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«Sergiy Gorovyy Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the ...»

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Hedge Fund Essays

Sergiy Gorovyy

Submitted in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

under the Executive Committee

of the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

UMI Number: 3507173

All rights reserved

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789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 © 2012 Sergiy Gorovyy All rights reserved ABSTRACT Hedge Fund Essays Sergiy Gorovyy This dissertation analyzes hedge fund leverage and its determinants, investigates optimal hedge fund manager behavior induced by hedge fund contracts, and uncovers an evidence of a hedge fund transparency risk premium. The first essay investigates the leverage of hedge funds in the time series and cross-section. Hedge fund leverage is found to be counter-cyclical to the leverage of listed financial intermediaries. Changes in hedge fund leverage tend to be more predictable by economy-wide factors than by fund-specific characteristics. In particular, decreases in funding costs and increases in market values both forecast increases in hedge fund leverage. Decreases in fund return volatilities predict future increases in leverage. In the second essay, I investigate hedge fund compensation from an investor's point of view in a model with a risk neutral fund manager who can continuously rebalance the fund's holdings. I solve for the optimal leverage level in a fund that has a compensation contract with a high-water mark and hurdle rate provisions where management and performance fees are paid at discrete time moments. The compensation contract induces risk-loving behavior with managers often choosing the maximum leverage. Third essay investigates risk premia associated with hedge fund transparency, liquidity, complexity, and concentration over the period from April 2006 to March 2009. Consistent with factor models of risk, we find that during normal times low-transparency, low-liquidity, and high-concentration funds delivered a return premium, with economic magnitudes of 5% to 10% per year, while during bad states of the economy, these funds experienced significantly lower returns. We also offer a novel explanation for why highly concentrated funds command a risk premium by revealing that the risk premium is mostly prevalent among non-transparent funds where investors are unaware about the exact risks they are facing and hence cannot diversify

–  –  –

Hedge Fund Leverage

1. Introduction

2. The Mechanics of Hedge Fund Leverage

2.1. Gross, Net, and Long-only Leverage

2.2. How do Hedge Funds Obtain Leverage?

2.3. Reported Hedge Fund Leverage

3. Data

3.1. Macro Data

3.2. Hedge Fund Data

3.2.1. Hedge Fund Leverage

3.2.2. Hedge Fund Returns, Volatilities, and Flows

3.3. Summary Statistics

4. Methodology

4.1. Predictive Model

4.2. Contemporaneous Model

5. Empirical Results

5.1. Time Series of Leverage

5.1.1. Gross Leverage

5.1.2. Dispersion of Gross Leverage

5.1.3. Gross vs. Net and Long-only Leverage

5.2. Macro Predictors of Hedge Fund Leverage

5.3. Fund-specific Predictors of Hedge Fund Leverage

–  –  –

5.5. Hedge Fund Leverage vs. Finance Sector Leverage

5.6. Hedge Fund vs. Finance Sector Exposure

6. Conclusions

Appendices

References

Tables

Figures

Hedge Fund Compensation

1. Introduction

2. Hedge Fund Fees

3. Model Setup

3.1. Model

3.2. Solution

3.3. Extension: Model Without Margins

3.4. Extension: Liquidation by the Investor

3.5. Extension: Liquidation by the Prime Broker

3.6. Extension: Multiple Margin States

3.7. Testable Implications

4. Costs of the High-water Mark and the Hurdle Rate Provisions

5. Conclusions

Appendices

References

–  –  –

Figures

Hedge Fund Risk Premia: Transparency, Liquidity, Complexity, and Concentration...... 99

1. Introduction

2. Data

3. Empirical Strategy

4. Results

4.1. Univariate Results

4.2. Multivariate Results

4.3. Robustness Checks

4.4. Concentration and Transparency Interactions

4.5. Hedge Fund Volatility and Flows

5. Conclusions

References

Tables

–  –  –

Essay 1: Hedge Fund Leverage

LIST OF TABLES

Margin requirements by security type Summary statistics of data Correlations of gross, net, and long-only leverage Cross-correlations of hedge fund leverage within sectors Macro predictors of hedge fund leverage Fund-specific predictors of hedge fund leverage Contemporaneous relations with gross hedge fund leverage Correlations of hedge fund and finance sector leverage A sample hedge fund risk exposure report

LIST OF FIGURES





–  –  –

Rolling 12-month hedge fund volatilities Hedge fund volatilities vs. HFR volatilities Hedge fund gross leverage Cross-sectional dispersion of gross hedge fund leverage Gross, net, and long-only hedge fund leverage Hedge fund and finance sector leverage

–  –  –

Relative gross exposures of hedge funds to investment banks and the finance sector Essay 2: Hedge Fund Compensation

LIST OF TABLES

Values of parameters used in estimations

–  –  –

Equivalent no-performance fee contracts

LIST OF FIGURES

Optimal portfolio with liquidation by the investor Optimal portfolio with liquidation by the prime broker CME margin requirements for S&P 500 futures contracts Comparison of average hedge fund leverage and an inverse of the CME margin

–  –  –

Essay 3: Hedge Fund Risk Premia: Transparency, Liquidity, Complexity, and Concentration

LIST OF TABLES

Summary statistics of data Hedge fund performance: Univariate regression results

–  –  –

Hedge fund performance: Balanced multivariate regression results Hedge fund performance: Transparency and concentration interaction results Hedge fund return volatility: Multivariate regression results Hedge fund flows: Multivariate regression results

–  –  –

Though only my name appears on the cover of this dissertation, it became possible thanks to a number of people. I am extremely grateful to all of them.

My adviser, Prof. Andrew Ang, showed me an example of hard work and dedication to financial research. He also taught me how to write high quality academic papers that I followed to the best of my abilities. I’m thankful for the numerous times he was able to proofread this dissertation in order to make it better.

I’m also grateful to Prof. Suresh Sundaresan who always had time to discuss my papers. I thank him for the advice and information provided that made “Hedge Fund Compensation” possible.

I’d like to thank also to Prof. Robert Hodrick, Greg van Inwegen, James H. Scott, and Olga Kuzmina for their help.

Most importantly, none of this would be possible without continuous support of my family and my girlfriend.

–  –  –

This dissertation is dedicated to my parents Nataliya and Oleg Gorovyy, who brought me to life and made all of this possible through their love, support, and hard work. Their contribution cannot be overestimated.

–  –  –

Abstract We investigate the leverage of hedge funds in the time series and cross-section. Hedge fund leverage is counter-cyclical to the leverage of listed financial intermediaries and decreases prior to the start of the financial crisis in mid-2007. Hedge fund leverage is lowest in early 2009 when the market leverage of investment banks is highest. Changes in hedge fund leverage tend to be more predictable by economy-wide factors than by fund-specific characteristics. In particular, decreases in funding costs and increases in market values both forecast increases in hedge fund leverage. Decreases in fund return volatilities predict future increases in leverage.

JEL Classification: G11, G18, G23, G32 Keywords: Capital structure, long-short positions, alternative investments, exposure, hedging, systemic risk ∗ We thank Viral Acharya, Tobias Adrian, Zhiguo He, Arvind Krishnamurthy, Stefan Nagel (the referee), Tano Santos, Roberto Savona, Suresh Sundaresan, and seminar participants at Columbia University, Risk USA 2010, and 3rd Annual Conference on Hedge Funds for helpful comments.

† Columbia University and NBER; Email: aa610@columbia.edu ‡ Columbia University; Email: sgorovyy14@gsb.columbia.edu § Citi Private Bank; Email: greg.vaninwegen@citi.com

1. Introduction

The events of the financial crisis over 2007–2009 have made clear the importance of leverage of financial intermediaries to both asset prices and the overall economy. The observed “deleveraging” of many listed financial institutions during this period has been the focus of many regulators and the subject of much research.1 The role of hedge funds has played a prominent role in these debates for several reasons. First, although in the recent financial turbulence no single hedge fund has caused a crisis, the issue of systemic risks inherent in hedge funds has been lurking since the failure of the hedge fund Long-Term Capital Management L.P. (LTCM) in 1998.2 Second, within the asset management industry, the hedge fund sector makes the most use of leverage. In fact, the relatively high and sophisticated use of leverage is a defining characteristic of the hedge fund industry. Third, hedge funds are large counterparties to the institutions directly overseen by regulatory authorities, especially commercial banks, investment banks, and other financial institutions which have received large infusions of capital from governments.

However, while we observe the leverage of listed financial intermediaries through periodic accounting statements and reports to regulatory authorities, little is known about hedge fund leverage despite the proposed regulations of hedge funds in the U.S. and Europe. This is because hedge funds are by their nature secretive, opaque, and have little regulatory oversight. Leverage plays a central role in hedge fund management. Many hedge funds rely on leverage to enhance returns on assets which on an unlevered basis would not be sufficiently high to attract funding. Leverage amplifies or dampens market risk and allows funds to obtain notional exposure at levels greater than their capital base. Leverage is often employed by hedge funds to target a level of return volatility desired by investors. Hedge funds use leverage to take advantage of mispricing opportunities by simultaneously buying assets which are See, for example, Adrian and Shin (2009), Brunnermeier (2009), Brunnermeier and Pedersen (2009), and He, Khang, and Krishnamurthy (2010), among many others.

Systemic risks of hedge funds are discussed by the President’s Working Group on Financial Markets (1999), Chan et al. (2007), Kambhu, Schuermann, and Stiroh (2007), Financial Stability Forum (2007), and Banque de France (2007).

perceived to be underpriced and shorting assets which are perceived to be overpriced. Hedge funds also dynamically manipulate leverage to respond to changing investment opportunity sets.

We are the first paper, to our knowledge, to formally investigate hedge fund leverage using actual leverage ratios with a unique data set from a fund-of-hedge-funds. We track hedge fund leverage in time series from December 2004 to October 2009, a period which includes the worst periods of the financial crisis from 2008 to early 2009. We characterize the crosssection of leverage: we examine the dispersion of leverage across funds and investigate the macro and fund-specific determinants of future leverage changes. We compare the leverage and exposure of hedge funds with the leverage and total assets of listed financial companies.

As well as characterizing leverage at the aggregate level, we investigate the leverage of hedge fund sectors.

The prior works on hedge fund leverage are only estimates (see, e.g., Banque de France, 2007; Lo, 2008) or rely only on static leverage ratios reported by hedge funds to the main databases. For example, leverage at a point in time is used by Schneeweis et al. (2004) to investigate the relation between hedge fund leverage and returns. Indirect estimates of hedge fund leverage are computed by McGuire and Tsatsaronis (2008) using factor regressions with time-varying betas. Even without considering the sampling error in computing time-varying factor loadings, this approach requires that the complete set of factors be correctly specified, otherwise the implied leverage estimates suffer from omitted variable bias. Regressions can also not adequately capture abrupt changes in leverage. Other work by Brunnermeier and Pedersen (2009), Gorton and Metrick (2009), Adrian and Shin (2010), and others, cites margin requirements, or haircuts, as supporting evidence of time-varying leverage taken by proprietary trading desks at investment banks and hedge funds. These margin requirements give maximum implied leverage, not the actual leverage that traders are using. In contrast, we analyze actual leverage ratios of hedge funds.



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