The Hedged Volatility Strategy

Being short regular Volatility ETFs or long Inverse Volatility ETFs are winning strategies…most of the time. The challenge is that when the VIX spikes or when the VIX futures curve is downward sloping instead of upward sloping, very significant losses can occur. Many people have built and back-tested models that attempt to move from long to short to neutral positions in the various Volatility ETFs, but almost all of them have one or both of these very significant flaws: 1) Failure to use “out of sample” back-testing and 2) Failure to protect against “black swan” events.

In this strategy a position and weighting in the appropriate Volatility ETFs are established based on a multi-factor model which always uses out of sample back-testing to determine effectiveness. Volatility Options are always used to protect against significant short-term moves which left unchecked could result in the total loss of one’s portfolio value; these options will usually lose money, but that is a small price to pay for the protection they provide. (Strategies should be scaled at a minimum of 20% to ensure options protection.)

This is a good strategy for IRA accounts in which short selling is not allowed. Long positions in Inverse Volatility ETFs are typically held. Suggested minimum capital: $26,000 (using 20% scaling).

Developing A Volatility Carry Strategy

By way of introduction we begin by reviewing a well known characteristic of the  iPath S&P 500 VIX ST Futures ETN (NYSEArca:VXX).  In common with other long-volatility ETF /ETNs, VXX has a tendency to decline in value due to the upward sloping shape of the forward volatility curve.  The chart below which illustrates the fall in value of the VXX, together with the front-month VIX futures contract, over the period from 2009.


VXXvsVX

 

 

This phenomenon gives rise to opportunities for “carry” strategies, wherein a long volatility product such as VXX is sold in expectation that it will decline in value over time.  Such strategies work well during periods when volatility futures are in contango, i.e. when the longer dated futures contracts have higher prices than shorter dated futures contracts and the spot VIX Index, which is typically the case around 70% of the time.  An analogous strategy in the fixed income world is known as “riding down the yield curve”.  When yield curves are upward sloping, a fixed income investor can buy a higher-yielding bill or bond in the expectation that the yield will decline, and the price rise, as the security approaches maturity.  Quantitative easing put paid to that widely utilized technique, but analogous strategies in currency and volatility markets continue to perform well.

The challenge for any carry strategy is what happens when the curve inverts, as futures move into backwardation, often giving rise to precipitous losses.  A variety of hedging schemes have been devised that are designed to mitigate the risk.  For example, one well-known carry strategy in VIX futures entails selling the front month contract and hedging with a short position in an appropriate number of E-Mini S&P 500 futures contracts. In this case the hedge is imperfect, leaving the investor the task of managing a significant basis risk.

SSALGOTRADING AD

The chart of the compounded value of the VXX and VIX futures contract suggests another approach.  While both securities decline in value over time, the fall in the value of the VXX ETN is substantially greater than that of the front month futures contract.  The basic idea, therefore, is a relative value trade, in which we purchase VIX futures, the better performing of the pair, while selling the underperforming VXX.  Since the value of the VXX is determined by the value of the front two months VIX futures contracts, the hedge, while imperfect, is likely to entail less basis risk than is the case for the VIX-ES futures strategy.

Another way to think about the trade is this:  by combining a short position in VXX with a long position in the front-month futures, we are in effect creating a residual exposure in the value of the second month VIX futures contract relative to the first. So this is a strategy in which we are looking to capture volatility carry, not at the front of the curve, but between the first and second month futures maturities.  We are, in effect, riding down the belly of volatility curve.

 

The Relationship between VXX and VIX Futures

Let’s take a look at the relationship between the VXX and front month futures contract, which I will hereafter refer to simply as VX.  A simple linear regression analysis of VXX against VX is summarized in the tables below, and confirms two features of their relationship.

Firstly there is a strong, statistically significant relationship between the two (with an R-square of 75% ) – indeed, given that the value of the VXX is in part determined by VX, how could there not be?

Secondly, the intercept of the regression is negative and statistically significant.  We can therefore conclude that the underperformance of the VXX relative to the VX is not just a matter of optics, but is a statistically reliable phenomenon.  So the basic idea of selling the VXX against VX is sound, at least in the statistical sense.

Regression

 

 

Constructing the Initial Portfolio

In constructing our theoretical portfolio, I am going to gloss over some important technical issues about how to construct the optimal hedge and simply assert that the best one can do is apply a beta of around 1.2, to produce the following outcome:

Table1

VXX-VX Strategy

 

While broadly positive, with an information ratio of 1.32, the strategy performance is a little discouraging, on several levels.  Firstly, the annual volatility, at over 48%, is uncomfortably high. Secondly, the strategy experiences very substantial drawdowns at times when the volatility curve inverts, such as in August 2015 and January 2016.  Finally, the strategy is very highly correlated with the S&P500 index, which may be an important consideration for investors looking for ways to diversity their stock portfolio risk.

 

Exploiting Calendar Effects

We will address these issues in short order.  Firstly, however, I want to draw attention to an interesting calendar effect in the strategy (using a simple pivot table analysis).

Calendar

As you can see from the table above, the strategy returns in the last few days of the calendar month tend to be significantly below zero.

The cause of the phenomenon has to do with the way the VXX is constructed, but the important point here is that, in principle, we can utilize this effect to our advantage, by reversing the portfolio holdings around the end of the month.  This simple technique produces a significant improvement in strategy returns, while lowering the correlation:

Table2

 

Reducing Portfolio Risk and Correlation

We can now address the issue of the residual high level of strategy volatility, while simultaneously reducing the strategy correlation to a much lower level.  We can do this in a straightforward way by adding a third asset, the SPDR S&P 500 ETF Trust (NYSEArca:SPY), in which we will hold a short position, to exploit the negative correlation of the original portfolio.

We then adjust the portfolio weights to maximize the risk-adjusted returns, subject to limits on the maximum portfolio volatility and correlation.  For example, setting a limit of 10% for both volatility and correlation, we achieve the following result (with weights -0.37 0.27 -0.65 for VXX, VX and SPY respectively):

 

Table3

 

 

VXX-VX-SPY

 

Compared to the original portfolio, the new portfolio’s performance is much more benign during the critical period from Q2-2015 to Q1-2016 and while there remain several significant drawdown periods, notably in 2011, overall the strategy is now approaching an investable proposition, with an information ratio of 1.6 and annual volatility of 9.96% and correlation of 0.1.

Other configurations are possible, of course, and the risk-adjusted performance can be improved, depending on the investor’s risk preferences.

 

Portfolio Rebalancing

There is an element of curve-fitting in the research process as described so far, in as much as we are using all of the available data to July 2016 to construct a portfolio with the desired characteristics. In practice, of course, we will be required to rebalance the portfolio on a periodic basis, re-estimating the optimal portfolio weights as new data comes in.  By way of illustration, the portfolio was re-estimated using in-sample data to the end of Feb, 2016, producing out-of-sample results during the period from March to July 2016, as follows:

Table4

 

A detailed examination of the generic problem of how frequently to rebalance the portfolio is beyond the scope of this article and I leave it to interested analysts to perform the research for themselves.

 

Practical Considerations

In order to implement the theoretical strategy described above there are several important practical steps that need to be considered.

 

  • It is not immediately apparent how the weights should be applied to a portfolio comprising both ETNs and futures. In practice the best approach is to re-estimate the portfolio using a regression relationship expressed in $-value terms, rather than in percentages, in order to establish the quantity of VXX and SPY stock to be sold per single VX futures contract.
  • Reversing the portfolio holdings in the last few days of the month will add significantly to transaction costs, especially for the position in VX futures, for which the minimum tick size is $50. It is important to factor realistic estimates of transaction costs into the assessment of the strategy performance overall and specifically with respect to month-end reversals.
  • The strategy assumed  the availability of VXX and SPY to short, which occasionally can be a problem. It’s not such a big deal if you are maintaining a long-term short position, but flipping the position around over a few ays at the end of the month might be problematic, from time to time.
  • Also, we should take account of stock loan financing costs, which run to around 2.9% and 0.42% annually for VXX and SPY, respectively. These rates can vary with market conditions and stock availability, of course.
  • It is highly likely that other ETFs/ETNs could profitably be added to the mix in order to further reduce strategy volatility and improve risk-adjusted returns. Likely candidates could include, for example, the Direxion Daily 20+ Yr Trsy Bull 3X ETF (NYSEArca:TMF).
  • We have already mentioned the important issue of portfolio rebalancing. There is an argument for rebalancing more frequently to take advantage of the latest market data; on the other hand, too-frequent changes in the portfolio composition can undermine portfolio robustness, increase volatility and incur higher transaction costs. The question of how frequently to rebalance the portfolio is an important one that requires further testing to determine the optimal rebalancing frequency.

 

Conclusion

We have described the process of constructing a volatility carry strategy based on the relative value of the VXX ETN vs the front-month contract in VIX futures.  By combining a portfolio comprising short positions in VXX and SPY with a long position in VIX futures, the investor can, in principle achieve risk-adjusted returns corresponding to an information ratio of around 1.6, or more. It is thought likely that further improvements in portfolio performance can be achieved by adding other ETFs to the portfolio mix.

 

How to Make Money in a Down Market

The popular VIX blog Vix and More evaluates the performance of the VIX ETFs (actually ETNs) and concludes that all of them lost money in 2015.  Yes, both long volatility and short volatility products lost money!

VIX ETP performance in 2015

Source:  Vix and More

By contrast, our Volatility ETF strategy had an exceptional year in 2015, making money in every month but one:

Monthly Pct Returns

How to Profit in a Down Market

How do you make money when every product you are trading loses money?  Obviously you have to short one or more of them.  But that can be a very dangerous thing to do, especially in a product like the VIX ETNs.  Volatility itself is very volatile – it has an annual volatility (the volatility of volatility, or VVIX) that averages around 100% and which reached a record high of 212% in August 2015.

VVIX

The CBOE VVIX Index

Selling products based on such a volatile instrument can be extremely hazardous – even in a downtrend: the counter-trends are often extremely violent, making a short position challenging to maintain.

Relative value trading is a more conservative approach to the problem.  Here, rather than trading a single product you trade a pair, or basket of them.  Your bet is that the ETFs (or stocks) you are long will outperform the ETFs you are short.  Even if your favored ETFs declines, you can still make money if the ETFs you short declines even more.

This is the basis for the original concept of hedge funds, as envisaged by Alfred Jones in the 1940’s, and underpins the most popular hedge fund strategy, equity long-short.  But what works successfully in equities can equally be applied to other markets, including volatility.  In fact, I have argued elsewhere that the relative value (long/short) concept works even better in volatility markets, chiefly because the correlations between volatility processes tend to be higher than the correlations between the underlying asset processes (see The Case for Volatility as an Asset Class).

 

The Case for Volatility as an Asset Class

Volatility as an asset class has grown up over the fifteen years since I started my first volatility arbitrage fund in 2000.  Caissa Capital grew to about $400m in assets before I moved on, while several of its rivals have gone on to manage assets in the multiple billions of dollars.  Back then volatility was seen as a niche, esoteric asset class and quite rightly so.  Nonetheless, investors who braved the unknown and stayed the course have been well rewarded: in recent years volatility strategies as an asset class have handily outperformed the indices for global macro, equity market neutral and diversified funds of funds, for example. Fig 1

The Fundamentals of Volatility

It’s worth rehearsing a few of the fundamental features of volatility for those unfamiliar with the territory.

Volatility is Unobservable

Volatility is the ultimate derivative, one whose fair price can never be known, even after the event, since it is intrinsically unobservable.  You can estimate what the volatility of an asset has been over some historical period using, for example, the standard deviation of returns.  But this is only an estimate, one of several possibilities, all of which have shortcomings.  We now know that volatility can be measured with almost arbitrary precision using an integrated volatility estimator (essentially a metric based on high frequency data), but that does not change the essential fact:  our knowledge of volatility is always subject to uncertainty, unlike a stock price, for example.

Volatility Trends

Huge effort is expended in identifying trends in commodity markets and many billions of dollars are invested in trend following CTA strategies (and, equivalently, momentum strategies in equities).  Trend following undoubtedly works, according to academic research, but is also subject to prolonged drawdowns during periods when a trend moderates or reverses. By contrast, volatility always trends.  You can see this from the charts below, which express the relationship between volatility in the S&P 500 index in consecutive months.  The r-square of the regression relationship is one of the largest to be found in economics. Fig 2 And this is a feature of volatility not just in one asset class, such as equities, nor even for all classes of financial assets, but in every time series process for which data exists, including weather and other natural phenomena.  So an investment strategy than seeks to exploit volatility trends is relying upon one of the most consistent features of any asset process we know of (more on this topic in Long Memory and Regime Shifts in Asset Volatility).

Volatility Mean-Reversion and Correlation

One of the central assumptions behind the ever-popular stat-arb strategies is that the basis between two or more correlated processes is stationary. Consequently, any departure from the long term relationship between such assets will eventually revert to the mean. Mean reversion is also an observed phenomenon in volatility processes.  In fact, the speed of mean reversion (as estimated in, say, an Ornstein-Ulenbeck framework) is typically an order of magnitude larger than for a typical stock-pairs process.  Furthermore, the correlation between one volatility process and another volatility process, or indeed between a volatility process and an asset returns process, tends to rise when markets are stressed (i.e. when volatility increases). Fig 3

Another interesting feature of volatility correlations is that they are often lower than for the corresponding asset returns processes.  One can therefore build a diversified volatility portfolio with far fewer assets that are required for, say, a basket of equities (see Modeling Asset Volatility for more on this topic).

Fig 4   Finally, more sophisticated stat-arb strategies tend to rely on cointegration rather than correlation, because cointegrated series are often driven by some common fundamental factors, rather than purely statistical ones, which may prove temporary (see Developing Statistical Arbitrage Strategies Using Cointegration for more details).  Again, cointegrated relationships tend to be commonplace in the universe of volatility processes and are typically more reliable over the long term than those found in asset return processes.

Volatility Term Structure

One of the most marked characteristics of the typical asset volatility process its upward sloping term structure.  An example of the typical term structure for futures on the VIX S&P 500 Index volatility index (as at the end of May, 2015), is shown in the chart below. A steeply upward-sloping curve characterizes the term structure of equity volatility around 75% of the time.

Fig 5   Fixed income investors can only dream of such yield in the current ZIRP environment, while f/x traders would have to plunge into the riskiest of currencies to achieve anything comparable in terms of yield differential and hope to be able to mitigate some of the devaluation risk by diversification.

The Volatility of Volatility

One feature of volatility processes that has been somewhat overlooked is the consistency of the volatility of volatility.  Only on one occasion since 2007 has the VVIX index, which measures the annual volatility of the VIX index, ever fallen below 60.

Fig 6   What this means is that, in trading volatility, you are trading an asset whose annual volatility has hardly ever fallen below 60% and which has often exceeded 100% per year.  Trading opportunities tend to abound when volatility is consistently elevated, as here (and, conversely, the performance of many hedge fund strategies tends to suffer during periods of sustained, low volatility)

SSALGOTRADING AD

Anything You Can Do, I Can Do better

The take-away from all this should be fairly obvious:  almost any strategy you care to name has an equivalent in the volatility space, whether it be volatility long/short, relative value, stat-arb, trend following or carry trading. What is more, because of the inherent characteristics of volatility, all these strategies tend to produce higher levels of performance than their more traditional counterparts. Take as an example our own Volatility ETF strategy, which has produced consistent annual returns of between 30% and 40%, with a Sharpe ratio in excess of 3, since 2012.   VALUE OF $1000

Sharpe

  Monthly Returns

 

(click to enlarge)

Where does the Alpha Come From?

It is traditional at this stage for managers to point the finger at hedgers as the source of abnormal returns and indeed I will do the same now.   Equity portfolio managers are hardly ignorant of the cost of using options and volatility derivatives to hedge their portfolios; but neither are they likely to be leading experts in the pricing of such derivatives.  And, after all, in a year in which they might be showing a 20% to 30% return, saving a few basis points on the hedge is neither here nor there, compared to the benefits of locking in the performance gains (and fees!). The same applies even when the purpose of using such derivatives is primarily to produce trading returns. Maple Leaf’s George Castrounis puts it this way:

Significant supply/demand imbalances continuously appear in derivative markets. The principal users of options (i.e. pension funds, corporates, mutual funds, insurance companies, retail and hedge funds) trade these instruments to express a view on the direction of the underlying asset rather than to express a view on the volatility of that asset, thus making non-economic volatility decisions. Their decision process may be driven by factors that have nothing to do with volatility levels, such as tax treatment, lockup, voting rights, or cross ownership. This creates opportunities for strategies that trade volatility.

We might also point to another source of potential alpha:  the uncertainty as to what the current level of volatility is, and how it should be priced.  As I have already pointed out, volatility is intrinsically uncertain, being unobservable.  This allows for a disparity of views about its true level, both currently and in future.  Secondly, there is no universal agreement on how volatility should be priced.  This permits at times a wide divergence of views on fair value (to give you some idea of the complexities involved, I would refer you to, for example, Range based EGARCH Option pricing Models). What this means, of course, is that there is a basis for a genuine source of competitive advantage, such as the Caissa Capital fund enjoyed in the early 2000s with its advanced option pricing models. The plethora of volatility products that have emerged over the last decade has only added to the opportunity set.

 Why Hasn’t It Been Done Before?

This was an entirely legitimate question back in the early days of volatility arbitrage. The cost of trading an option book, to say nothing of the complexities of managing the associated risks, were significant disincentives for both managers and investors.  Bid/ask spreads were wide enough to cause significant heads winds for strategies that required aggressive price-taking.  Mangers often had to juggle two sets of risks books, one reflecting the market’s view of the portfolio Greeks, the other the model view.  The task of explaining all this to investors, many of whom had never evaluated volatility strategies previously, was a daunting one.  And then there were the capacity issues:  back in the early 2000s a $400m long/short option portfolio would typically have to run to several hundred names in order to meet liquidity and market impact risk tolerances. Much has changed over the last fifteen years, especially with the advent of the highly popular VIX futures contract and the newer ETF products such as VXX and XIV, whose trading volumes and AUM are growing rapidly.  These developments have exerted strong downward pressure on trading costs, while providing sufficient capacity for at least a dozen volatility funds managing over $1Bn in assets.

Why Hasn’t It Been Done Right Yet?

Again, this question is less apposite than it was ten years ago and since that time there have been a number of success stories in the volatility space. One of the learning points occurred in 2004-2007, when volatility hit the lows for a 20 month period, causing performance to crater in long volatility funds, as well as funds with a volatility neutral mandate. I recall meeting with Nassim Taleb to discuss his Empirica volatility fund prior to that period, at the start of the 2000s.  My advice to him was that, while he had some great ideas, they were better suited to an insurance product rather than a hedge fund.  A long volatility fund might lose money month after month for an entire year, and with it investors and AUM, before seeing the kind of payoff that made such investment torture worthwhile.  And so it proved.

Conversely, stories about managers of short volatility funds showing superb performance, only to blow up spectacularly when volatility eventually explodes, are legion in this field.  One example comes to mind of a fund in Long Beach, CA, whose prime broker I visited with sometime in 2002.  He told me the fund had been producing a rock-steady 30% annual return for several years, and the enthusiasm from investors was off the charts – the fund was managing north of $1Bn by then.  Somewhat crestfallen I asked him how they were producing such spectacular returns.  “They just sell puts in the S&P, 100 points out of the money”, he told me.  I waited, expecting him to continue with details of how the fund managers handled the enormous tail risk.  I waited in vain. They were selling naked put options.  I can only imagine how those guys did when the VIX blew up in 2003 and, if they made it through that, what on earth happened to them in 2008!

Conclusion

The moral is simple:  one cannot afford to be either all-long, or all-short volatility.  The fund must run a long/short book, buying cheap Gamma and selling expensive Theta wherever possible, and changing the net volatility exposure of the portfolio dynamically, to suit current market conditions. It can certainly be done; and with the new volatility products that have emerged in recent years, the opportunities in the volatility space have never looked more promising.