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1 Banknotes, seignorage, and liquidation risk

1 Banknotes, seignorage, and liquidation risk

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Central banks and public institutions as investors

currency will never wane – at least in the black-market transactions that
arguably account for a large fraction of aggregate currency demand – owing
to its distinctive advantages in allowing for unrecorded transactions. The
evolution of banknotes in circulation over the last years in both USD and
EUR, has not given any indication of a decreasing trend (more the contrary). Another indicator against the hypothesis of a forthcoming disappearance of the circulation of banknotes and coins in the case of the euro
area is a look at denominations in circulations. In fact, only 83 out of EUR
620 billion of currency in circulation was denominated in banknotes with a
nominal value of less than EUR 50 or in coins, i.e. the typical transaction
balances. More than 50 per cent of the value of currency in circulation was
in denominations above EUR 50, i.e. denominations one rarely is confronted with. In line with this observation, Fischer et al. (2004) conclude
that the various methods they apply all indicate rather low levels of transaction balances used within the euro area, namely of around 25–35 per cent
of total currency.
In case one would be able to establish a probability distribution for the
evolution of banknotes in circulation over a certain, say ten-year horizon –
how to integrate exactly the risk factor ‘volume of banknotes in circulation’
into a risk management model for central banks? Two main types of risks
may be distinguished in relation to banknotes. First, a decline of banknotes
would imply a decline of seignorage, even if the assets counterbalancing
banknotes would be perfectly liquid. This is the topic of Section 7. Second,
in the short term, the decline of banknotes creates liquidation and liquidity
risk. ‘Liquidation risk’ is the risk that assets need to be liquidated before
the end of the investment horizon. In such a case, the originally assumed
investment horizon would have been wrong, and accordingly the assumed
optimum asset allocation would actually not have been optimal. ‘Liquidity
risk’ is the risk that due to the need to undertake large rapid sales, prices
obtained are influenced in a non-favourable manner. For the issue considered here (reversal of trend growth in banknotes in circulation), liquidation risk could appear more important than liquidity risk. It should be
noted that it is not only the uncertainty about the demand for banknotes
which creates liquidation risk. Similar risk factors are: (i) for domestic
financial assets, the need to build up foreign reserves; (ii) for foreign
reserves assets, the need to liquidate those assets for foreign reserve interventions; (iii) the need to buy assets for some other policy reasons, such as
emergency liquidity assistance to banks. The case with uncertainty of nonmaturing liabilities has been modelled e.g. by Kalkbrener and Willing (2004),

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who propose a general quantitative framework for liquidity risk and interest
rate risk management for non-maturing liabilities, i.e. allowing to model
both an optimal liquidity and maturity structure of assets on the basis of the
stochastic factors (which includes interest rate risks) of liabilities. Overall, it
appears that banknotes are much more important in terms of risk factors as
putting seignorage at risk, than to create liquidation and liquidity risks.
6.2 Monetary policy interest rates
Another major risk factor to the long-term profitability and positive capital
of the central bank is that the currency falls into the deflationary trap, as did
the JPY in the 1990s, or as other currencies did e.g. in the 1930s. Monetary
policy rates need to be set by a central bank according to an objective –
normally to maintain price stability. To model this, it may be assumed that
there is a Wicksellian relationship between inflation tomorrow and inflation
today, i.e. inflation normally accelerates if interest rates on monetary policy
operations are below the sum of the real rate on capital and the current
inflation rate.10 This Wicksellian relationship is also the basis for the central bankers’ Angst from a deflationary spiral: if deflation ever reaches a
momentum to be larger than the real interest rate, then negative nominal
interest rates would be required to change this deflation again into price
stability or inflation. As negative nominal interest rates are however in
principle impossible, at least as long as banknotes in their current form
exist, deflation would accelerate more and more, and prices could never
stop falling again, eventually making a total monetary reform unavoidable.
While long-lasting deflations in which the central bank put nominal interest
rates to zero without this solving quickly the problem have indeed been
observed, a true deflationary spiral which ended in ever-accelerating price
decreases has not.
Modelling the deflation risk factor from a financial investment perspective requires understanding to the largest possible extent the factors
determining the setting of the policy rate by central banks, i.e. what the
macro model of the central bank looks like, and how the exogenous variables deemed relevant by the central bank will evolve and possibly exert
shocks pushing the system into deflation. The model in Section 7 provides
more detailed insights into how one may imagine a stylized relationship
between macroeconomic shocks, the monetary policy strategy of the central
10

See Woodford (2003) for a discussion of such Wicksellian inflation functions.

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bank, and the financial situation of the central bank. What should be
retained here is that on average, monetary policy rates will reflect the sum
of the real interest rate and the central bank’s inflation target. Real interest
rates fluctuate with the business cycle, and may be exposed to a certain
downward trend in an aging society (on this, see for instance Saarenheimo
(2005) who predicts as a result of ageing a possible decline of worldwide
real interest rates by 70 basis points, or possibly more in case of restrictive
changes in the pension system). For a credible central bank, average inflation rates should equal the inflation target (or benchmark inflation rate).
A higher inflation rate is in principle better for central bank income than
a lower inflation target. However, of course, the choice of the inflation
target should be dominated by monetary policy considerations. Moreover,
the amount of banknotes in circulation will depend on the expected
inflation rate, i.e. the central bank will face a Laffer curve in the demand for
banknotes (see e.g. Calvo and Leiderman 1992; Guitierrez and Vazquez
2004). Therefore, the income maximizing inflation rate will not be infinite.
For a proper modelling of the short-term interest rate and its impact on
the real wealth of the central bank (including correlation with other risk
factors), it will be relevant to also distinguish shocks to the real rate from
shocks to the inflation rate. This is an issue often neglected by investors.
6.3 Foreign exchange reserves and exchange rate changes
Foreign exchange rate policy is one of the traditional elements of central
bank policy. This typically implies the holding of foreign exchange reserves,
creating the risks of mark-to-market losses. ECB internal estimates show
that, at conventional confidence levels, around 95 per cent of the total VaR
of the ECB can be attributed to exchange rate risks (including gold). Also
independently of foreign exchange rate movements, holding foreign exchange
reserves is typically costly for central banks, in particular for countries which
have (i) a need to mop up excess liquidity in their domestic money market;
(ii) have higher domestic interest rates than the interest rate of the reserve
currency; (iii) of which the currency is subject to revaluation gains. While
this situation appears in contradiction with covered interest rate parity, it
has actually been relevant for a large number of development and transition
countries for a number of years. Rodrik (2006), for example, estimates the
income loss for these countries to have been on average around 1 per cent of
their GDP, whereby he also concludes that ‘this does not represent too steep
a price as an insurance premium against financial crises’. Interestingly the

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survey of Dalton and Dziobek (2005, 8) reveals that all of the substantial
central bank losses they detected during the 1990s, concerning Brazil, Chile,
the Czech Republic, Hungary, Korea and Thailand, reflected some foreign
reserves issue. In fact all of these reflected a mismatch between returns on
foreign reserves assets and higher costs of absorbing domestic liquidity
(reflecting both interest rate differentials and revaluation effects.). In
Schobert’s analysis,11 74 per cent of observed annual central bank losses
were due to FX issues.
6.4 The central bank as financial crisis manager
Financial crisis management measures often imply particular financial risk
taking by the central bank (see Chapter 11 for details). This should be
factored into an integrated long-term risk management of the central bank:
in bad tail events, the central bank may not only make losses with its
investments, but may also have to do costly crisis management operations,
implying possibly losses from two sides. As indicated by Schobert, only
3 per cent of annual central bank losses would have been driven clearly by
credit losses, of which those driven by emergency liquidity assistance
operations would be a subset. A typical problem in developing countries’
central banks are non-performing loans to banks in central bank balance
sheets which are not really originating from ELA, but from the granting of
credit to banks without following prudent central banking principles,
maybe upon request or order of the Government (see e.g. Dalton and
Dziobek 2005, 6). Although relevant for many central banks, in particular in
developing countries, the model in Section 7 does not include this risk.

7. The role of central bank capital – a simple model
Capital plays a key role in integrated risk management for any financial
institution, as it constitutes the buffer against total losses and thereby
protects against insolvency. The Basel accords document the importance
attached to bank capital from the supervisory perspective. This section
provides a short summary of a model of central bank capital by Bindseil,
Manzanares and Weller (2004a), in the following referred to as ‘BMW’. The
11

Schobert, F. 2007. ‘Risk management at central banks’, unpublished presentation given in a central banking course at
Deutsche Bundesbank.

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main purpose of BMW had been to show how central bank capital may
matter for the achievement of the central bank’s policy tasks. The mechanisms by which central bank capital can impact on a central bank’s ability
to achieve price stability were illustrated in this paper by a simple model in
which there is a kind of dichotomy between the level of capital and inflation
performance. The model is an appropriate starting point to derive the actual
reasons for the relevance of central bank capital in the most transparent
way. The starting point of the model specification is the following central
bank balance sheet.
Stylised balance sheet of a central bank
Assets

Liabilities

Monetary policy operations (‘M’)
Other financial assets (‘F’)

Banknotes (‘B’)
Capital (‘C’)

Banknotes are assumed to always appear on the liability side, while the
three other items can be a priori on any side of the balance sheet. For the
purpose of the model, a positive sign is given to monetary policy and other
financial assets when they appear on the asset side and a positive sign to
capital when it appears on the liability side. The following assumptions are
taken on each of these items:
 Monetary policy operations can be interpreted as the residual of the balance
sheet. This position is remunerated at iM per cent, the operational target
interest rate of the central bank. Assume that the central bank, when
setting, follows a kind of simplified Taylor rule of the type iM,t ¼ 4 þ 1.5
(pt À 1À2). According to this rule, the real rate of interest is 2 per cent and
the inflation target is also 2 per cent.12 An additional condition has also
been introduced in the Taylor rule, namely that in case it would imply
pushing expected inflation in the following year into negative values, the
rule is modified so as to imply an expected inflation of 0 per cent. It will
later be modelled that for profitability/capital reasons, i.e., reasons not
relating directly to its core task, the central bank may also deviate from
this interest rate setting rule.
 Other financial assets contain foreign exchange reserves including gold
but possibly also domestic financial assets clearly not relating to monetary
policy. Assume it is remunerated at iF per cent. The rate iF per cent may
12

See e.g. Woodford 2003 for a discussion of the properties of such policy rules.