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Convertible Arbitrage: Risk, Return and Performance

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Convertible Arbitrage: Risk, Return and Performance Convertible arbitrage: risk, return and performance by Mark C. Hutchinson BSc MSc Thesis subm itted for the degree of D octor o f Philosophy January 2006 Supervisor: Professor Liam Gallagher D C U Business School, D ublin City University I hereby certify that this material, which I now submit for assessment on the programme of study leading to the award of Doctor of Philosophy is entirely m y own work and has not been taken from the work of others save and to the extent that such work has been cited and acknowledged within the text of mv work. ID No.: 53148126 2 T a b le o f c o n te n ts Table o f co n te n ts ............................................................................................................................. 3 A b s tra c t...............................................................................................................................................8 A cknow ledgem ents..........................................................................................................................9 Index o f tables..................................................................................................................................11 Index o f fig u re s ...............................................................................................................................14 C h a p te r 1: In tro d u c tio n ......................................................................................................... 15 1.1 Intro d u ctio n ..................................................................................................................... 15 1.2 D e fin itio n o f hedge fu n d s ......................... ...................................................................18 1.3 Hedge fund trading styles.................................................................... ....................... 20 1.4 Strategy returns............................................................................................... ..............26 1.5 The structure o f the thesis............................................................................................ 28 1.6 The research objectives....... .........................................................................................29 1.6.1 Construction and evaluation of a simulated convertible arbitrage portfolio (Chapter 3 ) .................................................................................................................................30 1.6.2 Identification and estimation of convertible arbitrage benchmark risk factors (Chapter 4 ) ................................................................................................................... 31 1.6.3 Identification and estimation of individual convertible arbitrage hedge fund risk and return (Chapter 5 )............................................................................................ 32 1.6.4 Identification and estimation of non-linearity in the relationship between convertible arbitrage index returns and risk factors (Chapter 7).....................................33 1.6.5 Robust estimation of convertible arbitrage risk factors and evaluation of third and fourth moment risk factors (Chapter 9 ) ............................................................. 34 1.7 Innovation o f this study.................................................................................................35 1.8 C onclusion....................................................................................................... ............37 Chapter 2: Convertible arbitrage and related hedge fund literature: A review ..... 38 2.1 Intro d u ctio n ........ ........................................................................................................... 38 2.2 Convertible arbitrage..................................................................................................... 40 2.3 Hedge fund lite ra tu re ....................................................................................................42 3 2.3.1 Biases in hedge fund data.....................................................................................43 2.3.2 Statistical properties of hedge funds ................................................................. 44 2.3.2.1 Skewness and kurtosis ......... 44 2.3.2.2 Serial correlation...............................................................................................45 2.3.3 Hedge fund performance evaluation models.................................................... 51 2.3.3.1 Performance indicator studies..........................................................................51 2.3.3.2 Linear normal factor model studies...............................................................53 2.3.3.3 Linear non-normal factor model studies...................................................... 55 2.3.3.4 Non-norm al studies..........................................................................................59 2.3.3.5 Performance persistence studies.....................................................................61 2.3.4 Convertible arbitrage hedge fund lite ra tu re ..................................................... 62 2.4 C onclusion.......................................................................................................................64 Chapter 3: Convertible bond arbitrage portfolio simulation and analysis of daily re tu rn s .............................................................................................................................................. 66 3.1 Introduction..................................................................................................................... 66 3.2 Description of a convertible bond arbitrage position and portfolio construction 68 3.3 Out o f sample com parison............................................................................................80 3.4 M arket model regressions............................................................................................ 88 3.5 C onclusion.......................................................................................................................96 3.6 Lim itations o f this analysis.......................................................................................... 97 3.6.1 O m itted variables...................................................................................................98 3.6.2 Specifying a linear m odel fo r non-linear data..................................................98 3.6.3 Beta estimation under thin tra d in g .....................................................................99 3.6.4 V o la tility .............................................................................................................. 100 3.6.5 Transaction costs and the analysis of convertible bond undervaluation 101 C h a p te r 3 A p p e n d ix: O rd in a ry Least Squares E s tim a tio n ..........................................102 Chapter 4: A m ulti-factor analysis of the risks in convertible arbitrage indices... 109 4.1 Introduction ................................................................................................................109 4.2 D a ta ...............................................................................................................................I l l 4 4.3 R isk factor m o d e ls...................................................................................................... 114 4.4 Analysis o f the hedge fund in d ice s.......................................................................... 127 4.4.1 Hypothesis to explain the observed autocorrelation....................................127 4.4.2 Univariate analysis..............................................................................................130 4.4.3 Specifying lagged hedge fund returns as a risk factor.................................! 35 4.5 Convertible bond arbitrage risk fa c to r.....................................................................139 4.6 Results o f the convertible arbitrage factor models................................................ 144 4.7 Robustness: Estimating the linear model in sub-samples ranked and subdivided by tim e and risk fa cto rs....................................................................................148 4.8 Conclusions................................................................................................................... 159 4.9 Lim itations o f this analysis......................................................................................160 4.9.1 Addressing potential non-linearity in the relationships..............................160 4.9.2 D istribution o f the factor model residuals......................................................160 Chapter 5: The risk and return of convertible arbitrage hedge funds: a multi-factor a n a lysis......................................................................................................................................... 162 5.1 In tro d u ctio n ...................................................................................................................162 5.2 D a ta ................................................................................................................................ 164 5.3 Individual fund empirical results............................................................................. 166 5.3 Results of regressions incorporating lags of the risk factors............................... 171 5.4 Fund
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