The Application of Volatility related Exchange Traded Products as Instruments for Volatility Hedging

Contents

1 Abstract

2 Introduction

3 Main Part

3.1 Volatility Basics

3.1.1 Types of Volatility

3.1.1.1 Historical Volatility (=Simple Volatility)

3.1.1.1.1 Introduction and Data Quality

3.1.1.1.2 Standard Deviation as Measurement of Volatility

3.1.1.1.3 Daily Returns as Basis

3.1.1.1.3.1 Discrete Returns

3.1.1.1.3.2 Constant (Log)-Returns

3.1.1.1.3.2.1 The Math behind It

3.1.1.1.3.2.2 From Log Returns and the Central Limit Theorem

3.1.1.1.3.2.3 Brownian Motion and Random Walk

3.1.1.1.4 Study of Time Series and Empirical Distributions

3.1.1.1.4.1 Augmented Dickey-Fuller Test for Stationarity

3.1.1.1.4.2 Kurtosis Analysis

3.1.1.1.4.3 Skewness Analysis

3.1.1.1.4.4 Jarque-Bera Test and Analysis Summary

3.1.1.1.5 Explanatory Power of Historical Volatilities

3.1.1.1.6 Alternative Approaches

3.1.1.1.6.1 Exponentially Weighted Moving Average

3.1.1.1.6.2 Generalized Autoregressive Conditional Heteroscedasticity

3.1.1.2 Implied Volatility

3.1.1.2.1 From the Binomial Tree to the Black-Scholes Model

3.1.1.2.2 The Basics of Options

3.1.1.2.3 The Black-Scholes Model

3.1.1.2.3.1 Introduction to the Black-Scholes Model

3.1.1.2.3.1.1 Model Assumptions

3.1.1.2.3.1.2 The Black-Scholes Formula

3.1.1.2.3.1.3 The Greeks

3.1.1.2.3.1.3.1 Delta (Δ)

3.1.1.2.3.1.3.1.1 Delta-Volatility Dynamics

3.1.1.2.3.1.3.1.2 Gamma (Γ)

3.1.1.2.3.1.3.2 Theta (ϴ)

3.1.1.2.3.1.3.3 Rho (p)

3.1.1.2.3.1.3.4 Vega (v)

3.1.1.2.3.1.4 Discussion of the Model

3.1.1.2.3.1.4.1 Volatility Smiles

3.1.1.2.3.1.4.2 Explanations for the Existence of Volatility Smiles

3.1.1.2.3.1.5 Modifications of the Black-Scholes Model

3.1.1.2.4 Calculation of Implied Volatility using the Black-Scholes Formula

3.1.1.2.5 Explanatory Power of Implied Volatilities vs. Historical Volatility

3.1.2 Chapter Summary

3.2 The Chicago Board Options Exchange (CBOE) Volatility Index (VIX)

3.2.1 History of the VIX

3.2.2 Importance of the VIX

3.2.3 The VIX in Detail

3.2.3.1 Methodology of Calculating the VIX

3.2.3.2 VIX Futures & Options

3.2.3.3 Average Daily Trading Volumes since 2006

3.2.3.4 VIX Dynamics

3.2.3.4.1 Correlation VIX vs. S&P500

3.2.3.4.2 Historical Volatility S&P500 vs. VIX and Variance Risk Premiums

3.2.3.4.3 Volatility of Volatility

3.2.3.4.4 Volume and Volatility

3.2.3.4.5 Distribution of Volatility

3.2.3.4.6 Asymmetric Volatility Phenomenon

3.2.4 Chapter Summary

3.3 Volatility Related Financial Instruments

3.3.1 Options based Strategies on Volatility

3.3.1.1 Butterfly Spread

3.3.1.2 Straddle

3.3.2 Variance Swaps

3.3.3 Volatility Related Exchange Traded Products

3.3.4 Volatility Related Exchange Traded Notes & Exchange Traded Funds

3.3.4.1 Introduction to VIX ETPs

3.3.4.1.1 Structure of ETPs in General

3.3.4.1.2 The S&P500 VIX Short-Term Futures TR Index

3.3.5 Chapter Summary

3.4 Case Study – Implementation of Volatility ETPs for Volatility Hedging

3.4.1 Construction and Purpose of the Study

3.4.2 Spread, Liquidity and Cost Analysis

3.4.2.1 Spread Analysis

3.4.2.2 Volume Analysis

3.4.2.3 Cost Analysis

3.4.2.4 Differences between ETNs and ETFs

3.4.3 Behavior of VXX and the VIX Futures Term Structure

3.4.3.1 Contango/Backwardation Induced VXX Performance (VIX as Benchmark)

3.4.3.2 Front-Term VIX Futures ETPs vs. Mid-Term VIX Futures ETPs

3.4.4 Hedge-Efficiency Analysis

3.4.4.1 Defining the Hedging Objective

3.4.4.2 Defining the Strategy and Necessary Assumptions

3.4.4.3 Considerations regarding Correlation Dynamics

3.4.4.4 Event Driven Hedge-Efficiency Analysis

3.4.4.4.1 Regression Analysis October 2014

3.4.4.4.2 Regression Analysis December 2014

3.4.4.5 Mean Reversion of Volatility

3.4.4.6 Overall Portfolio Impact of VXX/VIX Portions

3.4.4.6.1 S&P500 + VXX/VIX Portfolio Analysis

3.4.4.6.2 Interpretation of the Findings and Optimization of VXX/VIX Portions

3.4.5 Study Summary

3.5 VBA Solution for Volatility ETP Analyses

3.5.1 Aim of the Tool

3.5.2 Implementation

3.5.3 User Guide

3.5.4 Potential Drawbacks and Further Development

4 Conclusion

Objectives and Research Questions

The thesis aims to analyze stock market volatility as an asset class and investigate the efficiency of using volatility-linked Exchange Traded Products (ETPs) as hedging instruments. The primary research question is: "How efficient are volatility hedges through volatility-linked ETPs, compared to hedges through the VIX?"

• Theoretical fundamentals of volatility and its measurement.
• Comprehensive introduction to the VIX index and its dynamics.
• Structure, price behavior, and characteristics of volatility-linked ETPs.
• Empirical case study on the effectiveness of VXX/VIX for hedging market drawdowns.
• Development of a VBA-based analysis tool for volatility ETP evaluation.

Book Excerpt

Summary of Chapters

3. Volatility Basics: This chapter establishes the mathematical foundation of volatility by explaining historical volatility models and the theoretical framework of the Black-Scholes model for implied volatility.

3.2 The Chicago Board Options Exchange (CBOE) Volatility Index (VIX): The VIX is introduced as the market standard for measuring volatility, detailing its calculation methodology and dynamics in relation to the S&P 500.

3.3 Volatility Related Financial Instruments: This section covers derivatives like options and variance swaps before introducing ETPs as accessible instruments for non-professional investors.

3.4 Case Study – Implementation of Volatility ETPs for Volatility Hedging: This practical chapter analyzes the spread, liquidity, and cost efficiency of various ETPs and demonstrates their effectiveness in real market scenarios.

3.5 VBA Solution for Volatility ETP Analyses: The final chapter presents a custom-built VBA tool designed to automate statistical analysis and performance tracking for various volatility ETPs.

Keywords

Volatility, VIX, ETPs, Hedging, Black-Scholes Model, S&P 500, Variance Risk Premium, VBA, Financial Derivatives, Portfolio Management, Market Fear, Backtesting, Correlation, Contango, Backwardation.

Frequently Asked Questions

What is the core focus of this thesis?

The thesis investigates the utility and efficiency of using volatility-linked Exchange Traded Products (ETPs) as hedging tools for portfolio management against stock market drawdowns.

What are the primary themes discussed in the paper?

The paper covers the statistical foundations of volatility, the importance of the VIX index, the structure of ETPs, and practical case studies evaluating hedging efficiency and portfolio impact.

What is the main research question of this study?

The central question is: "How efficient are volatility hedges through volatility-linked ETPs, compared to hedges through the VIX?"

Which methodology does the author employ?

The author uses empirical market analysis of historical data, including statistical tests like the Augmented Dickey-Fuller test, regression analysis for hedge effectiveness, and the development of a custom VBA tool for data processing.

What does the main part of the thesis cover?

The main part encompasses the mathematical theory of volatility, a deep dive into the VIX index mechanics, an overview of available volatility instruments, and an extensive case study on implementation.

Which keywords characterize the work?

The core keywords include Volatility, VIX, ETPs, Hedging, S&P 500, and Portfolio Management.

How does the VIX futures term structure influence ETP performance?

The term structure, specifically contango and backwardation, significantly impacts performance. Contango often causes "rolling losses" for long ETP positions, making them less efficient for long-term holds.

What findings did the author regarding the inclusion of VIX versus VXX?

The case study found that including VIX in a portfolio could increase the Sharpe ratio and reduce volatility effectively, whereas VXX often performed poorly due to rolling costs.

Is the VBA tool provided in the thesis publicly usable?

Yes, the thesis provides a complete VBA solution (found in Appendix II) which allows users to automate volatility ETP analysis using free data from Yahoo Finance.