Hedging performance of multiscale hedge ratios

• Published date: 01 December 2019
• Author: Mohammad Hasan,Antonios K. Alexandridis,Xuxi Guo,Jahangir Sultan
• Date: 01 December 2019
• DOI: http://doi.org/10.1002/fut.22047

J Futures Markets. 2019;39:1613–1632. wileyonlinelibrary.com/journal/fut © 2019 Wiley Periodicals, Inc.

|

1613

Received: 17 March 2018

|

Accepted: 20 July 2019

DOI: 10.1002/fut.22047

RESEARCH ARTICLE

Hedging performance of multiscale hedge ratios

Jahangir Sultan

1

|

Antonios K. Alexandridis

2

|

Mohammad Hasan

2

|

Xuxi Guo

3

1

Department of Finance, Bentley

University, Waltham, Massachusetts

2

Finance group, Kent Business School,

University of Kent, Canterbury, Kent, UK

3

Department of Finance, Georgia State

University, Atlanta, Georgia

Correspondence

Antonios K. Alexandridis, Kent Business

School, University of Kent, Room 336,

Sibson Building, Canterbury CT2 7FS,

Kent, UK.

Email: A.Alexandridis@kent.ac.uk

Abstract

In this study, the wavelet multiscale model is applied to selected assets to hedge

time‐dependent exposure of an agent with a preference for a certain hedging

horizon. Based on the in‐sample and out‐of‐sample portfolio variances, the

wavelet‐based generalized autoregressive conditional heteroskedasticity

(GARCH) model produces the lowest variances. From a utility standpoint,

wavelet networks combined with GARCH have the highest utility. Finally, the

wavelet‐GARCH model has the lowest minimum capital risk requirements.

Overall, the wavelet GARCH and wavelet networks offer improvements over

traditional hedging models.

KEYWORDS

GARCH model, hedging effectiveness, multiscale hedge ratio, wavelet analysis, wavelet networks

JEL CLASSIFICATION

G1; G13; G15

1

|

INTRODUCTION

We study the impact of hedging horizon on the multiscale and multiperiod hedge ratio using wavelet‐decomposed

returns from three representative classes of assets: commodities, currency, and stock index. Multiscale and multiperiod

hedging decisions stem from the hedger’s preference for a certain hedge horizon, hedging instruments, and risk

tolerance. A wavelet is a small wave (signal) that grows over time but decays within a finite period. It has both the time

and frequency domains that characterize its evolution. A wavelet transform allows researchers to decompose time‐

series data into orthogonal components with different frequencies (scales) to accommodate structural changes,

discontinuity, and regime shifts (Conlon & Cotter, 2012). The wavelet analysis accommodates multiperiod decision‐

making models for heterogeneous economic agents weighing identical assets differently (see Kamara, Korajczyk, Lou,

& Sadka, 2016 for more on “clientele effects”).

1

Overall, for effective risk management, it is important to measure risk at

multiple scales of time.

Surprisingly, there is limited research to assess the hedging performance of the wavelet‐based hedge ratios from

scale‐dependent data. For instance, previous studies have utilized nonparametric wavelets (In & Kim, 2006), ordinary

least squares (OLS; Lien & Shrestha, 2007), and moving‐window OLS (Conlon & Cotter, 2012) methods to compute

multiscale hedge ratios and evaluate hedging effectiveness. None of the previous research accounted for the time

variation of the hedge ratios when return distributions are not normal. As Conlon and Cotter (2012) noted, by

smoothing time‐series data, traditional approaches to determine static multiscale hedge ratios underestimate the

information content of large dynamic changes. Furthermore, an analysis of the behavior of dynamic hedge ratios using

1

Kamara et al. (2016) noted that in a well‐segmented market with horizon clienteles, different assets are priced with different pricing kernels. They found that value (liquidity) risk is priced over

intermediate (short) horizons; long‐horizon investors focus on investing in less liquid but high‐return assets. For instance, highly leveraged hedge funds may prefer short‐run horizons and liquid

stocks. In comparison, pension funds, mutual funds, and long‐term investors prefer to invest in high yield but less liquid assets.

alternative variants of econometric models, such as nonparametric wavelet, OLS, and generalized autoregressive

conditional heteroskedasticity (GARCH) models and a comparative assessment of hedging performances of the optimal

hedge ratios across those models is lacking in the literature. Also, it is unclear whether hedgers derive higher utility

from multiperiod and multiscale hedging when portfolio returns have negative skewness and excess kurtosis. Finally,

within a wavelet‐based time‐varying hedging framework, the use of value at risk (VaR) and minimum capital risk

requirement (MCRR) as indicators of hedge effectiveness is limited.

In this study, we use wavelet‐decomposed returns from Brent crude oil, FTSE100 Index, Gold, and the US dollar

(USD) index for the period from January 3, 2005 to December 14, 2018 to evaluate five hedging models. We compare the

performance of these five models to evaluate their incremental contributions to portfolio variance reduction, utility

maximization, and reduction in the regulatory capital requirement. The in‐sample hedging models are wavelet

unhedged (WU), wavelet‐full hedge (WFH), wavelet‐OLS (WOLS), wavelet GARCH (WG), and wavelet hedge (WH).

The same models are used for out‐of‐sample evaluation with the exception that the WH strategy is replaced with the

wavelet neural networks hedging model (WN) that combines wavelet transformations and artificial neural networks.

The WN model is justified (to be discussed later) since the wavelet networks can be used for forecasting time‐varying

out‐of‐sample hedge ratios which the standard wavelets by themselves cannot do.

Based on the in‐sample portfolio variance of the assets considered, the WG model performs best, followed by the

WOLS strategy. For out‐of‐sample hedging, WG again is the best performing model, followed by WN. From a utility

standpoint using in‐sample wavelet‐decomposed returns, WH is the best strategy overall, followed by WG and WOLS,

respectively. In terms of out‐of‐sample performance based on wavelet‐decomposed returns, WG is the overall winner,

followed by WOLS. Finally, based on the MCRR, the WG model outperforms alternative models. The next best hedging

model is WOLS. Overall, WG offers improvements over traditional hedging models.

A key result in this study is that for all assets across all horizons and hedging strategies, the portfolio variance based

on the original returns exceeds the wavelet‐based portfolio variance. Furthermore, the standard GARCH model

performs worse than the WG model in terms of hedged portfolio variance. Overall, wavelet‐based multiscale hedging

performs far better than conventional and dynamic hedging.

The study makes several unique contributions to the literature on hedging. First, it applies the GARCH method to

combine time‐varying hedging, multiscale hedging horizon, and heterogeneous investors in a synthetic WG framework.

Unlike conventional approaches to estimating static multiscale hedge ratios, the synthetic WG framework captures

dynamic information content to produce time‐varying multiscale hedge ratios when asset returns are not normal.

Second, this study applies a new class of artificial neural networks, namely the wavelet networks (WNs) to examine out‐

of‐sample hedging effectiveness of multiscale hedge ratios. A combination of wavelet analysis and neural networks

improves significantly the forecast accuracy of out‐of‐sample hedge ratios even for longer horizons. Third, in addition to

variance reduction, hedging effectiveness is judged based on mean variance (MEV) and exponential utility functions,

certainty equivalent (CE) wealth, and risk‐adjusted information ratio (AIR). The utility analysis tests whether or not

there is an increase in utility from multiperiod and multiscale hedging especially when portfolio returns have negative

skewness and excess kurtosis. Finally, the MCRR is calculated to confirm the practical usefulness of wavelet‐based

hedging models for keeping risk capital requirement low. In other words, since the hedge ratios of various portfolios are

predictable, to achieve maximum risk reduction, a hedger would prefer a portfolio with the lowest MCRR.

The study proceeds as follows. Section 2 provides a brief survey of the hedging models considered in this paper. In

Section 3, empirical results are reported. The final section offers a summary of the key findings.

2

|

METHODOLOGY

Several recent studies have suggested that a wavelet‐based multihorizon hedging is a preferred strategy over

conventional methods (see Conlon, Lucy, & Uddin, 2017; Lien & Shrestha, 2007). The rationale is that a hedger makes

decisions in a multiperiod setting in the real world, taking into account hedging preference, hedging horizon length,

and hedge effectiveness. In short, the hedger’s exposure to the financial market depends upon the magnitude,

variability, and location of the shock. Consequently, there is a unique hedge ratio for each hedging horizon (Geppert,

1995). Most often, a single‐period hedging model is preferred due to its computational simplicity though it may not

adequately minimize risk when the hedger faces time‐dependent multihorizon exposure (Lien & Luo, 1993).

Multihorizon hedging also accommodates selective hedging. According to Conlon, Cotter, and Gençay (2016),

selective hedging is a form of speculation when hedgers and speculators prefer a policy of no‐hedge, partial‐hedge, and

1614

|

SULTAN ET AL.