This is a presentation on volatility, tail hedging, and alternative investments given at the Asian Insurance Forum.

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“Exchange-traded products (ETPs) linked to futures contracts on the CBOE S&P 500 Volatility Index (VIX) have grown in volume and assets under management in recent years,  in part because  of  their perceived potential to hedge against stock market losses.

“In this paper we study whether VIX-related ETPs can effectively hedge a portfolio of stocks. We find that while the VIX increases when large stock market losses occur, ETPs which track short term VIX futures indices are not effective hedges for stock portfolios because of the negative roll yield accumulated by such futures-based ETPs. ETPs which track medium term VIX futures indices suffer less from negative roll yield and thus appear somewhat better  hedges for stock portfolios. Our findings cast doubt on the potential diversification benefit from holding ETPs linked to VIX futures contracts.

“We also study the effectiveness of VIX ETPs in hedging Leveraged ETFs (LETFs) in which rebalancing effects lead to significant losses for buy-and-hold  investors during periods of high volatility. We find that VIX futures ETPs are usually not effective hedges for LETFs.”

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“Volatility has always been considered a key measure within the field of finance. Financial markets have changed significantly over the last century and the recent financial crises have reshaped the markets in such a way that the role of volatility has become even more pronounced than it was before. The concept finds its use within important areas such as risk management, valuation and asset pricing in general, trading and many more.

“Increased market complexity have historically spurred the demand for more exotic derivatives for directional trading and hedging. In the 1990s a new asset class arose which provided the investor with the opportunity to take a direct position, not in the underlying itself, but in its volatility. With this new derivative class, volatility is no longer viewed as side product inherent in other derivatives, but as an independent asset class of its own. Variance and volatility swaps were the first and most fundamental products to be introduced in this asset class and ever since their introduction, the market for them has exploded. The products are in nature forward contracts which at maturity exchange the difference between a fixed strike and realized variance/volatility, scaled by a predetermined notional. Both are traded OTC which makes it difficult to assess the true market size but recent estimates indicate daily trading volumes of more than $35 million notional. Both market and academic interest for these products has increased in line with demand and much research has recently been devoted to develop efficient pricing methods.”

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“What do academics have to offer market risk management practitioners in financial institutions? Current industry practice largely follows one of two extremely restrictive approaches: historical simulation or RiskMetrics. In contrast, we favor flexible methods based on recent developments in financial econometrics, which are likely to produce more accurate assessments of market risk. Clearly, the demands of real-world risk management in financial institutions — in particular, real-time risk tracking in very high-dimensional situations — impose strict limits on model complexity. Hence we stress parsimonious models that are easily estimated, and we discuss a variety of practical approaches for high-dimensional covariance matrix modeling, along with what we see as some of the pitfalls and problems in current practice. In so doing we hope to encourage further dialog between the academic and practitioner communities, hopefully stimulating the development of improved market risk management technologies that draw on the best of both worlds.”

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“Following previous work on the calibration of multifactor local stochastic volatility models to market smiles, Julien Guyon and Pierre Henry-Labordère show how to calibrate exactly any such model. Their approach, based on McKean’s particle method, extends to hybrid models, where interest rates are also stochastic. They illustrate the efficiency of their algorithm on hybrid local stochastic volatility models.”

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“There has been a long history of interaction between physics and quantitative finance. Now a technique for finding the effects of small fluctuations in quantum fields is being used to get a handle on the implied volatility smiles a stochastic model can create. Laurie Carver introduces this month’s technical articles.

“In Stochastic volatility’s orderly smiles (see pages 60–66), Lorenzo Bergomi, head of quantitative research, global markets at Société Générale Corporate & Investment Banking (SG CIB) in Paris, and Julien Guyon, a senior analyst in his team, use a quantum mechanical technique known as perturbation theory to determine the possible volatility smiles a stochastic volatility model can produce.
Exact equations are given for the form of the at-the-money implied volatility, the skew and the curvature.”

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“The ability to hedge market downturns without sacrificing upside returns has long been sought by all investors. We consider alternative methods of hedging the S&P 500 with assets that mimic the VIX index in hopes of taking advantage of the asymmetric relationship between volatility and returns. We first demonstrate that if the VIX was investable, and using the fact that volatility mean-reverts, can results in significantly improved portfolio performance over the buy-and-hold index portfolio. However, using VIX futures in a similar fashion does not provide the same results. As such, we deconstruct the VIX Index to find the relevant S&P 500 options that drive the VIX movements. In doing so, we then form a synthetic VIX portfolio using the S&P 500 options and capture returns similar to the VIX index. Our synthetic portfolio is highly liquid and investable, and when combined with a long position in the S&P 500, generates significantly higher returns with lower risk than the buy-and-hold S&P 500 index portfolio.”

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“Over the past several years, equity-index volatility products have emerged as an asset class in their own right. In particular, the use of variance swaps has skyrocketed in that time frame. A recent estimate from Risk magazine placed the daily volume in variance swaps on the major equity-indices to be US$5m vega (or dollar volatility risk per percentage point change in volatility). Furthermore, variance trading has roughly doubled every year for the past few years.

“Along with the proliferation of the breadth and complexity of available volatility products has come increased anxiety and confusion about how investors can most effectively and efficiently trade volatility. We offer a brief overview of the concept of variance and volatility; describe how a variance swap can be used to trade equity-index volatility; and illustrate some advantages that variance swaps offer over other volatility-based assets. Lastly, we will describe how CBOE variance futures contracts are essentially the same as an OTC variance swap.”

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“Standard option pricing models specify the dynamics of the security price and the instantaneous variance rate, and derives its no-arbitrage implication for the option implied volatility surface. Market models start with an initial implied volatility surface and a diffusion specification for the implied volatility dynamics, and derive the no-arbitrage constraints on the risk-neutral drift of the dynamics. This paper proposes a new approach, which specifies the security price and the implied volatility dynamics while leaving the instantaneous variance rate dynamics unspecified. The allowable shape for the initial implied volatility surface is then derived based on dynamic no-arbitrage arguments. Two parametric specifications for the implied volatility dynamics lead to extreme tractability, as the whole implied volatility surface is determined by a quadratic equation. The paper also proposes a dynamic calibration methodology and calibrates the two models to over-the-counter currency option and equity index option implied volatility surfaces over an 11-year period. The model with lognormal implied variance dynamics generates superior performance over standard option pricing models of similar complexities. Furthermore, constructing implied volatility surfaces using our two models is 100 times faster than using traditional option pricing models.”

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“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. Most
hedge fund strategies and commodity indices were not immune from declining. For example,
the HFRX Global Hedge Fund Index had a maximum drawdown of approximately 25% of its
value in 2008, with some of its sub-indexes dropping almost 60%. The drop in commodities was
even more significant. The S&P GSCI commodity index experienced a maximum drawdown of
about 2/3 of its value in 2008. 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.
Exhibit 1 provides a graphic illustration of the relative performance of a collection of diverse
assets from March 2006 to December 2008. The rapid rise of VIX futures in the end of 2008
strongly contrasts with the precipitous drop in almost all the other asset classes (managed
futures is an obvious exception). This anecdotal evidence leads one to wonder if some degree
of long VIX exposure would have provided effective diversification during the market meltdown
in which the standard diversifiers mentioned above failed to provide their expected
diversification benefits.

“Prior to the financial crisis of 2008, correlations between equities, bonds and alternative assets
tended to be relatively low. However, in 2007 and 2008 the correlations for many asset classes
rose significantly as a variety of assets dropped in value alongside the drop in equities. As a
result, many investors discovered that portfolios which they believed to be well diversified based
on historical data, were effectively not diversified at all. Exhibit 2 provides an illustration
of this phenomenon. The correlations with equity were often dramatically higher in the 2007 to
2008 period than in the 2004 to 2006 period. With the exception of managed futures, all
correlations were at least moderately higher in the latter period.”

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