongly influences the demand deposit dispersion: a random and more
volatile inflation broadens the confidence intervals for the value of the
demand deposit at a set date in the future.
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The degree of mobility of customers, which characterizes their
propensity to move easily from one financial state to another and to leave the
bank, largely conditions the volatility of the deposit balance. This means that
the more mobile the customers are, the more our predictive power on the
evolution of the demand deposit liability is deteriorating. Similarly, the
bank-leaving rate used to calibrate the model significantly modifies the
duration of demand deposit liability in the situation where the bank stops
issuing accounts.
The bank's customer base today's structure is the major driver
of the growth of its demand deposit balance in the short and in the mid term.
We have emphasized the fact, that within the framework of our model, the ageing
of the baby-boom generation is likely to cause in the near future an overgrowth
of the demand deposit balance compared to what we could expect first, given
that elderly people generally hold more liquidity on their accounts. Besides,
we have been able to prove that a bank whose customers are quite young
(typically the case of recently-appeared online banks) will see the growth of
its demand deposit balance overperform because of the ageing of its customers
and the increase in the number of them. On the contrary, an elderly customer
base can result in a stagnation or even a decrease in the demand deposit
liability in the short and in the mid term, due to the loss of the wealthiest
customers in the near future.
The second part of the study has aimed at analyzing the
performance of different investment strategies. The stake was to modelize the
compromise to reach (between investing in short-term and in long-term financial
assets) that raises while trying to ensure both a smooth and sustainable margin
and a low liquidity risk exposure. To achieve this goal, we have considered a
simple investment strategy for the retail bank, that consists in trading a set
and constant proportion of the demand deposit liability on short-term assets
and to invest the remaining on five-year maturity state bonds. Thanks to the
Hull and White classical financial model on market rates, we have generated
future evolution scenarios for the term structure of the rate curve. Each of
these simulations has provided a possible trajectory for the bonds prices and
the returns of the assets the bank can buy. By coupling this implementation
with the one on the stochastic evolution of the demand deposit balance built in
the first part, we have simulated the net margin the bank perceives over a
given period of time. The net margin is defined as the remuneration the bank
gets at each date from its past investments, that is to say the interest rate
cash-flows following its past trades. We have implemented this procedure for
different investment strategies, each one matching a specific allocation in the
demand deposit balance investment between short-term and long-term assets.
What's more, in order to analyze the robustness of the different strategies, we
have generated a stress test consisting in both a sudden and massive attrition
and a dramatic increase in market rates.
We have emphasized the fact that the more the retail bank
invests on long-term state bonds, the more it reduces the volatility of its net
margin but the more it is exposed to an important liquidity risk too : thus,
under the stress test we have simulated, the financial institution is all the
more exposed to a major loss since it has massively invested in long-term
securities. We were then able to plot graphs that give a visual illustration to
the compromise between smooth remuneration and liquidity risk : the optimality
of the investment is seen in the light of a margin volatility minimization
program with condition on the loss incurred under the stress test. This
optimality is then to be determined by each bank in regard of the risk-appetite
policy it follows. However, we have been able to establish that the age
structure of the retail bank's customer base impacts its investment choice.
Thus, for a given margin volatility (matching a specific allocation between
short and long-term investments), a bank whose customers are particularly young
(resp. elderly) is exposed to a lower (resp. higher) liquidity risk under the
simulated stress test. The reason for this result is the significant
differential in the growth of the deposit balance of these banks. As a matter
of fact, within
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our model framework, under the margin volatility minimization
program with condition on the loss incurred under the stress test, the retail
bank invests an all the more important part of its demand deposit liability in
long-term securities since its customers are young.
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