1. A SUGGESTED TREATMENT OF MARKET LIQUIDITY RISK
Chris Chan, 2013
Introduction
This is a review of the options available for incorporating market liquidity risk into a market risk
framework. Liquidity risk comprises of two key aspects - funding liquidity and market liquidity.
Funding liquidity is defined as "the risk that the firm will not be able to meet efficiently both
expected and unexpected current and future cashflows and collateral needs without affecting either
daily operations or the financial condition of the firm". Market liquidity risk, meanwhile, is described
as "the risk that a firm cannot easily offset or eliminate a position at the market price because of
inadequate market depth or market disruption". Funding liquidity risk will not be addressed in this
paper.
Market liquidity risk is attributed to both market-driven external factors (exogenous liquidity risk)
and internal portfolio characteristics; eg. position size, counterparties, etc (endogenous liquidity
risk). Market liquidity risk does not display positive homogeneity (ie. future price movements are not
always correlated to last quoted or traded price) so it is particularly difficult to model within the
market risk framework. In certain circumstances, endogenous liquidity risk may even result in
exogenous liquidity risk. For example, if the portfolio has an extremely large exposure (endogenous),
the act of disposing the exposure in the market will cause prices to change significantly and bid-ask
spreads to widen (exogenous).
Purpose of this Paper
The purpose of this paper is to highlight the widely-accepted market practices of incorporating
market liquidity alongside both current and potential regulatory treatment. This paper also seeks to
propose an appropriate methodology to account for market liquidity risk under normal market
conditions and to a lesser extent will also address liquidity risk in stressed scenarios (tail risk).
Background
Certain Value-at-Risk (“VaR”) frameworks use the mid-point of bid-ask spreads to calculate price risk.
As such, there is an assumption that a position can be liquidated at the mid-rate and hence ignores
the liquidity aspect, as implied from any bid-ask spread (exogenous liquidity risk). Additionally, we
are also ignoring lot size or market size considerations. To mitigate this, one might choose to adopt
various holding periods according to the perceived liquidity of a broad asset-type. For example, FX
products are assumed to have a 1-day holding period (to reflect its highly-liquid status in the market)
while certain private debt securities in the Fixed Income book may assume a 90-days holding period
to reflect its relatively illiquid status in the market. However, one of the disadvantages of assuming
differing holding period across product types and asset classes is the inability to calculate a
groupwide diversified VaR – this is assuming that a diversified risk measure is required, which is not
always the case. A groupwide diversified VaR is the current preferred method for market risk
management because it gives risk controllers and risk management a single number, which depicts
roughly the level of risk taken by the bank against approved (diversified) risk appetite levels.

2. The management of endogenous liquidity risk is via auxiliary controls such as concentration limits,
PV01 limits by tenors and currencies and country exposure limits, amongst others.
Overall Research and Findings
Overall findings are that most banks do not have any comprehensive liquidity risk strategy.
Particularly, there isn’t a methodology that addresses both exogenous and endogenous liquidity
risks concurrently. Lead regulators are also just beginning to investigate this issue, led by the recent
consultative document on “Fundamental review of the trading book” issued in May 2012 by Basel
Committee on Banking Supervision. There is also no conclusive treatment being proposed by BCBS
as yet, and is not expected to be one for the next 2 years.
The methodologies of various international financial institutions, lead regulators and various
literature materials were broadly investigated. It is unlikely that we get detailed information so this
is a general review based on available information.
Liquidity Horizons
A British bank uses a simple 10-day liquidity horizon, the same as for 10-day VaR and this is an
accepted practice by the Financial Services Authority UK. This may be because they trade mostly in
highly liquid assets. Utilising liquidity horizons is also one of the major recommendations in the
recent BCBS paper although it is note-worthy to mention that BCBS is also recommending Expected
Shortfall* (ES) to replace VaR (ES is VaR extended to incorporate tail risk).
Other regional regulators such as Bank of Thailand, Bangko Sentral Philippines and Australian
Prudential Regulation Authority (APRA) also recommend the usage of 10-day VaR to account for
market liquidity risk. This is by far the most common approach and widely accepted in the market, at
least for the moment.
Pros
Relatively practical to implement (10-day shifts are generally applied in any case)
No distribution assumptions
Cons
Different asset classes actually should have different liquidity horizons based on historical analysis
Does not address endogenous liquidity risk
* This new Expected Shortfall (ES) measure is not the same as Expected Shortfall as currently defined
by several risk vendors – their ES is the average of the largest tail P/L vectors outside the HVaR
quantile; ie. if HVaR is 99% out of 500 vectors, then current ES = (PL(496) + PL(497) + PL(498) + PL(499) +
PL(500)) / 5
Liquidity Stress Scenarios
A bank in Germany has taken the stressed scenarios approach on expected P/Ls, which has been
approved by the BaFin. Stress scenarios are applied for percentage haircuts (probably depending on
credit rating and exposure size) and used to stress valuations, based on historical performance data.
Pros
Better ability to include exogenous and endogenous risk

3. Simple to apply
Cons
Does not address market liquidity risk under normal conditions
Requires adequate market data
Complex calibration may be required, especially if there is insufficient market data
Applying 99th
Percentile Spreads to 99th
Percentile VaR
A Wharton paper from Bangia, Diebold, Schuermann and Stroughair proposed a method of
incorporating exogenous risk by adding the 99th
percentile of the observed movements of the bid-
ask spreads into the 99th
percentile of the movements of the underlying. This assumes both of these
1% tail events are perfectly correlated (which is quite conservative).
A variant based on bid-ask spreads is to add the worst observed bid-ask spread to the worst mid-
price. Another variant by Ernst, Stange & Kaserer uses non-normal distributions (based on Cornish-
Fisher approximation) for prices and spreads which can then account for skewness and kurtosis.
Pros
Independent method to incorporate exogenous risk
Relatively simple to apply
Cons
Works best with parametric VaR (but can be adapted for use with historical VaR)
Requires adequate market data for spreads and prices
Does not address endogenous risk adequately
Models Based on Transactions and Trade Volumes
Berkowitz determines liquidity price impact from a regression of past trades, while taking into
account the impact of other risk factors, such fluctuations of interest rates, FX rates and volatilities.
This approach tends to deliver rather “noisy” measures but may be of value where only transacted
price data is available (ie. without traded volumes). Another paper by Cosandrey proposed a
framework to estimate price impact from total market traded volume. The assumption is that a
known number of trades are done to generate the market traded volume and liquidating more than
the daily volume will have an impact on the net return either due to the injection of more trades, or
a number of trades being larger than the normal average trade size – basically an assessment of a
market’s ability to absorb trades that exceed the bounds of normal daily market volumes.
Pros
Data in available from the markets themselves
Relatively simple to derive exogenous risk
Cons
Requires adequate market data for spreads and prices
Endogenous risk not adequately addressed (based on simplistic assumptions)
Liquidity Reserves

4. A major Asian bank employs a periodic analysis of the trading portfolio, separate from daily VaR
calculation, to assess the level of exogenous liquidity risk that the bank faces. The impact is
calculated and reserves are held against potential losses.
Pros
Separate VaR need not be calculated and managed
Cons
Reserves need to be set up, which impacts the bank’s financials
Requires adequate market data
Complex calibration may be required, especially if there is insufficient market and trading data
Proposed Methodology
Any methodology that is proposed has to meet the following guiding principles:
1) Widely-accepted practice by both market and regulator
2) Ease of implementation and ease of understanding as BCBS is still in the midst of confirming
the approach
3) Applicability to the client’s portfolio
4) Applicability to the local regulatory regime
5) Consideration of tail risk events
The methodology proposed is a 3-pronged approach as detailed below:
(Note: Levels 1 & 2 are proposed to measure and manage exogenous liquidity risk)
Level 1 (Normal conditions): Calculate both 1-day and 10-day VaR, whereby limits will be set
against 1-day VaR and triggers will be set against 10-day VaR.
Justification: Currently, the bank adopts various holding periods depending on asset class or
instrument types.
(i) FX & Derivatives – 1 day
(ii) Fixed Income: Sovereigns – 1 day
(iii) Fixed Income: PDS – 90 days (but able to repo to national bank under the existing
daily standing facility window)
(iv) Equity: 3 days
As a consequence of adopting varying holding periods across asset classes, we are unable to derive a
Group-wide diversified VaR for effective price risk management. Calculating the 1-day and 10-day
VaR is used by many other banks and is accepted by regulators. This is also the recommended
approach in the current Basel 2 framework. This approach has been scoped into the business
requirement until the outcome of the FRTB review.
Level 2 (Tail risk events): Adopt specific stress scenarios to stress–test illiquid conditions where
warranted.
Justification: This will allow the bank to define specific scenarios to measure and subsequently,
manage the tail risk arising from illiquidity of positions held. This will be performed over and above
the existing daily CaR calculation and semi-annual regulatory stress test. The stress scenarios will be

5. customised and applied depending on the product, markets/counterparties and exposures, which
warrant concern. The ability to create such scenarios has been scoped into the risk project (it is
expected that such scenarios will be calibrated to reflect realistic tail risk probabilities).
Level 3: Continue to adopt existing auxiliary controls to manage endogenous liquidity risk.
Justification: Continuing the use of detailed management limits to manage market liquidity risk
arising from endogenous factors (ie. exposures to specific factors such as tenor, currency, country).
Such limits are:
(i) NOP / Room position size
(ii) PV01
(iii) Greeks eg. Delta, delta-gamma, vega, theta
(iv) Maximum tenor limit
(v) Approved instruments
(vi) Approved countries
(vii) Approved currencies
(viii) Concentration limit / Aggregate Portfolio Limit
These controls have been scoped into the market risk project.