"Liquidity Risk and Correlation Risk: Implications for Risk Management"

“Liquidity Risk and Correlation Risk:

Implications for Risk Management”


By


Viral V. Acharya1 and Stephen Schaefer2





First Draft: 1 September 20063

This Draft: 8 September 2006




1 Viral V. Acharya, Associate Professor of Finance, London Business School, and Research Affiliate of
Centre for Economic Policy Research (CEPR). Contact: London Business School, Regent’s Park,
London NW1 4SA, Tel: +44(0)20 7262 5050, e-mail: vacharya@london.edu.
2 Stephen Schaefer, Professor of Finance, London Business School. Contact: London Business School,
Regent’s Park, London NW1 4SA, Tel: +44(0)207262 5050, e-mail: sschaefer@london.edu
3 We are grateful to members of the International Financial Risk Institute (IFRI) for commissioning an
earlier article “Understanding and Managing Correlation Risk and Liquidity Risk” presented at the
IFRI Roundtable on September 29-30 2005. This article is partly based on that piece and we are
grateful to the members of IFRI for their feedback and comments. All errors remain our own.

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1. Introduction

There has been a surge in the recent academic literature on issues concerning
liquidity (starting with Amihud and Mendelson, 1986) and liquidity risk (Pastor and
Stambaugh, 2003, and Acharya and Pedersen, 2005). While practitioners would
perhaps question the relatively late arrival of these topics into academic focus,
academics have traditionally preferred to look at the world through the lens of
complete, or at least frictionless markets. The limitations of this traditional approach
have however become glaringly transparent over the last decade or two in the wake of
major financial events in which the ability to trade securities and access capital-
market financing declined substantially. The most striking of these events include the
stock market crash of 1987 in the United States, the Russian default in 1998, the Long
Term Capital Management episode that followed, and, most recently, the aftermath of
GM and Ford downgrade. It is thus timely and fitting to examine what we can learn
from these events about sources of (il)liquidity and liquidity risk, and their
implications for risk management at banks and financial institutions. As a part of this
investigation, we will also look at the relation between the developing theory on
liquidity risk and the apparently separate literature on correlation risk - the
fluctuations over time in the correlation of returns across securities.

A central difficulty with discussing issues relating to liquidity is the lack of
consensus on what it means. Liquidity is clearly multi-faceted and perhaps also a
somewhat loosely employed economic concept. To capital market participants,
liquidity generally refers to transaction costs arising from bid-ask spreads, price
impacts, and (limited) market depth for trading in securities. By token, liquidity risk

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for these participants generally refers to unpredictable variations in transaction costs.
We shall henceforth refer to this notion of liquidity and liquidity risk as pertaining to
“market liquidity.” In contrast, and often times in addition, risk managers at banks and
financial institutions are concerned about liquidity on the funding side, in other words,
the ease with which cash shortfalls of the enterprise can be funded through various
sources of internal or external financing. We shall refer to this as “funding liquidity”
and its unpredictable fluctuations over time as funding liquidity risk.4

In this paper, we start by observing that capital and collateral requirements for
trading of securities introduce an important linkage between market liquidity and
funding liquidity of financial intermediaries. This first step enables us to focus on
causes, effects and implications of market liquidity shocks, with the additional
consideration that these are also related to funding liquidity shocks: Lack of trading
capacity reduces profits of intermediaries, brings them closer to capital or collateral
constraints, and further restricts their ability to provide liquidity to markets.
Conversely, the collateral value of risky assets falls during periods of illiquidity and
restricts the amount of secured funding that intermediaries can raise. While this
linkage has been at the centre of some recent theoretical contributions (most notably,
Gromb and Vayanos, 2002, and Brunnermeier and Pedersen, 2005), we focus on two
important aspects that have hitherto received less direct attention in this literature.
First, that liquidity shocks are highly episodic and tend to be preceded by or
associated with large and negative asset return shocks, whereby liquidity risk is
rendered a particularly non-linear phenomenon. In particular, each of the striking
events referred to in the opening paragraph of this Introduction was preceded by a

4 Note that both these forms of liquidity risk pertain to uncertainty over prices, spreads, and the market
depth for instruments in question. The key difference between market liquidity risk and funding
liquidity risk can thus be understood as whether one is trying to trade some other entity’s instruments
or one’s own.

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significant shock to asset prices. Each of these shocks reduced the net worth of
financial intermediaries, and, in turn, led to disproportionately large effects on market
liquidity. An implication of this is that prices in capital markets effectively exhibit
two “regimes”. In the normal regime, intermediaries are well-capitalized and liquidity
effects are minimal: prices of assets reflect fundamentals and there is no (or little)
liquidity effect. In the illiquidity regime, intermediaries are close to their capital or
collateral constraints and there is “cash-in-the-market” pricing (Allen and Gale, 1994,
1998). Under cash-in-the-market pricing, market price of a security exhibits an
illiquidity discount that is declining in the total liquidity of market participants in that
particular security market. Thus, prices indirectly reflect the “shadow” cost of capital
to these intermediaries, that is, the cost they suffer from issuing an additional unit of
funding capital to undertake a transaction, this effect being stronger in markets where
financial intermediaries are more likely to be the marginal price-setters (for example,
derivatives and complex structured products). .
Second, that this view of prices as consisting of two regimes, in terms of
liquidity effects, helps in understanding the characteristics of a seemingly unrelated
phenomenon, the risk that correlation of returns across different markets (within a
country as well as across countries) fluctuates over time, the so-called “correlation
risk”. Two characteristics of correlation risk bear a striking relationship to liquidity
risk – the fact that correlations in returns of primitive securities (such as stocks and
bonds) appear to rise in bear markets relative to bull markets (Longin and Solnik,
2001 and Ang and Chen, 2002), and that implied correlation parameters produced by
traditional derivative-pricing models also exhibit such substantial fluctuations.
Our main thesis is that an important component of these fluctuations in
correlations is linked to liquidity risk and not to the correlation between cash flows

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and discount rates of underlying securities. In the normal regime, correlations across
asset prices are primarily driven by correlation in fundamentals of the underlying
entities or risks. In contrast, in the illiquidity regime, prices are also affected by the
liquidity position of market participants, and, in turn, by the shadow cost of capital
constraints faced by intermediaries. Since this liquidity effect is related to
intermediaries’ capital rather than to a security’s fundamentals, it affects prices of
securities traded by these intermediaries across the board, inducing a correlation in
securities’ market prices that is over and above the one induced by fundamentals.
Fluctuations in the capital of intermediaries and its issuance cost cause fluctuations in
measured correlations. Since traditional covariance calculations and derivative-pricing
models do not allow for such liquidity effects, they cannot isolate correlation risk due
to fundamentals from that due to liquidity risk.
To summarize, market liquidity risk, funding liquidity risk, and correlation
risk are all inter-twined and related in a non-linear fashion to the same underlying
asset return uncertainty. These relationships between different dimensions of liquidity
risk, and the seemingly unrelated correlation and asset return risks, have important
implications for risk managers and the hedging strategies their institutions employ.
We discuss different mechanisms to manage such risks and their relative merits, the
main observation being that in the normal regime, hedging of correlation risk by
model-implied hedging strategies is likely to be successful, whereas in the illiquidity
regime, model-implied hedging based on underlying risks or securities is unlikely to
be effective: in the illiquidity regime, hedging of liquidity risk and correlation risk
requires holding of liquidity buffers and access to funding sources.
The remainder of the article is organized as follows. In Section 2, we discuss
the types of financial intermediaries that play a role in the liquidity effects outlined

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above and also describe the nature of funding liquidity risk they face. In Section 3, we
establish the relationships between market liquidity risk, funding liquidity risk, and
correlation risk, and their origins in negative asset return shocks. In Section 4, we
document existing evidence on correlation risk and link it to liquidity-induced price
regimes. We provide an illustration of these relationships in Section 5 based on the
aftermath of GM and Ford downgrade in the bond market in May 2005. We present in
Section 6 implications of this linkage for hedging and risk management at financial
institutions. Section 7 concludes.
Parts of this article are based on a paper on this topic by the authors for the
Roundtable of the International Financial Risk Institute (IFRI) in September 2005. As
a part of that preparation, we asked the Chief Risk Officers of several leading
financial institutions, a number of questions concerning correlation risk, liquidity risk,
their approach to hedging and the overall scope of risk management. The questions
and their responses (an aggregated view) are presented in the Appendix. The themes
that emerged from this survey are broadly consistent with the views expressed in this
article, and, in turn, have shaped some of our thinking on the issues at hand.

2. Financial Institutions and Funding Liquidity Risk

“With market risk and credit risk, you could lose a fortune. With [funding] liquidity
risk, you could lose the bank!” – Bruce McLean Forrest, UBS Group Treasury.

Put simply, funding liquidity risk is the risk that an institution will have to
meet uncertain cash requirements in future arising from its day-to-day business
activities. From the standpoint of this article, we are primarily interested in funding

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liquidity risk faced by financial institutions that make markets in traded financial
securities. Within this class, the focus is on those institutions where such trading
constitutes a significant (possibly entire) portion of overall activity, for example,
brokerage firms, specialist firms, trading desks of large banks, and also hedge funds.
Such institutions face net cash outflows during periods of systematic asset or
liquidity shocks (recessions, e.g., the Great Depression, oil-price shocks, e.g., of mid
70’s, stock-market crashes, e.g., in the United States in 1987, and real-estate crashes,
e.g., in Japan in late 1980’s), as well as during periods of idiosyncratic or institution-
specific shocks (due to fraud, disclosure of accumulated losses or accounting
irregularities, legal settlements, significant model risk, poor risk management and the
resulting loss of reputation with capital providers). Some cases of such idiosyncratic
shocks are Continental Illinois’s collapse in 1989, the Metallegesellschaft meltdown
in 1993/94, the Barings disaster in 1995, and to an extent the distress of Long Term
Capital Management in 1998 in spite of its pre-existing complex web of borrowing
relationships.
During systematic asset or liquidity shocks, there is a net inflow of funds into
deposit-bearing institutions (commercial banks), away from institutions that rely on
market sources of financing. A recent study by Gatev and Strahan (2005) shows that
during times of systematic liquidity shocks, there is a “flight to quality” of deposits to
commercial banks. The authors measure systematic liquidity shocks by a widening of
the (non-financial) commercial-paper to treasury-bill spread; (the so-called “paper-bill
spread”). The authors find that when the paper-bill spread widens, commercial banks
in the United States experience an increase in deposit inflow.5 The paper-bill spread is

5 Furthermore, when the paper-bill spread widens, commercial banks experience a growth in assets, a
growth in their commercial and industrial lending, and even a growth in their liquidity buffers: a 25
basis points (bps) increase in the paper-bill spread causes assets of commercial banks to grow at 0.4%
weekly rate and their liquidity buffers to grow at 0.17%. Several additional aspects of this evidence are

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considered a good proxy for periods when liquidity risk rises, making it difficult for
non-deposit bearing institutions to raise financing from capital markets, as evidenced
during the Penn Central default in 1970, the LTCM episode in 1998, and recently, the
Enron bankruptcy in 2002.
In contrast, though idiosyncratic shocks are not accompanied by market-wide
liquidity shocks, these typically result in questions about the affected institution’s
solvency: the lack of correlated shocks affecting other institutions (in other words,
lack of other institutions to “share the blame with”) makes it hard to distinguish
institutional insolvency and illiquidity. The opaqueness of balance-sheets of financial
institutions, for instance, due to the large amount of off-balance-sheet activities and
difficult-to-value derivative transactions, aggravates the matter, calling into question
the institution’s overall management as well as specific risk-management practices.
Furthermore, if the affected institution is large, a disorderly liquidation of assets could
produce outcomes for the institution that could resemble those in times of market-
wide shocks.6 Finally, idiosyncratic liquidity needs often arise also on an intra-day
basis (for example, due to collateral requirements or margin calls on traded
securities).
When faced with such shocks (systematic or idiosyncratic), financial
institutions can in principle rely on external forms of financing such as equity,

noteworthy: (1) These effects are observed only for commercial banks and not for finance companies;
(2) These effects do not depend on the safety, that is, default risk, of the commercial banks; and (3)
Only the levels of deposit liabilities of commercial banks increase and not those of the non-deposit
liabilities. These facts put together suggest that the flight of deposits to commercial banks arises due to
their access to regulatory deposit insurance.

6 The distinction between commercial banks and financial institutions is again of importance: While
large commercial banks have a too-many-to-fail guarantee, such a guarantee has been witnessed for
non-deposit-bearing financial institutions only in case of the LTCM (which also was a Fed-coordinated
intervention rather than a government bailout).

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subordinated debt, secured debt against collateral, and undrawn lines of credit, and on
internal financing in the form of cash and retained earnings.
During times of systematic shocks, public markets such as equities and
subordinated debt tend to dry up the first. There is a market-wide decline in the
liquidity of securities that firms typically issue to raise capital. During times of
idiosyncratic shocks, there is a firm-specific decline in liquidity of capital (for reasons
discussed above). The increased risk premium and price impact in such times and the
resulting dilution cost implies that public markets are generally not available to
affected institutions as funding sources.7 An important observation is that these
funding sources – equity and subordinated debt – are price-sensitive.
Since price-sensitive funding sources are rendered too expensive, retained
earnings and undrawn lines of credit which represent price-insensitive sources of
funding (if they were arranged in advance) may constitute the first line of defence
against illiquidity. Note however that retaining large quantities of cash (usually in the
form of treasuries) entails significant opportunity costs for financial institutions and
funding from lines of credit is subject to the material adversity clause (MAC) not
being invoked by the lending institution. The affected institution would thus typically
have to resort to the second line of defence and undertake at least some form of
intermediate financing, such as secured borrowing against collateral.
The extent of collateralized borrowing that can be undertaken by the
institution depends upon the market value of the collateral and the size of hair-cuts
being charged by counterparties. Hair-cuts represent the percentage of value of an
asset that cannot be borrowed against, and as such is another form of illiquidity in
funding. Typically, hair-cuts are 2-5% for highly liquid assets such as OECD

7 Several academic studies, e.g., Choe, Masulis and Nanda (1993), have shown that the price-impacts
from equity issuances are greater in recessions than in expansions.

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government bonds, 10-25% for highly-rated industrials, and 25-50% for illiquid assets
like major-index equities, but are generally higher during liquidity crises. The
variation in hair-cuts over time, and, in turn, in collateral values, creates a role for
market liquidity in determining the institution’s funding liquidity risk. Below, we
explain how this effect of market liquidity on the funding liquidity of financial
institutions feeds back and further reduces market liquidity, and what causes market
liquidity to dry up in the first place.


3. Market Liquidity Risk, Funding Liquidity Risk and Correlation Risk

Recent evidence shows that asset shocks and liquidity shocks tend to be highly
correlated, in the aggregate as well as at the level of individual securities. Figure 1
from Acharya and Pedersen (2005) plots the time-series of innovations in stock-
market illiquidity computed using ILLIQ, the daily price-impact measure of Amihud
(2002) over the period 1964-2000, a measure that has been shown by Amihud (2002)
to be related to other measures of liquidity such as the bid-ask spread. The Amihud
(2002) measure is computed for each stock on a monthly basis as the average of daily
ratio of absolute return on the stock to total dollar volume traded. This monthly
measure of illiquidity for stocks is equally weighted to obtain a measure of overall
stock-market illiquidity. Finally, the time-series of stock-market illiquidity is analyzed
using an AR(2) specification and the residuals or the innovations are divided by their
standard deviation and plotted in the figure.
Strikingly, liquidity shocks are highly episodic. That is, innovations in market
illiquidity are generally small but occasionally quite large. The large innovations in
fact coincide with the periods that anecdotally were characterized by liquidity crisis,

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