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Liquidity NBER

Summary Statistics for Various Monthly Indexes

7/16/2010 © 2010 by Andrew W. Lo, All Rights Reserved Page 84

Liquidity NBER

Summary Statistics for Individual Mutual Funds and Hedge Funds
Start Sample
Fund Date End Date Size Mean SD ρ1 ρ2 ρ3 p(Q 11)
(%) (%) (%) (%) (%) (%)

Mutual Funds
Vanguard 500 Index Oct-76 Jun-00 286 1.30 4.27 -4.0 -6.6 -4.9 64.5
Fidelity Magellan Jan-67 Jun-00 402 1.73 6.23 12.4 -2.3 -0.4 28.6
Investment Company of America Jan-63 Jun-00 450 1.17 4.01 1.8 -3.2 -4.5 80.2
Janus Mar-70 Jun-00 364 1.52 4.75 10.5 0.0 -3.7 58.1
Fidelity Contrafund May-67 Jun-00 397 1.29 4.97 7.4 -2.5 -6.8 58.2
Washington Mutual Investors Jan-63 Jun-00 450 1.13 4.09 -0.1 -7.2 -2.6 22.8
Janus Worldwide Jan-92 Jun-00 102 1.81 4.36 11.4 3.4 -3.8 13.2
Fidelity Growth and Income Jan-86 Jun-00 174 1.54 4.13 5.1 -1.6 -8.2 60.9
American Century Ultra Dec-81 Jun-00 223 1.72 7.11 2.3 3.4 1.4 54.5
Growth Fund of America Jul-64 Jun-00 431 1.18 5.35 8.5 -2.7 -4.1 45.4

Hedge Funds
Convertible/Option Arbitrage May-92 Dec-00 104 1.63 0.97 42.7 29.0 21.4 0.0
Relative Value Dec-92 Dec-00 97 0.66 0.21 25.9 19.2 -2.1 4.5
Mortgage-Backed Securities Jan-93 Dec-00 96 1.33 0.79 42.0 22.1 16.7 0.1
High Yield Debt Jun-94 Dec-00 79 1.30 0.87 33.7 21.8 13.1 5.2
Risk Arbitrage A Jul-93 Dec-00 90 1.06 0.69 -4.9 -10.8 6.9 30.6
Long/Short Equities Jul-89 Dec-00 138 1.18 0.83 -20.2 24.6 8.7 0.1
Multi-Strategy A Jan-95 Dec-00 72 1.08 0.75 48.9 23.4 3.3 0.3
Risk Arbitrage B Nov-94 Dec-00 74 0.90 0.77 -4.9 2.5 -8.3 96.1
Convertible Arbitrage A Sep-92 Dec-00 100 1.38 1.60 33.8 30.8 7.9 0.8
Convertible Arbitrage B Jul-94 Dec-00 78 0.78 0.62 32.4 9.7 -4.5 23.4
Multi-Strategy B Jun-89 Dec-00 139 1.34 1.63 49.0 24.6 10.6 0.0
Fund of Funds Oct-94 Dec-00 75 1.68 2.29 29.7 21.1 0.9 23.4


Liquidity NBER

At Least Five Possible Sources of Serial Correlation:
1. Time-Varying Expected Returns
2. Inefficiencies
3. Nonsynchronous Trading
4. Illiquidity
5. Performance Smoothing
For Alternative Investments, (4) and (5) Most Relevant:
 (1) Is implausible over shorter horizons (monthly)
 (2) Unlikely for highly optimized strategies
 (3) Is related to (4)
 (4) is common among many hedge-fund strategies
 (5) may be an issue for some funds

7/16/2010 © 2010 by Andrew W. Lo, All Rights Reserved Slide 86

Liquidity NBER

Why Is Autocorrelation An Indicator?
 If this pattern exists and is strong, it can be exploited
– Large positive return this month ⇒ increase exposure
– Large negative return this month ⇒ decrease exposure
– This leads to higher profits, so why not?
 Two reasons that hedge funds don’t do this:
1. They are dumb (possible, but unlikely)
2. They can’t (assets are too illiquid)
 Illiquid assets creates the potential for fraud

How? Return-Smoothing


Liquidity NBER

What Is Return-Smoothing?
 Inappropriate valuation of illiquid fund assets
 In very good months, report less profits than actual
 In very bad months, report less losses than actual

What’s the Harm? Isn’t This Just “Conservative”?
 No, it’s fraud (GAAP fair value measurement, FAS 157)
 Imagine potential investors drawn in by lower losses
 Imagine exiting investors that exit with lower gains
 Imagine investors going in/out and “timing” these cycles
 Smoother returns imply higher Sharpe ratios (moth-to-flame)


Liquidity NBER

Smooth Returns Are Not Always Deliberate
 What is the monthly return of your house?
 Certain assets and strategies are known to be illiquid
 Smoothness is created by “three-quote rule” (averaging)
 For complex derivatives, mark-to-model is not unusual
 But these situations provide opportunities for abuse
 What to look for:
 Extreme autocorrelation (more than 25%, less than −25%)
 Mark-to-model instead of mark-to-market
 No independent verification of valuations
 Secrecy, lack of transparency


Liquidity NBER

Average ρ1 for Funds in the TASS Live and Graveyard Databases
February 1977 to August 2004


Liquidity NBER

A Model of Smoothed Returns
 Suppose true returns are given by:

 Suppose observed returns are given by:


Liquidity NBER

 This model implies:


Liquidity NBER

 Estimate MA(2) via maximum likelihood:


Liquidity NBER


Liquidity NBER

Managing Liquidity Exposure Explicitly
 Define a liquidity metric
 Construct mean-variance-liquidity-optimal
portfolios
 Monitor changes in surface over time and Mean-Variance-Liquidity Surface
market conditions
 See Lo, Petrov, Wierzbicki (2003) for
details

Tangency Portfolio Trajectories


Hedge Funds and
Systemic Risk
References
 Acharya, V. and M. Richardson, eds., 2009, Restoring Financial Stability: How to
Repair a Failed System. New York: John Wiley & Sons.
 Billio, M., Getmansky, M., Lo, A. and L. Pelizzon, 2010, “Econometric Measures of
Systemic Risk in the Finance and Insurance Sectors”, SSRN No. 1571277.
 Chan, N., Getmansky, M., Haas, S. and A. Lo, 2007, “Systemic Risk and Hedge
Funds”, in M. Carey and R. Stulz, eds., The Risks of Financial Institutions and the
Financial Sector. Chicago, IL: University of Chicago Press.


Hedge Funds and Systemic Risk NBER

Lessons From August 1998:
 Liquidity and credit are critical to the macroeconomy
 Multiplier/accelerator effect of leverage
 Hedge funds are now important providers of liquidity
 Correlations can change quickly
 Nonlinearities in risk and expected return
 Systemic risk involves hedge funds

But No Direct Measures of Systemic Risk


Hedge Funds and Systemic Risk NBER

Five Indirect Measures:
1. Liquidity Risk
2. Risk Models for Hedge Funds
3. Industry Dynamics
4. Hedge-Fund Liquidations
5. Network Models (preliminary)
For More Details, See:
 Chan, Getmansky, Haas, and Lo (2005)
 Getmansky, Lo, and Makarov (2005)
 Lo (2008)
 Billio, Getmansky, Lo, and Pelizzon (2010)


Early Warning Signs NBER



“The nightmare script for
Mr. Lo would be a series
of collapses of highly
leveraged hedge funds
that bring down the
major banks or brokerage
firms that lend to them.”



Some Experts Disagreed:

“In approaching its task, the
Policy Group shared a broad
consensus that the already low
statistical probabilities of the
occurrence of truly systemic
financial shocks had further
declined over time.”
– CRMPG II, July 27, 2005, p. 1



But CRMPG II Also Contained:
…Recommendations 12, 21 and 22, which call for
urgent industry-wide efforts (1) to cope with serious
“back-office” and potential settlement problems in
the credit default swap market and (2) to stop the
practice whereby some market participants “assign”
their side of a trade to another institution without the
consent of the original counterparty to the trade.
(CRMPG II, July 27, 2005, p. iv)



Firms Represented in CRMPG II:
 Bear Stearns  JPMorgan Chase
 Citigroup  Merrill Lynch
 Cleary Gottlieb  Morgan Stanley
 Deutsche Bank  Lehman Brothers
 GMAM  TIAA CREF
 Goldman Sachs  Tudor Investments
 HSBC


Granger Causality Networks (Billio et al. 2010) NBER
Granger Causality Is A Statistical Relationship

 Y ⇒G X if {bj} is different from 0
 X ⇒G Y if {dj} is different from 0
 If both {bj} and {dj} are different from 0, feedback relation
 Consider causality among the monthly returns of hedge funds,
publicly traded banks, brokers, and insurance companies


Granger Causality Networks NBER



LTCM 1998
Internet
Bubble
Crash

Financial
Crisis of
2007-2009


August 1998,
August 2007,
May 2010, ...
References
 Khandani, A. and A. Lo, 2007, “What Happened To The Quants In August 2007?”,
Journal of Investment Management 5, 29–78.
 Khandani, A. and A. Lo, 2010, “What Happened To The Quants In August 2007?:
Evidence from Factors and Transactions Data”, to appear in Journal of Financial
Markets.
 NANEX, 2010, “Analysis of the Flash Crash”,
http://www.nanex.net/20100506/FlashCrashAnalysis_CompleteText.html.


The Quant Meltdown of August 2007 NBER

Quantitative Equity Funds Hit Hard In August 2007
 Specifically, August 7–9, and massive reversal on August 10
 Some of the most consistently profitable funds lost too
 Seemed to affect only quants Wall Street Journal
 No real market news September 7, 2007

What Is The Future of Quant?
 Is “Quant Dead”?
 Can “it” happen again?
 What can be done about it?

But Lack of Transparency Is
Problematic!
 Khandani and Lo (2007, 2010)


A New Microscope NBER

Use Strategy As Research Tool
 Lehmann (1990) and Lo and MacKinlay (1990)
 Basic mean-reversion strategy:



Use Strategy As Research Tool
 Linearity allows strategy to be analyzed explicitly:



Simulated Historical Performance of Contrarian Strategy


Total Assets, Expected Returns, and Leverage NBER



Basic Leverage Calculations
 Regulation T leverage of 2:1 implies

 More leverage is available:

 Leverage magnifies risk and return:


Total Assets, Expected Returns, and Leverage NBER

How Much Leverage Needed To Get 1998 Expected Return Level?
 In 2007, use 2006 multiplier of 4
Required Leverage Ratios For Contrarian Strategy To Yield
 8:1 leverage 1998 Level of Average Daily Return
 Compute leveraged returns Average Required
 How did the contrarian strategy Daily Return Leverage
Year Return Multiplier Ratio
perform during August 2007?
 Recall that for 8:1 leverage: 1998 0.57% 1.00 2.00
1999 0.44% 1.28 2.57
– E[Rpt] = 4 × 0.15% = 0.60% 2000 0.44% 1.28 2.56
– SD[Rpt] = 4 × 0.52% = 2.08% 2001 0.31% 1.81 3.63
2002 0.45% 1.26 2.52
2003 0.21% 2.77 5.53
⇒ 2007 Daily Mean: 0.60% 2004 0.37% 1.52 3.04
2005 0.26% 2.20 4.40
⇒ 2007 Daily SD: 2.08% 2006 0.15% 3.88 7.76
2007 0.13% 4.48 8.96


What Happened In August 2007? NBER

Daily Returns of the Contrarian Strategy In August 2007


What Happened In August 2007? NBER
Daily Returns of Various Indexes In August 2007


Comparing August 2007 To August 1998 NBER

Daily Returns of the Contrarian Strategy In August and September 1998


The Unwind Hypothesis NBER

What Happened?
 Losses due to rapid and large unwind of quant fund (market-neutral)
 Liquidation is likely forced because of firesale prices (sub-prime?)
 Initial losses caused other funds to reduce risk and de-leverage
 De-leveraging caused further losses across broader set of equity funds
 Friday rebound consistent with liquidity trade, not informed trade
 Rebound due to quant funds, long/short, 130/30, long-only funds

Lessons
 “Quant” is not the issue; liquidity and credit are the issues
 Long/short equity space is more crowded now than in 1998
 Hedge funds provide more significant amounts of liquidity today
 Hedge funds can withdraw liquidity suddenly, unlike banks
 Financial markets are more highly connected ⇒ new betas


Factor-Based Strategies NBER

Construct Five Long/Short Factor Portfolios
 Book-to-Market
 Earnings-to-Price
 Cashflow-to-Price
 Price Momentum
 Earnings Momentum
 Rank S&P 1500 stocks monthly
 Invest $1 long in decile 10 (highest), $1 short in decile 1 (lowest)
 Equal-weighting within deciles
 Simulate daily holding-period returns


Cumulative Returns of Factor-Based Portfolios
January 3, 2007 to December 31, 2007


Using Tick Data, Construct Long/Short Factor Portfolios
 Same five factors
 Compute 5-minute returns from 9:30am to 4:00pm (no overnight returns)
 Simulate intra-day performance of five long/short portfolios


Proxies for Market-Making Profits NBER

What Happened To Market-Makers During August 2007?
 Simulate simpler contrarian strategy using TAQ data
– Sort stocks based on previous m-minute returns
– Put $1 long in decile 1 (losers) and $1 short in decile 10 (winners)
– Rebalance every m minutes
– Cumulate profits
 Profitability of contrarian strategy should proxy for market-making P&L
 Let m vary to measure the value of liquidity provision vs. horizons
 Greater immediacy ⇒ larger profits on average
 Positive profits suggest the presence of discretionary liquidity providers
 Negative profits suggest the absence of discretionary liquidity providers
 Given positive bid/offer spreads, on average, profits should be positive


Proxies for Market-Making Profits NBER

Cumulative m -Min Returns of Intra-Daily Contrarian Profits for Deciles 10/1 of
S&P 1500 Stocks July 2 to September 30, 2008
4.50
60 Min

4.00 30 Min
15 Min
3.50 10 Min
5 Min
3.00
Cumulative Return

2.50

2.00

1.50

1.00

0.50

0.00
7/2/07 7/11/07 7/19/07 7/27/07 8/6/07 8/14/07 8/22/07 8/30/07 9/10/07 9/18/07 9/26/07
12:00:00 12:00:00 12:00:00 12:00:00 12:00:00 12:00:00 12:00:00 12:00:00 12:00:00 12:00:00 12:00:00


August 2007: A Preview of May 2010? NBER

Profitability of Intra-Daily and Daily Strategies
Over Various Holding Period, August 1–15, 2007


NBER


Summary and
Conclusions
References
 Lo, A., 2009, “Regulatory Reform in the Wake of the Financial Crisis of 2007–2008”,
Journal of Financial Economic Policy 1, 4–43.
 Pozsar, Z., Adrian, T., Ashcraft, A. and H. Boesky, 2010, “Shadow Banking”, Federal
Reserve Bank of New York Staff Report No. 458.


Topics for Future Research NBER

 Time-varying parameters of hedge-fund returns
 Dynamic correlations, rare events, tail risk
 Funding risk, leverage, and market dislocation
 Hedge funds and the macroeconomy
 Welfare implications of hedge funds (how much is too
much liquidity?)
 Industrial organization of the hedge-fund industry
 Incentive contracts and risk-taking


Current Trends In The Industry NBER

 Hedge-fund industry has already changed dramatically
 Assets are near all-time highs again, and growing
 Registration is almost certain (majority already registered)
 Will likely have to provide more disclosure to regulators
– Leverage, positions, counterparties, etc.
 Financial Stability Oversight Council will have access
 Office of Financial Research (Treasury) will manage data
 If Volcker Rule passes, more hedge funds will be created!
 Traditional businesses will move closer to hedge funds
 Market gyrations will create more opportunities and risks
 Hedge funds will continue to be at the leading/bleeding edge


Additional References NBER
 Campbell, J., Lo, A. and C. MacKinlay, 1997, The Econometrics of Financial Markets. Princeton, NJ: Princeton
University Press.
 Chan, N., Getmansky, M., Haas, S. and A. Lo, 2005, “Systemic Risk and Hedge Funds”, to appear in M. Carey and
R. Stulz, eds., The Risks of Financial Institutions and the Financial Sector. Chicago, IL: University of Chicago Press.
 Getmansky, M., Lo, A. and I. Makarov, 2004, “An Econometric Analysis of Serial Correlation and Illiquidity in
Hedge-Fund Returns”, Journal of Financial Economics 74, 529–609.
 Getmansky, M., Lo, A. and S. Mei, 2004, “Sifting Through the Wreckage: Lessons from Recent Hedge-Fund
Liquidations”, Journal of Investment Management 2, 6–38.
 Haugh, M. and A. Lo, 2001, “Asset Allocation and Derivatives”, Quantitative Finance 1, 45–72.
 Hasanhodzic, J. and A. Lo, 2006, “Attack of the Clones”, Alpha June, 54–63.
 Hasanhodzic, J. and A. Lo, 2007, “Can Hedge-Fund Returns Be Replicated?: The Linear Case”, Journal of
Investment Management 5, 5–45.
 Khandani, A. and A. Lo, 2007, “What Happened to the Quants In August 2007?”, Journal of Investment
Management 5, 29−78.
 Khandani, A. and A. Lo, 2009, “What Happened to the Quants In August 2007?: Evidence from Factors and
Transactions Data”, to appear in Journal of Financial Markets.
 Lo, A., 1999, “The Three P’s of Total Risk Management”, Financial Analysts Journal 55, 13–26.
 Lo, A., 2001, “Risk Management for Hedge Funds: Introduction and Overview”, Financial Analysts Journal 57, 16–
33.
 Lo, A., 2002, “The Statistics of Sharpe Ratios”, Financial Analysts Journal 58, 36–50.


Additional References NBER
 Lo, A., 2004, “The Adaptive Markets Hypothesis: Market Efficiency from an Evolutionary Perspective”, Journal of
Portfolio Management 30, 15–29.
 Lo, A., 2005, The Dynamics of the Hedge Fund Industry. Charlotte, NC: CFA Institute.
 Lo, A., 2005, “Reconciling Efficient Markets with Behavioral Finance: The Adaptive Markets Hypothesis”, Journal
of Investment Consulting 7, 21–44.
 Lo, A., 2008, “Where Do Alphas Come From?: Measuring the Value of Active Investment Management”, Journal
of Investment Management 6, 1–29.
 Lo, A., 2008, Hedge Funds: An Analytic Perspective. Princeton, NJ: Princeton University Press.
 Lo, A., 2008, “Hedge Funds, Systemic Risk, and the Financial Crisis of 2007–2008: Written Testimony of Andrew
W. Lo”, Prepared for the U.S. House of Representatives Committee on Oversight and Government Reform
November 13, 2008 Hearing on Hedge Funds.
 Lo, A., 2009, “Regulatory Reform in the Wake of the Financial Crisis of 2007–2008”, to appear in Journal of
Financial Economic Regulation.
 Lo, A. and C. MacKinlay, 1999, A Non-Random Walk Down Wall Street. Princeton, NJ: Princeton University Press.
 Lo, A., Petrov, C. and M. Wierzbicki, 2003, “It's 11pm—Do You Know Where Your Liquidity Is? The Mean-
Variance-Liquidity Frontier”, Journal of Investment Management 1, 55–93.


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