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This study demonstrates that the VIX futures basis does not have significant forecast power for the change in the VIX spot index from 2006 through 2011 but does have forecast power for subsequent VIX futures returns. The study then demonstrates the profitability of shorting VIX futures contracts when the basis is in contango and buying VIX futures contracts when the basis is in backwardation with the market exposure of these positions hedged with mini-S&P 500 futures positions. The results indicate that these trading strategies are highly profitable and robust to transaction costs, out of sample hedge ratio forecasts and risk management rules. Overall, the analysis supports the view that the VIX futures basis does not accurately reflect the mean-reverting properties of the VIX spot index but rather reflects a risk premium that can be harvested.

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... We would like to thank Carol Alexander for the inspiration to investigate this topic. Campasano (2014) demonstrate that selling (buying) VIX futures contracts when the basis is in contango (backwardation) and hedging market exposure with short (long) S&P futures positions is highly profitable and robust to both conservative assumptions about transaction costs and the use of out-of-sample forecasts to set up hedge ratios. Eraker and Wu (2013) propose an equilibrium model to explain the negative return premium for both VIX ETNs and futures. ...

... However, even though Alexander and Korovilas (2012b) study VIX ETPs, the trading strategy they study is different than ours. Our strategy is mostly related to Simon and Campasano (2014), but they use VIX futures as traded instruments. Our result is different than theirs, we find that an unhedged version of this strategy is the most profitable. ...

... VIX futures are consistently overpriced relative to the subsequent moves in the underlying VIX index. Furthermore, Simon and Campasano (2014) present evidence that the futures prices can be predicted by looking at the difference between the VIX front month futures price and the VIX Index. If the futures are trading over the VIX, the futures tend to fall and if the futures are trading below the VIX they tend to rise. ...

This paper investigates the most traded VIX exchange traded products (ETPs) with focus on their performance, price discovery, hedging ability, and trading strategy. The VIX ETPs track their benchmark indices well. They are therefore exposed to the same time-decay (high negative expected returns) as these indices. This makes them unsuitable for buy-and-hold investments, but it gives rise to a highly profitable trading strategy. Despite being negatively correlated with the S&P 500, the ETPs perform poorly as a hedging tool; their inclusion in a portfolio based on S&P 500 will decrease the risk-adjusted performance of the portfolio.

... In the literature, evidence of futures basis has motivated several studies on related trading strategies. Simon and Campasano (2014) examine the VIX (volatility index) futures basis and discuss trading strategies involving VIX futures and S&P index futures. Buetow and Henderson (2016) present a link between the option market frictions to changes in the VIX futures basis and find that market information embedded in illiquid S&P options is reflected in the VIX but not in VIX futures. ...

We study the problem of dynamically trading multiple futures contracts on different underlying assets subject to portfolio constraints. The spreads between futures and spot prices are modeled by a multidimensional scaled Brownian bridge to account for their convergence at maturity. Under this stochastic basis model, we apply the stochastic control approach to rigorously derive the optimal trading strategies via utility maximization. This leads to the analysis of the associated system of Hamilton-Jacobi-Bellman equations, which are reduced to a system of ODEs. A series of numerical examples are provided to illustrate the optimal strategies and wealth distributions under different portfolio constraints.

... 2 A variety of papers have examined (synthetic) variance swap prices and VIX futures prices, including Carr and Wu (2009), Egloff, Leippold, and Wu (2010), Nossman and Wilhemsson (2009), and Simon and Campasano (2014). Other papers have examined the empirical link between index implied volatility and macroeconomic, risk, or sentiment variables, e.g., Corradi, Distaso, and Mele (2013), David and Veronesi (2014), Glatzer and Scheicher (2005), Han (2008), Mixon (2002), Mixon (2007, and Vähämaa and Äijö (2011). ...

We use unique regulatory data to examine open positions and activity in both listed and OTC volatility derivatives. Gross vega notional outstanding for index variance swaps is similar in size to that of S&P 500 options, with dealers short vega in order to supply the long vega demand of asset managers, but VIX futures are the dominant instrument for maturities less than one year. We find two distinct channels by which VIX trading activity manifests itself into futures prices: a risk-based level effect and an order flow effect. We estimate that the long volatility bias of asset managers puts upward pressure on VIX futures prices. Hedge funds have offset this potential impact by actively taking a net short position in nearby contracts. We also find that the front part of the curve is steepened by the order flow effect. In our 2011-2015 sample, the net impact added less than half a volatility point, on average, to nearby VIX futures contracts but added approximately one volatility point for contracts in less liquid, longer-dated parts of the curve. We find no evidence that this price impact forces VIX futures outside no-arbitrage bounds., (202) 418-6146. We thank seminar participants at the CFTC, SEC, and the Federal Reserve Board of Governors for helpful comments. The research presented in this paper was co-authored by Scott Mixon and Esen Onur in their official capacities with CFTC. The Office of the Chief Economist and CFTC economists produce original research on a broad range of topics relevant to the CFTC's mandate to regulate commodity future markets, commodity options markets, and the expanded mandate to regulate the swaps markets pursuant to the Dodd-Frank Wall Street Reform and Consumer Protection Act. These papers are often presented at conferences and many of these papers are later published by peer-review and other scholarly outlets. The analyses and conclusions expressed in this paper are those of the authors and do not reflect the views of other members of the Office of Chief Economist, other Commission staff, or the Commission itself.

We examine the effect of VIX futures’ new trading hours on price discovery as these causal relations have not been investigated before and are consequential for regulators and practitioners involved in the VIX futures market. Our data include VIX futures and VIX ETPs for four different periods in which trading hours were changed. Employing three different measures of information share, we find that VXX ETN leads VIX futures in 2009 and 2010, while in 2011 and 2013, the ETPs’ leadership varies depending on the exchange-traded product under consideration. Furthermore, in 2013 before the change of trading hours, the VIX futures contribute more to price discovery than they do after trading hours expansion. Less of the price discovery occurs from the exchange-traded products in the latter half of the trading period in 2010. OLS regression results of the determinants of price discovery as well as panel regression results show that the effect of volume and spread, which are the main determinants of price discovery in the prior literature, change significantly before and after futures trading hour expansions, for both VIX futures and ETPs.

We utilize the respective information share and common factor component weight approaches of Hasbrouck (1995) and Gonzalo and Granger (1995) to examine price discovery competition between the VIX and VIX futures. Our results show that VIX futures prices play a dominant role in the overall process of price discovery. An increase in the price difference between the VIX and VIX futures, commonly referred to as the futures basis, causes a corresponding increase in the contribution to price discovery made by VIX futures. Our empirical results also show that news announcements on macro-economic issues in the United States increase the dominant role of VIX futures in the overall process of price discovery. This dominant role remains unchanged when compared to VIX exchange-traded products and the volatility indices on non-US equity exchange-traded funds.

Currencies that are at a forward premium tend to depreciate. This `forward-premium puzzle' is an egregious deviation from uncovered interest parity. We document the properties of the carry trade, a currency speculation strategy that exploits this anomaly. This strategy consists of borrowing low-interest-rate currencies and lending high-interest-rate currencies. We first show that the carry trade yields a high Sharpe ratio that is not a compensation for risk. We then consider a hedged version of the carry trade, which protects the investor against large, adverse currency movements. This strategy, implemented with currency options, yields average payoffs that are statistically indistinguishable from the average payoffs to the standard carry trade. We argue that this finding implies that the peso problem cannot be a major determinant of the payoff to the carry trade.

Investors face numerous challenges when seeking to estimate the prospective performance of a long-only investment in commodity futures. For instance, historically, the average annualized excess return of the average individual commodity futures has been approximately zero and commodity futures returns have been largely uncorrelated with one another. The prospective annualized excess return of a rebalanced portfolio of commodity futures, however, can be "equity-like." Some security characteristics (such as the term structure of futures prices) and some portfolio strategies have historically been rewarded with above-average returns. It is important to avoid naive extrapolation of historical returns and to strike a balance between dependable sources of return and possible sources of return.

We examine the issue of non-convergence of the VIX futures to the cash VIX, the associated expiration day effects, and their sources. Significant disparities are found between the value of the cash VIX and the VIX futures at settlement of the contract. The reasons for this difference include the settlement procedure of the exchange and the underlying S&P 500 options order imbalances at settlement, the latter affected by traders unwinding arbitrage positions. We propose an alternative settlement procedure that mitigates these problems.

In 2008, the S&P 500 experienced a drawdown of about 50% from peak to trough. Many assets which are typically considered effective equity diversifiers also faced precipitous losses. In stark contrast, volatility levels as measured by VIX experienced significant increases and in 2008 repeatedly set new highs not seen since the crash of 1987. This anecdotal evidence leads one to wonder whether some degree of long VIX exposure would have provided effective diversification during the 2008 financial crisis when standard diversifiers failed to provide their expected diversification benefits. This study assesses the impact of long VIX futures and call positions as diversifiers for a stock portfolio, a stock/bond portfolio and a typical well-diversified institutional investment portfolio. The analysis covers the period of March 2006 to December 2008, with a focus on the latter part of 2008. While a long volatility exposure may result in negative excess returns over the long term, the study shows that investable VIX products could have been used to provide some much needed diversification during the crisis of 2008. In addition, the results of this study suggest that, dollar-for-dollar, VIX calls could have provided a more efficient means of diversification than provided by SPX puts.

This paper tests the expectation hypothesis by using the volatility index VIX and the futures written on that index. Because the VIX index is negatively correlated with the S&P 500 index returns, the VIX futures price should contain a negative risk premium, which we do confirm in this study. When the futures price is not adjusted with the risk premium, the expectation hypothesis is rejected at the 5 percent significance level for 20 of 21 forecast horizons. However when we adjust the futures price with the risk premium, obtained from a stochastic volatility model, the expectation hypothesis cannot be rejected. Further, we find that the risk premium adjusted futures price forecasts the direction of the VIX index well. The one day ahead forecast predicts the direction correctly in 73 percent of the times.

VIX futures are exchange-traded contracts on a future volatility index level (VIX) derived from a basket of SPX stock index options. The paper posits a stochastic variance model of VIX time evolution, and develops an expression for VIX futures. Free parameters are estimated from market data over the past few years. It is found that the model with parameters estimated from the whole period from 1990 to 2005 overprices the futures contracts by 16-44%. But the discrepancy is dramatically reduced to 2-12% if the parameters are estimated from the most recent one-year period.

Recent research advocates volatility diversification for long equity investors. It can even be justified when short-term expected returns are highly negative, but only when its equilibrium return is ignored. Its advantages during stock market crises are clear but we show that the high transactions costs and negative carry and roll yield on volatility futures during normal periods would outweigh any benefits gained unless volatility trades are carefully timed. Our analysis highlights the difficulty of predicting when volatility diversification is optimal. Hence insitutional investors should be sceptical of studies that extol its benefits. Volatility is better left to experienced traders such as speculators, vega hedgers and hedge funds.

We develop a general model to price VIX futures contracts. The model is adapted to test both the constant elasticity of variance (CEV) and the Cox–Ingersoll–Ross formulations, with and without jumps. Empirical tests on VIX futures prices provide out-of-sample estimates within 2% of the actual futures price for almost all futures maturities. We show that although jumps are present in the data, the models with jumps do not typically outperform the others; in particular, we demonstrate the important benefits of the CEV feature in pricing futures contracts. We conclude by examining errors in the model relative to the VIX characteristics. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:307–339, 2011

This study analyses the new market for trading volatility; VIX futures. We first use market data to establish the relationship between VIX futures prices and the index itself. We observe that VIX futures and VIX are highly correlated; the term structure of average VIX futures prices is upward sloping, whereas the term structure of VIX futures volatility is downward sloping. To establish a theoretical relationship between VIX futures and VIX, we model the instantaneous variance using a simple square root mean-reverting process with a stochastic long-term mean level. Using daily calibrated long-term mean and VIX, the model gives good predictions of VIX futures prices under normal market situation. These parameter estimates could be used to price VIX options. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 30:809–833, 2010

We study the properties of the carry trade, a currency speculation strategy in which an investor borrows low-interest-rate currencies and lends high-interest-rate currencies. This strategy generates payoffs that are on average large and uncorrelated with traditional risk factors. We argue that these payoffs reflect a peso problem. The underlying peso event features high values of the stochastic discount factor rather than very large negative payoffs. The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Studying all possible pairs of 11 major currencies and 11 portfolios in 1976–2008 we show that, when there is no leverage, carry trade is significantly profitable for most currency pairs and portfolios. Positive returns do not diminish in time providing a strong case against the hypothesis of uncovered interest rate parity. We explain these findings with the leveraged nature of carry trade: leverage may increase profitability but it materially increases downside risk. We argue that market inefficiency is related to the level of leverage.

Historically, commodity futures have had excess returns similar to those of equities. But what should we expect in the future? The usual risk factors are unable to explain the time-series variation in excess returns. In addition, our evidence suggests that commodity futures are an inconsistent, if not tenuous, hedge against unexpected inflation. Further, the historically high average returns to a commodity futures portfolio are largely driven by the choice of weighting schemes. Indeed, an equally weighted long-only portfolio of commodity futures returns has approximately a zero excess return over the past 25 years. Our portfolio analysis suggests that the a long-only strategic allocation to commodities as a general asset class is a bet on the future term structure of commodity prices, in general, and on specific portfolio weighting schemes, in particular. In contrast, we provide evidence that there are distinct benefits to an asset allocation overlay that tactically allocates using commodity futures exposures. We examine three trading strategies that use both momentum and the term structure of futures prices. We find that the tactical strategies provide higher average returns and lower risk than a long-only commodity futures exposure.

We construct an equally-weighted index of commodity futures monthly returns over the period between July of 1959 and March of 2004 in order to study simple properties of commodity futures as an asset class. Fully-collateralized commodity futures have historically offered the same return and Sharpe ratio as equities. While the risk premium on commodity futures is essentially the same as equities, commodity futures returns are negatively correlated with equity returns and bond returns. The negative correlation between commodity futures and the other asset classes is due, in significant part, to different behavior over the business cycle. In addition, commodity futures are positively correlated with inflation, unexpected inflation, and changes in expected inflation.

In many domains the decisions of experts are inferior to the decisions of statistical models of experts. The aim of this paper is to test this proposition in the financial markets, where genuine expertise is hard to find and the drivers of success are unclear. We exploit a unique database containing the recommended trading positions of technical analysts following the German bond market, and questionnaires revealing the technical indicators they used. The analysts have only average directional forecasting ability, but make consistent profits through superior market timing. Ordered-response models describing their positions in each market, driven by a subset of the technical indicators they claim to use, make even more profits. Models based on pooled data from several markets do better still. However, the pattern of model based trades is different from, and more risky than, the pattern of analyst trades. So it cannot be claimed that the models mimic the judgement process, or that the outcomes clearly dominate those from expert judgement.

Current research on financial risk management applications of econometrics centres on the accurate assessment of individual market and credit risks with relatively little theoretical or applied econometric research on other types of risk, aggregation risk, data incompleteness and optimal risk control. We argue that consideration of the model risk arising from crude aggregation rules and inadequate data could lead to a new class of reduced form Bayesian risk assessment models. Logically, these models should be set within a common factor framework that allows proper risk aggregation methods to be developed. We explain how such a framework could also provide the essential links between risk control, risk assessments and the optimal allocation of resources.

Technical analysis, also known as 'charting,' has been a part of financial practice for many decades, but this discipline has not received the same level of academic scrutiny and acceptance as more traditional approaches such as fundamental analysis. One of the main obstacles is the highly subjective nature of technical analysis-the presence of geometric shapes in historical price charts is often in the eyes of the beholder. In this paper, we propose a systematic and automatic approach to technical pattern recognition using nonparametric kernel regression, and we apply this method to a large number of U.S. stocks from 1962 to 1996 to evaluate the effectiveness of technical analysis. By comparing the unconditional empirical distribution of daily stock returns to the conditional distribution-conditioned on specific technical indicators such as head-and-shoulders or double bottoms-we find that over the 31-year sample period, several technical indicators do provide incremental information and may have some practical value. Copyright The American Finance Association 2000.

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