Variance Risk Premiums of Commodity ETFs

• Date: 01 May 2017
• DOI: http://doi.org/10.1002/fut.21802
• Published date: 01 May 2017

Variance Risk Premiums of

Commodity ETFs

Chyng Wen Tee*and Christopher Ting

Wepropose a model-independent method to account for the early exercise premiums in Amer-

ican options on non-dividend paying stocks. We find that our estimates of early exercise pre-

mium are generally larger than the estimates by existing methods. Given the American options

on the Exchange-TradedFunds (ETFs) of gold, silver, natural gas, and crude oil, we find strong

empirical evidence of variance risk premiums for these commodities, over a volatility term

structure up to 18 months. Furthermore, we show that volatility indexes constructed by using

existing methods tend to overestimate the risk-neutral variance, and consequently the magni-

tude of variance risk premium. ©2016 Wiley Periodicals,Inc. Jrl Fut Mark 37:452–472, 2017

1. INTRODUCTION

Volatility is a widely used gauge in the financial market to convey information about the

extent of fluctuation in the asset return. Even when the underlying asset prices remain largely

unchanged, option prices can increase whenever market participants perceive future volatility

to rise, and vice versa. In this sense, option traders are short-term volatility forecasters,

supplying the market with their views on the expected volatility for the period from the

current business day up to the option expiry date. Volatilitycan also be viewed as a market risk

indicator, since stock return and the return’s volatility are known to be negatively correlated

(see Black, 1976). In addition, investors’ and traders’ fear of a market crash is reflected in

their willingness to insure against volatility risk, which in turn is manifested in the observed

variance risk premiums (see A¨

ıt-Sahalia, Karaman, & Mancini, 2013).

A significant development in volatility estimation is the model-free approach. Instead

of explicitly using an option pricing formula, the model-free method pioneered by Bakshi

and Madan (2000), Carr and Madan (1998), and Derman, Demeterfi, Kamal, and Zou

(1999)does not require an option pricing model to be explicitly specified. Different ap-

proaches to the derivation of the model-free method and its application in the equity market

have been further expounded by Andersen and Bondarenko (2007), Britten-Jones and Neu-

berger (2000), Carr and Wu (2006), and Carr and Wu (2009), to name a few. The main

Chyng Wen Tee is Assistant Professor of Quantitative Finance, Lee Kong Chian School of Business, Sin-

gapore Management University, 50 Stamford Road, Singapore. Christopher Ting is Associate Professor of

Quantitative Finance, Lee Kong Chian School of Business, Singapore Management University,50 Stamford

Road, Singapore 178899. We thank an anonymous reviewer and the editor for the invaluable suggestions to

improve the paper.

*Correspondence author,Lee Kong Chian School of Business, Singapore Management University, 50 Stamford

Road, Singapore 178899. Tel: +65 6828 0819, Fax:+65 6828 0777, e-mail: cwtee@smu.edu.sg

Received January 2016; Accepted June 2016

The Journal of Futures Markets, Vol. 37, No.5, 452–472 (2017)

©2016 Wiley Periodicals, Inc.

Published online 8 August 2016 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21802

Variance Risk Premiums of Commodity ETFs 453

advantage of the model-free method is that it is unaffected by model risks, since it relies

solely on the general principle of no risk-free arbitrage profit opportunity. Jiang and Tian

(2005) show that the model-free volatility subsumes all information contained in the Black–

Scholes implied volatility.

With the creation of the CBOE VIX index (see CBOE, 2009) and the subsequent

successful introductions of volatility derivatives, taking a direct exposure in volatility as an

asset class has become more prevalent. This is an important development, as Szado (2009)

has shown that although a long position in volatility may result in negative returns in the

long term, it may nevertheless provide significant protection during downturns. In a similar

vein, Black (2006) and Dash and Moran (2005) argue that due to the negative correlation

between VIX and S&P 500 index, adding a small VIX position to an investment portfolio can

significantly reduce portfolio volatility.

The 2007–2009 crisis has highlighted the need for market indicators to measure the risk

aversion of market participants across different asset classes. It has also become increasingly

clear that changes in risk appetites are an important determinant of asset prices. Indeed,

the model-free volatility methodology has been applied to commodities. For instance, the

presence of variance risk premiums in commodity markets has been studied for crude oil and

natural gas (see Trolle & Schwartz, 2010), and corn (see Wang, Fausti, & Qasmi, 2011). Pan

and Kang (2011) analyze the variance risk premium and related issues in the energy market.

Kang and Pan (2015) use a mean-variance model with stochastic variance in commodity

market to show the negative relationship between the variance risk premium and expected

commodity futures return.

Notably, Prokopczuk and Wese Simen (2013) perform an empirical analysis on the

variance risk premiums for 21 commodities over more than two decades, demonstrating that a

portfolio of short commodity variance swaps significantly outperforms that of long commodity

futures. In Prokopczuk and Wese Simen (2014) the model-free volatility methodology is

the main tool used to analyze the variance risk premium in the commodity market. They

find compelling evidence that the model-free method outperforms other models in terms of

minimizing bias. An important observation is that accounting for the variance risk premium

results in superior volatility forecasting performance.

The ability to transact financial products based on volatility indexes will enable investors

to not only manage volatility risk but also trade volatility spreads, as discussed in Bakshi

and Madan (2006), and also in Carr and Lee (2009). Whaley (1993) argues that volatility

derivatives are useful in providing a simple, cost-effective means to hedge the volatility of

portfolios that contain options or securities with option-like features for any type of asset

class.

The rapid expansion in the commodity market, along with the increased participation

by hedge funds, has drastically increased volatility in this asset class (see, for instance,

Brooks, Prokopczuk, & Wu, 2015). Heightened risks in the gold and crude oil markets put

the spotlight on the need for more effective tools to manage volatilities, or to seize the

alpha-generating opportunities presented by those big swings. Following the research papers

reviewed earlier,we formulate a model-free approach to construct the volatility indexes for the

commodity Exchange-Traded Funds (ETFs), as the current studies of variance risk premiums

in commodity markets tend to use futures on options for empirical analysis.

A key problem that impedes the direct application of the model-free approach is the

need to adjust for the early exercise premiums in the American options, since the method is

only applicable to European options. This adjustment is typically performed by applying an

option pricing model, which inevitably introduces model dependency and risk to an otherwise

model-free approach. For instance, commonly used methods to adjust for early exercise

premiums include the binomial tree model (see Cox, Ross, & Rubinstein, 1979) and an