Regime-switching advantage in statistical arbitrage strategies conditioned on time series momentum and volatility in leveraged exchange traded funds : theory and evidence

The phenomena of volatility decay (also known as time decay) and path dependence in leveraged exchange traded funds (ETF) markets have been documented in the literature. This dissertation examined whether it is possible to exploit these market conditions for leveraged ETF (LETF) trading using statistical arbitrage (StatArb) strategies. The study proposed a regime switching model tailored for LETF markets to predict volatility and time-series momentum in the behavior of the underlying indexes of the LETFs. The study then used this model to test short pair trading strategies on a varied set of commodity LETFs to see if theoretical intuitions informed by these analyses were empirically supported by data. The study also introduced the concept of lag relative expected volatility (LREV) based on inductive learning in a binary classification framework to model upward shocks in expected volatility on any given trading day. The results of this study showed that an active short pair trading strategy in commodity LETFs, conditioned on momentum and volatility, outperforms an unconditioned and passive sell-and-hold StatArb trading strategy on a risk-adjusted basis. This outperformance was, REGIME-SWITCHING IN LEVERAGED ETF STATARB v however, found to be present in Sortino ratios only. The study did not find any evidence of outperformance for the active trading strategy in either Sharpe ratios or absolute returns. The results also provided further evidence that LETFs tracking equity indexes are poor candidates for active StatArb trading strategies due to low volatility. Further, the results also indicated that any incremental deterioration in the efficiency of LETF products in rapidly fluctuating markets appears to be mostly attributable to systemic jumps in the implied volatility and less due to any incremental inefficiency in their daily rebalancing process. This finding may be of interest to the regulators. Lastly, the study also provided evidence from the LETF markets for an inverse relationship between volatility and momentum, as established in some recent studies. REGIME-SWITCHING IN LEVERAGED ETF STATARB vi TABLE OF CONTENTS ACKNOWLEDGEMENTS . ii LIST OF TABLES . x LIST OF FIGURES . xi Regime-switching Advantage in Statistical Arbitrage Strategies Conditioned on Time Series Momentum and Volatility in Leveraged Exchange Traded Funds: Theory and Evidence . 1 Motivation . 1 Problem Statement . 2 Research Questions . 3 Hypotheses . 4 Contribution . 5 Leveraged Exchange Traded Funds and Sample Periods . 6 Findings . 6 Literature Review. 9 Time Decay and Path-Dependence of Leveraged ETFs . 9 Leveraged Exchange Traded Funds Return Predictability vis-à-vis Return Predictability in Exchange Traded Funds and Commodities . 12 Market Efficiency . 14 A Regime-Switching Framework for Leveraged Exchange Traded Funds . 18 REGIME-SWITCHING IN LEVERAGED ETF STATARB vii TABLE OF CONTENTS (CONT.) Modeling Trading Strategies Based on Leveraged Exchange Traded Funds Regime-Switching . 18 Econometric Operationalization of Leveraged Exchange Traded Funds Market RegimeSwitching . 19 Trading Strategies . 22 Robustness Check for Momentum Detector used in Variant 1 of Volatility Short Momentum Neutral Trading Strategy . 24 Robustness Check for Variant 1 of Volatility Short Momentum Neutral Trading Strategy 25 Selection of Leveraged Exchange Traded Funds Industry Sectors . 25 Selection of Trading Signal . 26 Volatility Forecasting Models . 27 Seasonal Random Walk -SRW . 27 Implied VolatilityIV . 28 Simple Moving Average-SMA . 28 Exponentially Weighted Moving Average-EWMA . 28 Autoregressive Integrated Moving AverageARIMA (0,1,0) . 29 Generalized Autoregressive Conditional HeteroscedasticityGARCH (p,q) . 30 Loss Functions for Model Selection . 31 Calculation of Realized Volatility used in Volatility Forecasting Models . 31 Calculation of Forecasting Errors for Model Selection . 32 REGIME-SWITCHING IN LEVERAGED ETF STATARB viii TABLE OF CONTENTS (CONT.) Out-of-Sample Data for Calculation of Forecasting Errors . 33 Commission Cost Model . 34 Slippage Model . 34 Sharpe Ratio . 36 Sortino Ratio . 36 Assumptions about the Minimal Acceptable Return for the Sortino Ratio. 36 Relevance and Efficacy of the Sortino Ratio as a Performance Measure . 37 Assumptions about the Risk-Free Rate . 38 Derivation of the Theoretical Compound Annual Growth Rate . 38 Portfolio Net Asset Value . 39 The t Test and z Test . 41 Number of Periods Test. 41 Results . 52 The t Value and z Score Tables . 52 Results for Hypotheses Verification . 64 Hypothesis: H1a . 64 Hypothesis: H1b . 65 Hypothesis: H2 . 67 Hypothesis: H3 . 68 REGIME-SWITCHING IN LEVERAGED ETF STATARB ix TABLE OF CONTENTS (CONT.) Results for Robustness Checks . 70 Appendix A . 87 Appendix B . 95 REGIME-SWITCHING IN LEVERAGED ETF STATARB x LIST OF TABLES Table Page Table 1 .