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Portfolio selection and hedge funds : linearity, heteroscedasticity, autocorrelation and tail-risk

By Robert John Bianchi


Portfolio selection has a long tradition in financial economics and plays an integral role in investment management. Portfolio selection provides the framework to determine optimal portfolio choice from a universe of available investments. However, the asset weightings from portfolio selection are optimal only if the empirical characteristics of asset returns do not violate the portfolio selection model assumptions. This thesis explores the empirical characteristics of traditional assets and hedge fund returns and examines their effects on the assumptions of linearity-in-the-mean testing and portfolio selection. The encompassing theme of this thesis is the empirical interplay between traditional assets and hedge fund returns. Despite the paucity of hedge fund research, pension funds continue to increase their portfolio allocations to global hedge funds in an effort to pursue higher risk-adjusted returns. This thesis presents three empirical studies which provide positive insights into the relationships between traditional assets and hedge fund returns. The first two empirical studies examine an emerging body of literature which suggests that the relationship between traditional assets and hedge fund returns is non-linear. For mean-variance investors, non-linear asset returns are problematic as they do not satisfy the assumption of linearity required for the covariance matrix in portfolio selection. To examine the linearity assumption as it relates to a mean-variance investor, a hypothesis test approach is employed which investigates the linearity-in-the-mean of traditional assets and hedge funds. The findings from the first two empirical studies reveal that conventional linearity-in-the-mean tests incorrectly conclude that asset returns are nonlinear. We demonstrate that the empirical characteristics of heteroscedasticity and autocorrelation in asset returns are the primary sources of test mis-specification in these linearity-in-the-mean hypothesis tests. To address this problem, an innovative approach is proposed to control heteroscedasticity and autocorrelation in the underlying tests and it is shown that traditional assets and hedge funds are indeed linear-in-the-mean. The third and final study of this thesis explores traditional assets and hedge funds in a portfolio selection framework. Following the theme of the previous two studies, the effects of heteroscedasticity and autocorrelation are examined in the portfolio selection context. The characteristics of serial correlation in bond and hedge fund returns are shown to cause a downward bias in the second sample moment. This thesis proposes two methods to control for this effect and it is shown that autocorrelation induces an overallocation to bonds and hedge funds. Whilst heteroscedasticity cannot be directly examined in portfolio selection, empirical evidence suggests that heteroscedastic events (such as those that occurred in August 1998) translate into the empirical feature known as tail-risk. The effects of tail-risk are examined by comparing the portfolio decisions of mean-variance analysis (MVA) versus mean-conditional value at risk (M-CVaR) investors. The findings reveal that the volatility of returns in a MVA portfolio decreases when hedge funds are included in the investment opportunity set. However, the reduction in the volatility of portfolio returns comes at a cost of undesirable third and fourth moments. Furthermore, it is shown that investors with M-CVaR preferences exhibit a decreasing demand for hedge funds as their aversion for tail-risk increases. The results of the thesis highlight the sensitivities of linearity tests and portfolio selection to the empirical features of heteroscedasticity, autocorrelation and tail-risk. This thesis contributes to the literature by providing refinements to these frameworks which allow improved inferences to be made when hedge funds are examined in linearity and portfolio selection settings

Topics: autocorrelation, conditional value at risk (CVaR), heteroscedasticity, heteroscedasticity and autocorrelation consistent (HAC), linearity, mean-conditional value at risk (M-CVaR), mean-value at risk (M-VaR), mean variance analysis (MVA), modern portfolio theory (MPT), portfolio selection, tail-risk, value at risk (VaR), ODTA
Publisher: Queensland University of Technology
Year: 2007
OAI identifier:

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  1. 1965a, Portfolio analysis in a stable paretian market,
  2. 1965b, The behaviour of stock market prices,
  3. (1983). A characterization of the distributions that imply mean-variance utility functions,
  4. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity,
  5. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle,
  6. (1997). A nonparametric model of term structure dynamics and the market price of interest rate risk,
  7. (1974). A note on the implications of quadratic utility for portfolio theory,
  8. (1981). A possible explanation of the small firm effect,
  9. (1987). A simple positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix,
  10. (1963). A simplified model for portfolio selection,
  11. (1987). A test for independence based on the correlation dimension, unpublished paper,
  12. (1987). A test for normality of observations and regression residuals,
  13. (1999). A transactions data analysis of nonsynchronous trading,
  14. (1985). A Tukey non-additivity type test for time series nonlinearity,
  15. (1962). Admissibility and measurable utility functions,
  16. (1996). Against The Gods,
  17. (2002). An analysis of hedge fund performance using loess fit regression,
  18. (1990). An econometric analysis of nonsynchronous-trading,
  19. (2004). An econometric model of serial correlation and illiquidity in hedge fund returns,
  20. (1986). An empirical Bayes approach to portfolio selection,
  21. (2002). An excursion into the statistical properties of hedge fund returns, Working paper,
  22. (1963). An expected gain-confidence limit criterion for portfolio selection,
  23. (1984). An Introduction to Bispectral Analysis and Bilinear Time Series Models,
  24. (2002). Analysis of Financial Time Series,
  25. (2004). Analysis of hedge fund performance,
  26. (1992). ARCH modeling in finance: A review of the theory and empirical evidence,
  27. (1991). Asset allocation in a downside risk framework,
  28. (1991). Asset allocation under shortfall constraints,
  29. (1992). Asset allocation: Management style and performance measurement.”
  30. (2007). Australian Prudential Regulation Authority (APRA),
  31. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation,
  32. (2003). Basle Committee of Banking Supervision,
  33. (2002). Battle for alphas: Hedge funds versus long-only portfolios,
  34. (1986). Bayes-stein estimation for portfolio analysis,
  35. (1991). Bayesian and CAPM estimators of the means: Implications for portfolio selection,
  36. (2000). Bayesian portfolio selection: An empirical analysis of the S&P 500 Index 1970-1996,
  37. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk,
  38. (1971). Capital growth and the mean-variance approach to portfolio selection,
  39. (1977). Capital market equilibrium in a mean, lower partial moment framework,
  40. (1972). Capital market equilibrium with restricted borrowing,
  41. (1991). Chaos and non-linear dynamics: Application to financial markets,
  42. (2001). Characteristics of risk and return in risk arbitrage,
  43. (1993). Common risk factors in the returns on bonds and stocks,
  44. (2005). Computing implied returns in a meaningful way,
  45. (2002). Conditional value at risk for general loss distributions,
  46. (1999). Correlation and dependence properties in risk management: Properties and pitfalls,
  47. (1959). Criteria for choice among risky ventures,
  48. (2002). CVaR models for selective hedging for international asset allocation,
  49. (1983). Diagnostic checking ARMA time series models using squared-residual autocorrelations,
  50. (2006). Dissecting some recent empirical non-linear real exchange rate models, Working Paper,
  51. (2001). Do hedge funds hedge?,
  52. (2006). Downside risk in practice,
  53. (1992). Dynamic equilibrium and the real exchange rate in a spatially separated world,
  54. (2000). Econometric Analysis, 4 th edition,
  55. (2002). Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis,
  56. (1998). Efficient Asset Management,
  57. (2006). Efficient fund of hedge funds under downside risk measures,
  58. (1997). Empirical characteristics of dynamic trading strategies: The case of hedge funds,
  59. (1966). Equilibrium in a capital asset market,
  60. (1993). Estimating market values from appraised values without assuming an efficient market,
  61. (1973). Estimating the dependence structure of share prices,
  62. (2001). Estimating the number of clusters in a data set via the gap statistic,
  63. (1981). Estimation for Markowitz efficient portfolios,
  64. (1961). Estimation with quadratic loss,
  65. (1988). Exchange rate uncertainty, forward contracts, and international portfolio selection,
  66. (2004). Extreme value dependence in financial markets: Diagnostics, models, and financial implications,
  67. (2005). Fat-tail risk in portfolios of hedge funds and Traditional Investments, in Hedge Funds: Insights in Performance Measurement, Risk Analysis and Portfolio Allocation, by
  68. (1986). Generalized autoregressive conditional heteroskedasticity,
  69. (1969). Geometric mean approximations of individual security and portfolio performance,
  70. (1992). Global portfolio optimization,
  71. (1999). Global stock markets in the twentieth century,
  72. (2002). Handbook of Alternative Assets,
  73. (2004). Hedge fund benchmarks: A risk based approach,
  74. (2005). Hedge fund data biases
  75. (2007). Hedge Fund Industry Asset Flow and Trends Report
  76. (2001). Hedge fund performance and manager skill,
  77. (2001). Hedge fund performance: 1990-1999,
  78. (2007). Hedge fund portfolio construction: A comparison of static and dynamic approaches,
  79. (2006). Hedge fund risk factors and the value at risk of fixed income strategies,
  80. (2004). Hedge fund risk factors with option like structures: Examples and explanations,
  81. (2006). Hedge fund style analysis with the gap statistic, Working Paper,
  82. (2001). Hedge funds – A new asset class or just a change in perspective, Alternative Investment Management Association (AIMA),
  83. (2002). Hedge funds and hope,
  84. (2000). Hedge Funds and Managed Futures, Verlag Paul Haupt,
  85. (2003). Hedge funds revisited: Distributional characteristics, dependence structure and diversification,
  86. (1999). Hedge funds versus managed futures as asset classes,
  87. (2003). Hedge funds with style,
  88. (2004). Hedge Funds: Quantitative Insights,
  89. (2005). Hedge funds: Risk and returns,
  90. (2000). Hedge funds: The living and the dead,
  91. (2004). Honey, I shrunk the covariance matrix,
  92. (1979). Improved estimation for Markowitz efficient portfolios using James-Stein type estimators,
  93. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection,
  94. (1955). Inadmissibility of the usual estimator of the mean of a multivariate normal distribution,
  95. (1970). Increasing risk I: A definition,
  96. (1985). International portfolio diversification with estimation risk,
  97. (1983). J.M. Keynes’s investment performance: A note,
  98. (1969). Lifetime portfolio selection by dynamic stochastic programming,
  99. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case,
  100. (1995). Market frictions and consumption based asset pricing,
  101. (2006). Master funds in portfolio analysis with general deviation measures,
  102. (1977). Mean-risk analysis with risk associated with below-target returns,
  103. (1994). Measuring investment risk: A review,
  104. (2006). Minimizing CVaR and VaR for a portfolio of derivatives,
  105. (1998). Modelling economic relationships with smooth transition regressions,
  106. (1993). Modelling Nonlinear Economic Relationships,
  107. (2006). Mutual fund dilution from market timing trades,
  108. (1997). Mutual fund styles,
  109. (1988). Non-Linear and Non-Stationary Time Series Analysis,
  110. (1999). Non-linear dependence in stock returns: Does trading frequency matter?,
  111. (1989). Non-linear dynamics and stock returns,
  112. (2005). Non-linear dynamics in international stock market returns,
  113. (2004). Non-linear predictability of value and growth stocks and economic activity,
  114. (1986). Non-linearity tests for time series,
  115. (2001). Nonlinear adjustment in real exchange rates: Towards a solution to the purchasing power parity puzzles,
  116. (2000). Nonlinear adjustment, long-run equilibrium and exchange rate fundamentals,
  117. (2003). Nonlinear mean reversion in the short term interest rate,
  118. (1997). Nonlinearities in the relation between the equity risk premium and the term structure,
  119. (1987). Nonsynchronous data and the covariance factor structure of returns,
  120. (1987). Nonsynchronous security trading and market index autocorrelation,
  121. (1999). Offshore hedge funds: Survival and performance, 1989-95,
  122. (1980). On estimating the expected return on the market,
  123. (1997). On persistence of mutual fund performance,
  124. (2002). On the coherence of expected shortfall,
  125. (1980). On the direction of preference for moments of higher order than the variance,
  126. (1991). On the frequency of large stock returns: Putting booms and busts into perspective,
  127. (2001). On the perils of financial intermediaries setting security prices: The mutual fund wild card option,
  128. (1996). On the use and misuse of downside risk,
  129. (1970). Optimal growth portfolios when yields are serially correlated,
  130. (2005). Optimal hedge fund allocations,
  131. (1968). Optimal multiperiod portfolio choices,
  132. (1976). Optimal portfolio choice under uncertainty: A Bayesian approach,
  133. (2001). Optimal portfolio selection in a value-at-risk framework,
  134. (1975). Optimal rules for ordering uncertain prospects,
  135. (2000). Optimization of conditional value at risk,
  136. (2002). Partial adjustment or stale prices? Implications from stock index and futures return autocorrelations,
  137. (2000). Performance characteristics of hedge funds and CTA funds: Natural versus spurious biases,
  138. (2000). Pioneering Portfolio Management,
  139. (1998). Pitfalls and opportunities in the use of extreme value theory in risk management, Financial institutions
  140. (1977). Portfolio choice and equilibrium in capital markets with safety-first investors,
  141. (2002). Portfolio Construction and Risk Budgeting, Risk Books,
  142. (2005). Portfolio Management with Heuristic Optimization,
  143. (2002). Portfolio optimization with conditional value at risk objective and constraints,
  144. (1989). Portfolio optimization with shortfall constraints: A confidence limit approach to managing downside risk,
  145. (2000). Portfolio selection with limited downside risk,
  146. (1952). Portfolio selection,
  147. (1959). Portfolio Selection: Efficient Diversification of Investment,
  148. (1982). Potential performance and tests of portfolio efficiency,
  149. (1993). Power of the neural network linearity test,
  150. (1999). President’s Working Group on Financial Market,
  151. (1987). Professionally managed, publicly traded commodity funds,
  152. (1987). Property portfolio allocation: a multi-factor model,
  153. (1981). Putting Markowitz theory to work,
  154. (1983). Regression, prediction and shrinkage,
  155. (1991). Returns and volatility of low-grade bonds 1977-1989,
  156. (1964). Risk aversion in the small and in the large,
  157. (2002). Risk in fixed-income hedge fund styles,
  158. (2002). Risk management for hedge fund portfolios,
  159. (2001). Risk management for hedge funds: introduction and overview,
  160. (1979). Risk measurement when shares are subject to infrequent trading,
  161. (2003). Risk reduction in large portfolios: Why imposing the wrong constraints helps,
  162. (2004). Risks and portfolio decisions involving hedge funds,
  163. (1994). Role of hedge funds: International capital markets. Developments, prospects and policy issues, September,
  164. (1969). Rules for ordering uncertain prospects,
  165. (1955). Safety first and hedging,
  166. (1952). Safety first and the holding of assets,
  167. (1978). Safety-first, stochastic dominance, and optimal portfolio choice,
  168. (1965). Security prices, risk and maximal gains from diversification,
  169. (1974). Semi-variance and stochastic dominance: A comparison,
  170. (1991). Smoothing in appraisal based returns,
  171. (1947). Some consequences when the assumptions for the analysis of variance are not satisfied,
  172. (1966). Some new stock market indices,
  173. (1994). Specification, estimation and evaluation of smooth transition autoregressive models,
  174. (2002). Spectral measures of risk: A coherent representation of subjective risk aversion,
  175. (1977). Stein’s paradox in statistics,
  176. (1988). Stock market prices do not follow random walks: Evidence from a simple specification test,
  177. (2003). Stocks, bonds and hedge funds,
  178. (1993). Strategies for modeling nonlinear time-series relationships,
  179. (1997). Survivorship bias and investment style in the returns of CTAs,
  180. (2002). Tail estimation and mean-VaR portfolio selection in markets subject to financial instability,
  181. (1996). Testing continuous time models of the spot interest rate,
  182. (1982). Testing for gaussianity and linearity of a stationary time series,
  183. (1993). Testing for neglected non-linearity in time series models: A comparison of neural networks and alternative tests,
  184. (1969). Tests for specification errors in classical linear least-squares regression,
  185. (1976). The arbitrage theory of capital asset pricing,
  186. (1947). The assumptions underlying the analysis of variance,
  187. (1999). The behaviour of some UK equity indices: An application of Hurst and BDS test,
  188. (1992). The cross-section of expected stock returns,
  189. (1972). The distribution of stock returns,
  190. (1997). The Econometrics of Financial Markets,
  191. (1993). The effect of errors in means, variances and covariances on optimal portfolio choice,
  192. (1979). The effect of estimation risk on capital market equilibrium,
  193. (1976). The effect of estimation risk on optimal portfolio choice,
  194. (1998). The efficacy of neural networks in predicting returns on stock and bond indices,
  195. (1969). The efficiency analysis of choices involving risk,
  196. (1995). The exchange rate in the presence of transaction costs: Implications for test of purchasing power parity,
  197. (1996). The financial performance of low-grade municipal bond funds,
  198. (1966). The Jones nobody keeps up with, Fortune Magazine,
  199. (1997). The limits of arbitrage,
  200. (1989). The Markowitz optimization enigma: Is optimized optimal?,
  201. (1983). The potential role of managed commodity financial futures accounts (and/or funds) in portfolios of stocks and bonds. Paper presented at the annual conference of the Financial Analysts Federation,
  202. (1973). The pricing of options and corporate liabilities,
  203. (2002). The random walk hypothesis in the emerging Indian stock market,
  204. (1987). The relevance of the distributional form of common stock returns to the construction of optimal portfolios,
  205. (2001). The risk in hedge fund strategies: Theory and evidence from trend followers,
  206. (1999). The sampling error in estimates of mean-variance efficient portfolio weights,
  207. (2002). The statistical properties of hedge fund index returns and their implications for investors,
  208. (2002). The statistics of sharpe ratios,
  209. (2003). The Stochastic Programming Approach to Asset, Liability and Wealth Management,
  210. (2006). The term structure of the risk-return trade-off,
  211. (1947). The use of transformations,
  212. (1970). Third degree stochastic dominance,
  213. (1995). Time-varying expected returns in international bond markets,
  214. (2006). Tremont Asset Flows Report-Third Quarter 2006, Tremont Capital Management, Corporate Center at Rye, 555 Theodore Fremd Avenue,
  215. (2001). Value-at-risk based risk management: Optimal policies and asset prices,
  216. (2006). World Federation of Exchanges,

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