Liquidity Risk and the Structure of Financial...

Liquidity Risk and the Structure of Financial Crises

Lasse Heje PedersenNYU, CEPR, NBER

October, 2008

Prepared for theInternal Monetary Fund

and Federal Reserve Board

See also my related blog: http://sternfinance.blogspot.com

A Report from an Academic Returning from the Trenches

Overview of Talk

Theory• What is liquidity risk?• How should liquidity risk affect prices and returns?• What happens during liquidity crisis?

Evidence from notable liquidity crisis:• The current crisis• 2007 quant equity • 2005 convertible bond market • 1998 LTCM • 1987 stock market crash

Conclusion• Will it happen again? • How do we solve the crisis and reduce the risk of future ones?• Liquidity risk lessons

What is Liquidity Risk

Market liquidity: • A security is considered liquid if it is “easy” to trade: Low bid-ask spread,

small price impact, high resilience, easy search (in OTC markets)

Market liquidity risk:• The risk that the market liquidity worsens when you need to unwind

Funding liquidity:• A trader’s available funding from own capital and (collateralized) loans

Funding liquidity risk: • The risk that a trader cannot fund his position and is forced to unwind

The Pricing of Market Liquidity Risk: Introducing Liquidity Betas

Investors care about returns net of trading costs• They want to be compensated for illiquidity and liquidity risk• CAPM holds for net returns in an OLG model.

Decomposing systematic risk of return net of trading costs:

total systematic risk component sign interpretation

Cov(Ri – Ci, RM – CM) = Cov(Ri , RM) + standard market beta + Cov(Ci , CM) + commonality in liquidity– Cov(Ri , CM) – return exposure to market liquidity– Cov(Ci , RM) – liquidity exposure to market risk

Three liquidity betas, after division by Var(RM– CM)

The Pricing of Market Liquidity Risk: Liquidity-Adjusted CAPM

Liquidity-adjusted CAPM:

Et(rt+1) = rf + Et (ct+1) + λt ( βtM + βt

L1 - βtL2 - βt

L3 )

Empirical tests consistent with predictions: explanatory power in the cross-section, positive risk premium, expected signs of betas.

An increase in illiquidity increases the required return:

and contemporaneous returns are low.

Source: Acharya and Pedersen (Journal of Financial Economics, 2005)

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Real World Examples

• Securities with high liquidity risk: high average return empirically

• Lesson from LTCM: liquidity important risk factor

• Current crisis:Ct is increasedλt is increasedLiquidity risk increased

→ Prices are down

What Drives Market Liquidity Risk

Liquidity is provided by market makers, hedge funds, prop. traders, “speculators”

Speculators must be able to fund their positions, both long positions x+ and short ones x- :

If speculators are well funded (large capital W and/or low margins m), then• they can trade more (larger x+ and x- )

→ which enhances market liquidity• “Funding liquidity” is a driver of market liquidity

There is also feedback in the opposite direction:• Better market liquidity can lower margins because

financiers more willing to lend when they can more easily and quickly sell the collateralmarket liquidity can lower volatility

→ eases funding restriction

This mutual feedback can give rise to liquidity spirals

Liquidity Spirals

Sources: Garleanu and Pedersen (2007) and Brunnermeier and Pedersen (2008)

Some traders hit or near margin constraints (or risk limits) and reduce positions, which• moves prices against them (and others with similar positions) leading to further losses• increases volatility and reduces market liquidity, leading to increased margins and

tightened risk management (including reduction in counterparty exposure)

These effects continue until a new equilibrium is reached• loss-spiral• margin-spiral• risk-management-spiral

funding problems

reduced positions

higher margins

prices move away from fundamentals

initial losses e.g. due to credit

losses on existing positions

tighter risk management

Speculators consider each security j to maximize expected profit per capital use • So, in equilibrium, profit-per-capital-use must be equal for all securities • The common profit per capital use is the shadow cost of capital, denoted φ

profitj / capital-usej = φ (I)

Note that: Cj = market illiquidityj = trading cost of liquidity-demanderj = profit of speculatorsj (II)mj = marginj = capital-use of securityj (III)

Combining (I), (II), and (III) yields

Cj / mj = φ =>

Cj = mj * φ

I.e. equilibrium a security’s market liquidity is the product of• its capital use i.e. margin

which depends on its risk, trading characteristics• the general scarcity of speculator capital, i.e. funding liquidity

See Brunnermeier and Pedersen (2007) for a formal theory.

Market Liquidity Risk Across Securities: Commonality and Differences

Real World Example:

Currently funding liquidity is low,i.e. bank balance sheet is scarce

Hence, market liquidity is low,especially for high margin securitieslike convertible bonds

Market Liquidity and Funding Liquidity: Explaining the Stylized Facts

Sudden liquidity “dry-ups”• liquidity spirals for market and funding liquidity• destabilizing margins, risk controls, redemptions

Commonality of liquidity:• these funding problems affect many securities

Market liquidity correlated with volatility:• volatile securities require more capital to finance

Flight to quality / flight to liquidity:• when capital is scarce, traders withdraw more from “capital intensive” high-margin

securities

Market liquidity moves with the market• because funding conditions do

See Brunnermeier and Pedersen (2007) for a formal theory.

Commonality of Liquidity and Flight to Quality: Example

wealth shock to liquidity providers

pric

e of

ass

ets

1 an

d 2

asset 2 with high risk

asset 1 with low risk Jump leading tosudden liquiditydry up

Funding Liquidity Leads to Conditional Skewness and Kurtosis

• Price moves associated with losses for liquidity providers: amplified by liquidity spirals• Price moves associated with gains: not amplified

Real World Example:

FX carry trade unwind

“investment currencies go up by the stairsand down by the elevator”

Source: Brunnermeier, Nagel, and Pedersen (2008)

Source: Brunnermeier and Pedersen (2008)

Examples of Liquidity Events

Examples of Liquidity Events

What happens in the real world liquidity crisis:

• Current crisis• 2007 August quant equity• 2005 Convertible bonds• 1998 LTCM and convertible bonds• 1987 Stock market crash and merger arbitrage

The Current Crisis

Housing bubble and burst

Large losses in the levered financial sector

Liquidity spirals as• banks’ balance sheets deteriorate • banks de-lever, selling assets• risk management tighten, lending reduced, counterparty exposures minimized• margins increase• liquidity vanishes• prices drop

Extreme liquidity risk• Extreme funding liquidity risk: your bank may default• Extreme market liquidity risk: dealers shutting down (no bids!)

The Trigger: Housing Bubble and Bust

Case-Shiller CSXR

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ABX AAA (2006-1)CMBX NA.1 AAAIG

This Creates Losses and Funding Liquidity Problems for Banks

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Banks Tighten Risk Management and Reduce Inter-bank Lending: Funding Spreads Rise

TED Spreads

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BD CN JP UK US

Funding Liquidity Problems for Everyone: Banks Unwillingness to Lend

% Increasing Spreads of Loan Rates over Banks' Cost of Funds (source: FRB)

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Further Funding Problems: Volatility Spikes, increasing Margins

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VIX Realized Volatility

Further Funding Problems: Commercial Paper Market

Outstandings

Rates

Source: Federal Reserve Bank

Market Liquidity Deteriorates: Bid-Ask Spreads

Percentage Bid-Ask Spread

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ABX-HE-AAA 06-1 ABX-HE-AAA 06-2 ABX-HE-AAA 07-1 HY (right axis)

Extreme Liquidity Crisis: Covered Interest Rate Parity Fails

Deviation of Covered Interest-Rate Parity vs. USD

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Perc

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s (a

nnua

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AU BD CN JP NW NZ SD SW UK

Prices Drop, Especially of Illiquid Assets: Losses by Hedge Funds

CS Tremont HF Index

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Convertible Arbitrage Dedicated Short Bias Emerging Markets Equity Market Neutral Event Driven Distressed Multi-Strategy Risk Arbitrage Fixed Income Arbitrage Global Macro Long/Short Equity Managed Futures Multi-Strategy

Correlations Increase: Everything Trades on Liquidity

Commonality among SP500, Bonds, Crude, $-Yen, Gold:Percent of Correlation Explained by First Principle Component

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Correlation between Value and Momentum

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All These Liquidity Effects are Connected in Equilibrium

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VIX/10 CIP deviation US TED ABX AAA06 ABX Bid-Ask short SP500

August 2007 Quant Equity Event Background: What is a Quant Hedge Fund

Traditional non-quant hedge funds: “discretionary trading”:• Buy/sell based on an analyst’s overall assessment of certain selected

securities

Quantitative method:• Define trading rules explicitly• Back test using historical data• Build a system that implements trading idea systematically • Using economics, novel data, and novel data processing to identify

relationships market participants may missFinding subtle relationships that the market does not easily understandSuperior processing of ideas using a wealth of data that cannot be easily processed using non-quantitative methods

Chronology of the 2007 Quant Event

July 2007:• Credit spreads started to widen after sub-prime mortgage turmoil• Losses in certain multi-strategy hedge funds, who started reducing risk and raise cash

by selling liquid instruments• Money pulled out of potential LBO candidates with strong value and cash flow

characteristics, hurting the value strategy• Fund-of-fund hit loss triggers and redeem from certain hedge funds• Value stocks behave poorly with unusual correlation structure

August 2007• Major de-levering of quant strategies• Spill-over

from value to other quant factorsfrom the US to international markets

• Since the large price movements were created by de-leveraging, prices bounced back

Estimated Reduction of Overall Quant Positions

$300-$400 billion oflong exposures $175-$250 billion of

long exposures

$300-$400 billion ofshort exposures

$175-$250 billion ofshort exposures

Pre Sell-Off Post Sell-Off

Spillover from US to other Markets

Valuation Factor Returns, July 1 – August 24

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ul

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US Valuation JP Valuation Aus Valuation

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2007080609:31:00

2007080709:31:00

2007080809:31:00

2007080909:31:00

2007081009:31:00

2007081309:31:00

2007081409:31:00

Minute-by-Minute Cumulative Return to Value Factor, August 6 - 14

7 % annualized vol ~ 7% / Sqrt(252) = 44 bps daily vol (vol. estimates from BARRA)

Move largest for illiquid stocks

Mon Tue Wed Thu Fri Mon Tue

Evidence of Liquidity Event due to Unwinding

Mon Tue Wed Thu Fri Mon Tue

Return -1.34% -4.52% -6.20% -4.23% 9.82% 2.20% 0.35%

# Stds (1 std is 0.44%) -3 -10 -14 -10 22 5 1

P-value "normal" day 0.23% 0.00% 0.00% 0.00% 0.00% 0.00% 42%

Positive returns (%) 31% 10% 32% 41% 75% 43% 56%

Negative returns (%) 69% 90% 68% 59% 25% 57% 44%

Positive returns (%) 42% 32% 35% 42% 67% 47% 52%

Negative returns (%) 58% 68% 65% 58% 33% 53% 48%

P-value random walk 0.10% 0.00% 0.00% 0.10% 0.00% 24% 39%

1 minute intervals

10 minute intervals

Interpretation

Liquidity events can happen even in the most liquid markets in the world

Market and funding liquidity are related

Liquidity shocks are• sudden• common and spill over• affect mostly risky and illiquid securities

Everyone seeks the highest alpha portfolio• The best quants are likely to be correlated• One needs to stay one step ahead

Prices drop more and rebound slower in more illiquid markets • Cf. Duffie, Garleanu, Pedersen (Review of Financial Studies, 2007)

2005 Convertible Bond Event

Capital outflow due to redemptions from convertible bond hedge funds

Single-strategy hedge funds: • forced sellers of convertible bonds

Multi-strategy hedge funds• had a choice: what do you think that they did?

What happens to the price of convertible bonds?

Background: What is a Convertible Bond

Convertible bond: • Corporate bond + call option (+ more)

Theoretical value can be inferred from• Issuer stock price• Stock price volatility• Option-implied volatility• Risk-free interest rates• Credit spreads • Just like the price of a “Gin and Tonic” can be inferred from the respective

prices of gin and tonic, and the amounts of each needed

Convertible Bond Arbitrage

Buy convertible bond if it trades at a discount

Short the issuer’s stock

Potentially:• Short risk-free bonds• Short non-convertible bonds (or buy CDS)• Short stock options

Convertible Bond Arbitrage Capital Outflows in 2005

Natural liquidity providers: Convertible Bond Arbitrage Hedge Funds (HFs)

Capital outflows in 2005:• 2005Q1: 20% capital redeemed• 2005Q1 – 2006Q1: assets fell by half

Convert Arb HFs sold convertible bonds

Redemptions in 2005

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So urce: B arclay Gro up

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$B)

Redemptions Led to Selling: Adjusted Holdings of Convertible Bonds

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Convert Mutual Funds

Source: Mitchell, Pedersen, and Pulvino (American Economic Review, 2007)

Convertible Bond Arbitrage Returns and Market Price / Theoretical Value

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Market Price/Theoretical Value(left scale)

Cumulative Return(right scale)


Interpretation

Prices drop and rebound

Price-to-fundamentals lowest around redemption notices (45 days before end of June and end of December)

Returns negative, then positive

Response by other traders:• Multi-strategy hedge funds• Mutual funds

The Case of Amaranth

In 2005, Amaranth had• Losses in convertible bonds• Profits in energy trading• Overall profit and no capital problems

Decided to liquidate convertible bonds at time of significant cheapness

Collapsed in 2006 due to losses in energy

LTCM Blowup in 1998: Implications for Convertible Bonds

Large hedge fund LTCM had losses due to Russian default, option positions, etc.

Had to liquidate large position in convertible bonds

What happened to the price of the bonds and how was the subsequent return?

Convertible Bond Arbitrage Returns and Market Price / Theoretical Value

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Market Price/Theoretical Value(left scale)



1987 Crash: Implications for Merger Arbitrage

Oct. 14-16: U.S. House Ways and Means Committee proposed legislation

Oct. 19 (Black Monday) and 20: crash

Oct: 21-31: • Stock market rebounds• Congress backs off proposed legislation• But, merger-arbitrage proprietary traders

had lost a significant amount of capital Did they start buying or keep selling?What happed to merger spreads?

Berkshire Hathaway Annual Report (Warren Buffett):

“During 1988 we made unusually large profits from [risk] arbitrage … the trick, a la Peter Sellers in the movie, has simply been ‘Being There.’ ”

Background on Merger Arbitrage

In a merger, “target” is bought at a premium, say 20-30%.At announcement, target price increases to a value close to the offer value. But, there remains a “deal spread,” typically around 3%

Due to• Risk of deal failure• Selling pressure: Mutual funds sell after announcement

Merger arbitrageurs buy target• Stock deal: hedge by shorting acquirer• Cash deal: no hedge

pricetarget price– target eoffer valu spread deal =

Merger Arbitrage and the 1987 Crash

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

1987

1001

1987

1015

1987

1029

1987

1112

1987

1127

1987

1211

1987

1228

Date0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

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Median Deal Spread(left scale)

Prop Desk Net Purchases(left scale)


Med

ian

Mer

ger A

rbitr

age

Dea

l Spr

ead,

and

Net

Pur

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s %

of L

ong

Mar

ket V

alue


Conclusions

Conclusion: Will Liquidity Events Happen Again?

Yes, almost surely in some markets• Certain trades often get crowded over time• Sudden losses can lead to simultaneous unwind and liquidity spirals

Liquidity crisis is part of the equilibrium:• If there was no risk of crisis, traders will have an incentive to lever up more

Crises are (somewhat) rare• Banks try to stay liquid and traders actively try to stay away from margin

constraint• Most likely to occur in illiquid markets in which levered specialized traders

play a large role• Least likely in liquid market using unique strategies

Conclusion: How do We Solve the Crisis and Reduce the Risk of Future Ones?

Recapitalize banks• Raise new capital, dilute old equity, possibly reduce face value of old debt• Quick resolution bankruptcy for institutions with systemic risk, i.e. causing liquidity

spirals

Improve funding markets and trust• Broaden bank guarantees, open discount window (collateralized funding with reasonable

margins), ensure CP market

Risk management• must acknowledge systemic risk due to liquidity spirals• Policy and regulations must consider system, as opposed to each institution in isolation

How do We Solve the Crisis and Reduce the Risk of Future Ones, Continued

Trading with a clearing house preferable • allows netting out• reduce counterparty co-dependencies• increases transparency

Stock transaction taxes not a good idea:• moves trading away and into the land of OTC derivatives with no clearing house• reduces liquidity and, hence, increases firms’ cost of capital (liquidity-adjusted

CAPM)• importance of the ability to raise capital is what this crisis is all about

Shortselling ban is not a good idea:• Shortsellers bring new information to the market, increase liquidity, and reduce

bubbles (remember the housing bubble started this crisis) • Prohibiting shortselling does not solve the general funding problem. • Temporarily banning new short sales of financial institutions can be justified if there

is risk of predatory trading, but often firms on trouble look for scapegoats

Conclusion: Liquidity Risk Lessons

Liquidity risk important for• security prices (liquidity-adjusted CAPM)• risk management• the speed of arbitrage

Funding liquidity of banks and “speculators” is a driver of market liquidity risk

Liquidity crisis:• Driven by liquidity spirals:

loss spiral margin spiralrisk management spiral

• Liquidity providers become demanders• New capital arrives slowly• Prices drop and rebound

Related Papers

“Carry Trades and Currency Crashes,” Markus Brunnermeier, Stefan Nagel, and Lasse Heje Pedersen (2008)NBER Macroeconomics Annual, forthcoming. Link

“Market Liquidity and Funding Liquidity,” Markus Brunnermeier and Lasse Heje Pedersen (2008)Review of Financial Studies, forthcoming. Link

“Demand-Based Option Pricing,” Nicolae Garleanu, Lasse Heje Pedersen, and Allen Poteshman (2008)Review of Financial Studies, forthcoming. Link

“Valuation in Over-the-Counter Markets,” Darrell Duffie, Nicolae Garleanu, and Lasse H. Pedersen (2007) The Review of Financial Studies, vol. 20, no. 5, pp 1865-1900. Link

“Liquidity and Risk Management” Nicolae Garleanu and Lasse Heje Pedersen (2007)American Economic Review, P&P, 2007, vol. 97, no. 2, pp. 193-197. Link

“Slow Moving Capital,” Mark Mitchell, Lasse Heje Pedersen, and Todd Pulvino (2007)The American Economic Review, P&P, 2007, vol. 97, no. 2, pp. 215-220. Link

“Asset Pricing with Liquidity Risk,” Viral Acharya and Lasse Heje Pedersen (2005)Journal of Financial Economics, vol. 77, pp. 375-410. Link

“Predatory Trading,” Markus K. Brunnermeier and Lasse Heje Pedersen (2005)The Journal of Finance, vol. 60, no. 4, pp. 1825-1863. Link

“Liquidity and Asset Prices,” Yakov Amihud, Haim Mendelson, and Lasse Heje Pedersen (2005) Foundations and Trends in Finance, vol.1, no. 4, pp. 269-364. Link

“Securities Lending, Shorting, and Pricing,” Darrell Duffie, Nicolae Garleanu, and Lasse Heje Pedersen (2002)Journal of Financial Economics, vol. 66, pp. 307-339. Link

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