Downside Risk and Portfolio Optimization of Energy Stocks: A Study on the Extreme Value Theory and the Vine Copula Approach.

• Author: Karmakar, Madhusudan

1. INTRODUCTION

   Energy stocks are potentially a hedge against inflation and macroeconomic shocks (Oh and Nash, 2006). Energy price spikes hurt global economic growth. But, energy stocks benefit from higher energy prices (Al-Mudhaf and Goodwin, 1993; Boyer and Filion, 2007). (1) Anecdotally, some sophisticated investors, such as foundations and endowments in the U.S. do incorporate a separate portfolio allocation to energy stocks in recognition of these factors (Jennings, 2012). The noted features also drive many mutual funds in the U.S. to allocate a significant portion of their funds to energy stocks.

   In fact, the global economy is highly linked with the energy price. Bredin et al. (2011) show that energy price hike has a negative effect on the real economy of the advanced countries, most of which are oil importers. (2) In a recent paper, Azad and Serletis (2020) document that oil price hike has a negative effect on the economic activity of the oil-importing emerging countries. Although energy price hikes directly affect the economic growth of the oil-importing countries, it indirectly hurts the global economy too. International Energy Agency (2004) observes that a $10 increase in oil prices per barrel reduces global economic growth by 0.5 percentage. Economists at the St. Louis Federal Reserve Bank believe that energy price spikes increase the probability of entering a recession (Engemann et al., 2011). Energy shock not only affects the real economy but also affects equity markets. Chen (2010) observes that higher oil prices increase the probability of a bear market in equity. Thus, energy price shocks hurt both the real economy and the financial markets. So when energy stocks benefit from higher energy prices, individuals, in general, use energy stocks to hedge their economic condition.

   Many investors consider real assets such as real estate, commodities, agricultural land, and infrastructure investments as inflation-sensitive investing. Pension fund managers, as well as individuals saving for retirement, use these real assets to hedge their liability: an inflation-sensitive retirement. Empirical researches show that during a high-inflation and increasing interest-rate environment, energy stocks significantly outperform broad-market stocks (Jennings, 2012). Since this evidence supports the fact that energy stocks benefit a portfolio in inflationary periods, the pension fund managers and the retired individual investors may view energy stocks as another inflation-sensitive investment.

   Some may argue that inflation-sensitive investors can directly invest in energy commodities or energy commodities futures to hedge their liabilities. But since energy stocks are stocks, they have a number of advantages over other forms of energy investing. Investors can easily control the timing of cash flows. They can invest money immediately. They can easily reinvest the interim cash flows and liquidate their investment as and when they desire so. Moreover, information on energy stocks is more readily available. Unlike commodity-based exposure to energy, investing in energy stocks attracts less regulatory scrutiny. Also, unlike futures-based exposure to energy, the energy stocks are not required to be 'rolled' at the expiry of the contract period. The advantages mentioned above make a compelling case for a number of foundations and endowments in the U.S. to have a separate allocation to energy stocks as an inflation-sensitive investment. (3)

   Notably, interest in energy stocks as a separate portfolio allocation is not only limited to non-profit investors. Many mutual funds in the U.S. also prefer to allocate a significant portion of their funds to energy stocks. As reported by Morningstar, over 83 distinct mutual funds had allocated fifty percent of their funds in the energy stocks during December 2009. The Vanguard Energy Fund, which belongs to Morningstar's equity energy category, has total stocks of about $6.18 billion, invested in 126 different holdings as of February 21, 2020. Fidelity Select Energy Portfolio is another fund within this category, and as of February 21, 2020, it has invested $789.37 million. In addition, there are many more energy funds, which include Fidelity@ Select Natural Resources Port, Fidelity Advisor@ Energy Fund, Cavanal Hill World Energy Fund, and Tortoise Energy Evolution Fund, among others.

   Taken together, these factors--the importance of the energy sector to the global economy, energy stocks' potential to hedge energy risks, the prospect of energy stock to be inflation-sensitive investments, the advantages of energy stocks over other forms of energy investing, mutual funds preference for energy sector funds and anecdotes of sophisticated investors such as foundations and endowments focusing on energy investments motivate us to study on portfolio management of energy stocks. A study on energy stocks portfolio management is indeed an important area of research in financial risk management as the research findings can provide potential implications not only for sophisticated investors such as energy fund managers, foundations and endowments but also for individual investors and policymakers.

   Most of the existing researches in the area of financial economics of energy markets explore the energy price dynamics, linkages between oil price and equity markets, volatility spillover between crude oil and equity markets, hedging strategies in energy markets and estimation of energy portfolio downside risk such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) (Chan and Grant, 2016; Tchatoka, Masson and Parry, 2019; Maghyereh, Awartani and Bouri, 2016; Reboredo, Juan C and Andrea Ugolini, 2016; Zhang, D., 2017; Ma et al., 2019; Hou, Li and Wen, 2019; Basher and Sadorsky, 2016; Boroumand et al., 2015; Aas and Berg, 2009; Hammoudeh et al., 2013; Yu et al., 2018). However, existing literature investigating the portfolio optimization of energy stocks is rather sparse. In particular, the downside risk and portfolio optimization strategy of energy stocks have not been investigated in detail.

   Notably, over the last decade, many researchers examine the hedge and safe haven features of different energy stocks and evaluate their risk diversification benefits against stocks and other assets, optimizing the portfolio weights based on downside risk hedging strategy. However, they do not investigate the portfolio optimization strategy of energy stocks. Reboredo (2015) uses standard bivariate copulas to characterize the dependence structure and to compute the CVaR measure of systemic risk between oil prices and a set of global and sectoral renewable energy indices. Their results suggest that oil price dynamics contribute around 30% to the downside risk of renewable energy companies. Sukcharoen and Leatham (2017) use a vine copula approach to estimate multi-product hedge ratios that minimize the downside risk of the refinery using crude oil, gasoline, and heating oil futures. They evaluate and compare the out-of-sample hedging effectiveness of C- and D-vine copula models with that of a widely used nonparametric method and three standard copula models. The empirical results reveal that the D-vine copula model performs best in managing the downside risk of the refinery. Bouri et al. (2019) use a blended copula approach to measure the dependence structure and examine the potential roles of gold and crude oil as safe-haven stocks against extreme down movements in clean energy stock indices. They show that both crude oil and gold are only weak safe-haven stocks for clean energy indices. In a recent study, Dutta et al. (2020) investigate whether crude oil, gold, and silver volatility indexes can be used as hedging instruments against downside risk associated with clean energy equity indexes. They observe that the downside risk of clean energy stocks can be diversified if renewable energy stocks are combined with commodity volatility indexes in a portfolio. Thus, they show that the volatility indexes can act as an effective tool for hedging clean-energy stock indexes. Very recently, using a time-varying optimal copula (TVOC) approach, Shahzad et al. (2021) assess the effectiveness of hedging and measure the conditional diversification benefits of investing in crude oil for BRIC stock indices. The positive relationship between BRIC stock indices and crude oil suggests that a long (short) position in BRIC stock can be hedged by taking a short (long) position in oil. They also observe that the Chinese and Indian equity markets offer higher conditional diversification benefits when combined with oil in an equally weighted portfolio.

   Although some researchers examine the dependence structure and measure portfolio downside risks in the energy sector, they do not focus on portfolio optimization per se. For example, Aas and Berg (2009) compare D-vine copula and nested Archimedean copula (NAC) in estimating dependence between two energy and two IT stocks. They observe that the D-vine copula is more suitable than NAC for high-dimensional modeling. Moreover, they find that the D-vine copula model forecasts out-of-sample portfolio VaR very well. Hammoudeh et al. (2013) use VaR to analyze market downside risk associated with precious metals, oil, and the S&P 500 index and construct VaR-based optimal portfolio using these stocks. They evaluate the VaR forecasting ability of different risk models and observe that the conditional EVT-sstd model is the best performer. Yu et al. (2018) measure the VaR and CVaR of a portfolio consisting of four crude oil stocks by using GARCH-type models, extreme value theory (EVT) and vine copulas. The back-testing results show that the Mixed regular-vine (Mixed R-vine) copula is superior to R-vine all Gumbel and R-vine all Joe copulas in forecasting oil portfolio VaR and CVaR.

   A few studies, of course, investigate the dependence structure and optimized portfolios of energy stocks over...