Volatility Modeling Archives - Page 2 of 4 - QUANTITATIVE RESEARCH AND TRADING

July 28, 2020

Volatility Trading Styles

The VIX Surge of Feb 2018

Volatility trading has become a popular niche in investing circles over the last several years. It is easy to understand why: with yields at record lows it has been challenging to find an alternative to equities that offers a respectable return. Volatility, however, continues to be volatile (which is a good thing in this context) and the steepness of the volatility curve has offered investors attractive returns by means of the volatility carry trade. In this type of volatility trading the long end of the vol curve is sold, often using longer dated futures in the CBOE VIX Index, for example. The idea is that profits are generated as the contract moves towards expiration, “riding down” the volatility curve as it does so. This is a variant of the ever-popular “riding down the yield curve” strategy, a staple of fixed income traders for many decades. The only question here is what to use to hedge the short volatility exposure – highly correlated S&P500 futures are a popular choice, but the resulting portfolio is exposed to significant basis risk. Besides, when the volatility curve flatten and inverts, as it did in spectacular fashion in February, the transition tends to happen very quickly, producing a substantial losses on the portfolio. These may be temporary, if the volatility spike is small or short-lived, but as traders and investors discovered in the February drama, neither of these two desirable outcomes is guaranteed. Indeed as I pointed out in an earlier post this turned out to be the largest ever two-day volatility surge in history. The results for many hedge funds, especially in the quant sector were devastating, with several showing high single digit or double-digit losses for the month.

Over time, investors have become more familiar with the volatility space and have learned to be wary of strategies like volatility carry or option selling, where the returns look superficially attractive, until a market event occurs. So what alternative approaches are available?

An Aggressive Approach to Volatility Trading

In my blog post Riders on the Storm I described one such approach: the Option Trader strategy on our Algo Trading Platform made a massive gain of 27% for the month of February and as a result strategy performance is now running at over 55% for 2018 YTD, while maintaining a Sharpe Ratio of 2.23.

The challenge with this style of volatility trading is that it requires a trader (or trading system) with a very strong stomach and an investor astute enough to realize that sizable drawdowns are in a sense “baked in” for this trading strategy and should be expected from time to time. But traders are often temperamentally unsuited to this style of trading – many react by heading for the hills and liquidating positions at the first sign of trouble; and the great majority of investors are likewise unable to withstand substantial drawdowns, even if the eventual outcome is beneficial.

The Market Timing Approach

So what alternatives are there? One way of dealing with the problem of volatility spikes is simply to try to avoid them. That means developing a strategy logic that step aside altogether when there is a serious risk of an impending volatility surge. Market timing is easy to describe, but very hard to implement successfully in practice. The VIX Swing Trader strategy on the Systematic Algotrading platform attempts to do just that, only trading when it judges it safe to do so. So, for example, it completely side-stepped the volatility debacle in August 2015, ending the month up +0.74%. The strategy managed to do the same in February this year, finishing ahead +1.90%, a pretty creditable performance given how volatility funds performed in general. One helpful characteristic of the strategy is that it trades the less-volatile mid-section of the volatility curve, in the form of the VelocityShares Daily Inverse VIX MT ETN (ZIV). This ensures that the P&L swings are much less dramatic than for strategies exposed to the front end of the curve, as most volatility strategies are.

A potential weakness of the strategy is that it will often miss great profit opportunities altogether, since its primary focus is to keep investors out of trouble. Allied to this, the system may trade only a handful of times each month. Indeed, if you look at the track record above you find find months in which the strategy made no trades at all. From experience, investors are almost as bad at sitting on their hands as they are at taking losses: patience is not a highly regarded virtue in the investing community these days. But if you are a cautious, patient investor looking for a source of uncorrelated alpha, this strategy may be a good choice. On the other hand, if you are looking for high returns and are willing to take the associated risks, there are choices better suited to your goals.

The Hedging Approach to Volatility Trading

A “middle ground” is taken in our Hedged Volatility strategy. Like the VIX Swing Trader this strategy trades VIX ETFs/ETNs, but it does so across the maturity table. What distinguishes this strategy from the others is its use of long call options in volatility products like the iPath S&P 500 VIX ST Futures ETN (VXX) to hedge the short volatility exposure in other ETFs in the portfolio. This enables the strategy to trade much more frequently, across a wider range of ETF products and maturities, with the security of knowing that the tail risk in the portfolio is protected. Consequently, since live trading began in 2016, the strategy has chalked up returns of over 53% per year, with a Sharpe Ratio of 2 and Sortino Ratio above 3. Don’t be confused by the low % of trades that are profitable: the great majority of these loss-making “trades” are in fact hedges, which one would expect to be losers, as most long options trades are. What matters is the overall performance of the strategy.

All of these strategies are available on our Systematic Algotrading Platform, which offers investors the opportunity to trade the strategies in their own brokerage account for a monthly subscription fee.

The Multi-Strategy Approach

The approach taken by the Systematic Volatility Strategy in our Systematic Strategies hedge fund again seeks to steer a middle course between risk and return. It does so by using a meta-strategy approach that dynamically adjusts the style of strategy deployed as market conditions change. Rather than using options (the strategy’s mandate includes only ETFs) the strategy uses leveraged ETFs to provide tail risk protection in the portfolio. The strategy has produced an average annual compound return of 38.54% since live trading began in 2015, with a Sharpe Ratio of 3.15:

A more detailed explanation of how leveraged ETFs can be used in volatility trading strategies is given in an earlier post:

http://jonathankinlay.com/2015/05/investing-leveraged-etfs-theory-practice/

Conclusion: Choosing the Investment Style that’s Right for You

There are different styles of volatility trading and the investor should consider carefully which best suits his own investment temperament. For the “high risk” investor seeking the greatest profit the Option Trader strategy in an excellent choice, producing returns of +176% per year since live trading began in 2016. At the other end of the spectrum, the VIX Swing trader is suitable for an investor with a cautious trading style, who is willing to wait for the right opportunities, i.e. ones that are most likely to be profitable. For investors seeking to capitalize on opportunities in the volatility space, but who are concerned about the tail risk arising from major market corrections, the Hedge Volatility strategy offers a better choice. Finally, for investors able to invest $250,000 or more, a hedge fund investment in our Systematic Volatility strategy offers the highest risk-adjusted rate of return.

May 26, 2020

Finding Alpha in 2018

Given the current macro-economic environment, where should investors focus their search for sources of alpha in the year ahead? By asking enough economists or investment managers you will find as many different opinions on the subject as would care to, no doubt many of them conflicting. These are some thoughts on the subject from my perspective, as a quantitative hedge fund manager.

Global Market Performance in 2017

Let’s begin by reviewing some of the best and worst performing assets of 2017 (I am going to exclude cryptocurrencies from the ensuing discussion). Broadly speaking, the story across the piste has been one of strong appreciation in emerging markets, both in equities and currencies, especially in several of the Eastern European economies. In Government bond markets Greece has been the star of the show, having stepped back from the brink of the economic abyss. Overall, international diversification has been a key to investment success in 2017 and I believe that pattern will hold in 2018.

US Yield Curve and Its Implications

Another key development that investors need to take account of is the extraordinary degree of flattening of the yield curve in US fixed income over the course of 2017:

This process has now likely reached the end point and will begin to reverse as the Fed and other central banks in developed economies start raising rates. In 2018 investors should seek to protect their fixed income portfolios by shortening duration, moving towards the front end of the curve.

US Volatility and Equity Markets

A prominent feature of US markets during 2017 has been the continuing collapse of equity index volatility, specifically the VIX Index, which reached an all-time low of 9.14 in November and continues to languish at less than half the average level of the last decade:

Source: Wolfram Alpha

One consequence of the long term decline in volatility has been to drastically reduce the profitability of derivatives markets, for both traders and market makers. Firms have struggled to keep up with the high cost of technology and the expense of being connected to the fragmented U.S. options market, which is spread across 15 exchanges. Earlier in 2017, Interactive Brokers Group Inc. sold its Timber Hill options market-making unit — a pioneer of electronic trading — to Two Sigma Securities. Then, in November, Goldman Sachs announced it was shuttering its option market making business in US exchanges, citing high costs, sluggish volume and low volatility.

The impact has likewise been felt by volatility strategies, which performed well in 2015 and 2016, only to see returns decline substantially in 2017. Our own Systematic Volatility strategy, for example, finished the year up only 8.08%, having produced over 28% in the prior year.

One side-effect of low levels of index volatility has been a fall in stock return correlations, and, conversely, a rise in the dispersion of stock returns. It turns out that index volatility and stock correlation are themselves correlated and indeed, cointegrated:

http://jonathankinlay.com/2017/08/correlation-cointegration/

In simple terms, stocks have a tendency to disperse more widely around an increasingly sluggish index. The “kinetic energy” of markets has to disperse somewhere and if movements in the index are muted then relative movement in individual equity returns will become more accentuated. This is an environment that ought to favor stock picking and both equity long/short and market neutral strategies should outperform. This certainly proved to be the case for our Quantitative Equity long/short strategy, which produced a net return of 17.79% in 2017, but with an annual volatility of under 5%:

Looking ahead to 2018, I expect index volatility and equity correlations rise as the yield curve begins to steepen, producing better opportunities for volatility strategies. Returns from equity long/short and market neutral strategies may moderate a little as dispersion diminishes.

Futures Markets

Big increases in commodity prices and dispersion levels also lead to improvements in the performance of many CTA strategies in 2017. In the low frequency space our Futures WealthBuilder strategy produced a net return of 13.02% in 2017, with a Sharpe Ratio above 3 (CAGR from inception in 2013 is now at 20.53%, with an average annual standard deviation of 6.36%). The star performer, however, was our High Frequency Futures strategy. Since launch in March 2017 this has produce a net return of 32.72%, with an annual standard deviation of 5.02%, on track to generate an annual Sharpe Ratio above 8 :

Looking ahead, the World Bank has forecast an increase of around 4% in energy prices during 2018, with smaller increases in the price of agricultural products. This is likely to be helpful to many CTA strategies, which will likely see further enhancements in performance over the course of the year. Higher frequency strategies are more dependent on commodity market volatility, which is seen more likely to rise than fall in the year ahead.

Conclusion

US fixed income investors are likely to want to shorten duration as the yield curve begins to steepen in 2018, bringing with it higher levels of index volatility that will favor equity high frequency and volatility strategies. As in 2017, there is likely much benefit to be gained in diversifying across international equity and currency markets. Strengthening energy prices are likely to sustain higher rates of return in futures strategies during the coming year.

April 21, 2020

The Story of a HFT Strategy

VIX HFT Scalper

March 31, 2020

Correlation Cointegration

In a previous post I looked at ways of modeling the relationship between the CBOE VIX Index and the Year 1 and Year 2 CBOE Correlation Indices:

http://jonathankinlay.com/2017/08/modeling-volatility-correlation/

The question was put to me whether the VIX and correlation indices might be cointegrated.

Let’s begin by looking at the pattern of correlation between the three indices:

If you recall from my previous post, we were able to fit a linear regression model with the Year 1 and Year 2 Correlation Indices that accounts for around 50% in the variation in the VIX index. While the model certainly has its shortcomings, as explained in the post, it will serve the purpose of demonstrating that the three series are cointegrated. The standard Dickey-Fuller test rejects the null hypothesis of a unit root in the residuals of the linear model, confirming that the three series are cointegrated, order 1.

Vector Autoregression

We can attempt to take the modeling a little further by fitting a VAR model. We begin by splitting the data into an in-sample period from Jan 2007 to Dec 2015 and an out-of-sample test period from Jan 2016 to Aug 2017. We then fit a vector autoregression model to the in-sample data:

When we examine how the model performs on the out-of-sample data, we find that it fails to pick up on much of the variation in the series – the forecasts are fairly flat and provide quite poor predictions of the trends in the three series over the period from 2016-2017:

Conclusion

The VIX and Correlation Indices are not only highly correlated, but also cointegrated, in the sense that a linear combination of the series is stationary.

One can fit a weakly stationary VAR process model to the three series, but the fit is quite poor and forecasts from the model don’t appear to add much value. It is conceivable that a more comprehensive model involving longer lags would improve forecasting performance.

March 24, 2020

Modeling Volatility and Correlation

In a previous blog post I mentioned the VVIX/VIX Ratio, which is measured as the ratio of the CBOE VVIX Index to the VIX Index. The former measures the volatility of the VIX, or the volatility of volatility.

http://jonathankinlay.com/2017/07/market-stress-test-signals-danger-ahead/

A follow-up article in ZeroHedge shortly afterwards pointed out that the VVIX/VIX ratio had reached record highs, prompting Goldman Sachs analyst Ian Wright to comment that this could signal the ending of the current low-volatility regime:

A linkedIn reader pointed out that individual stock volatility was currently quite high and when selling index volatility one is effectively selling stock correlations, which had now reached historically low levels. I concurred:

What’s driving the low vol regime is the exceptionally low level of cross-sectional correlations. And, as correlations tighten, index vol will rise. Worse, we are likely to see a feedback loop – higher vol leading to higher correlations, further accelerating the rise in index vol. So there is a second order, Gamma effect going on. We see that is the very high levels of the VVIX index, which shot up to 130 last week. The all-time high in the VVIX prior to Aug 2015 was around 120. The intra-day high in Aug 2015 reached 225. I’m guessing it will get back up there at some point, possibly this year.

As there appears to be some interest in the subject I decided to add a further blog post looking a little further into the relationship between volatility and correlation. To gain some additional insight we are going to make use of the CBOE implied correlation indices. The CBOE web site explains:

Using SPX options prices, together with the prices of options on the 50 largest stocks in the S&P 500 Index, the CBOE S&P 500 Implied Correlation Indexes offers insight into the relative cost of SPX options compared to the price of options on individual stocks that comprise the S&P 500.

CBOE calculates and disseminates two indexes tied to two different maturities, usually one year and two years out. The index values are published every 15 seconds throughout the trading day.

Both are measures of the expected average correlation of price returns of S&P 500 Index components, implied through SPX option prices and prices of single-stock options on the 50 largest components of the SPX.

Dispersion Trading

One application is dispersion trading, which the CBOE site does a good job of summarizing:

The CBOE S&P 500 Implied Correlation Indexes may be used to provide trading signals for a strategy known as volatility dispersion (or correlation) trading. For example, a long volatility dispersion trade is characterized by selling at-the-money index option straddles and purchasing at-the-money straddles in options on index components. One interpretation of this strategy is that when implied correlation is high, index option premiums are rich relative to single-stock options. Therefore, it may be profitable to sell the rich index options and buy the relatively inexpensive equity options.

The VIX Index and the Implied Correlation Indices

Again, the CBOE web site is worth quoting:

The CBOE S&P 500 Implied Correlation Indexes measure changes in the relative premium between index options and single-stock options. A single stock’s volatility level is driven by factors that are different from what drives the volatility of an Index (which is a basket of stocks). The implied volatility of a single-stock option simply reflects the market’s expectation of the future volatility of that stock’s price returns. Similarly, the implied volatility of an index option reflects the market’s expectation of the future volatility of that index’s price returns. However, index volatility is driven by a combination of two factors: the individual volatilities of index components and the correlation of index component price returns.

Let’s dig into this analytically. We first download and plot the daily for the VIX and Correlation Indices from the CBOE web site, from which it is evident that all three series are highly correlated:

An inspection reveals significant correlations between the VIX index and the two implied correlation indices, which are themselves highly correlated. The S&P 500 Index is, of course, negatively correlated with all three indices:

Modeling Volatility-Correlation

The response surface that describes the relationship between the VIX index and the two implied correlation indices is locally very irregular, but the slope of the surface is generally positive, as we would expect, since the level of VIX correlates positively with that of the two correlation indices.

The most straightforward approach is to use a simple linear regression specification to model the VIX level as a function of the two correlation indices. We create a VIX Model Surface object using this specification with the Mathematica Predict function:The linear model does quite a good job of capturing the positive gradient of the response surface, and in fact has a considerable amount of explanatory power, accounting for a little under half the variance in the level of the VIX index:

However, there are limitations. To begin with, the assumption of independence between the explanatory variables, the correlation indices, clearly does not hold. In cases such as this, where explanatory variables are multicolinear, we are unable to draw inferences about the explanatory power of individual regressors, even though the model as a whole may be highly statistically significant, as here.

Secondly, a linear regression model is not going to capture non-linearities in the volatility-correlation relationship that are evident in the surface plot. This is confirmed by a comparison plot, which shows that the regression model underestimates the VIX level for both low and high values of the index:

We can achieve a better outcome using a machine learning algorithm such as nearest neighbor, which is able to account for non-linearities in the response surface:

The comparison plot shows a much closer correspondence between actual and predicted values of the VIX index, even though there is evidence of some remaining heteroscedasticity in the model residuals:

Conclusion

A useful way to think about index volatility is as a two dimensional process, with time-series volatility measured on one dimension and dispersion (cross-sectional volatility, the inverse of correlation) measured on the second. The two factors are correlated and, as we have shown here, interact in a complicated, non-linear way.

The low levels of index volatility we have seen in recent months result, not from low levels of volatility in component stocks, but in the historically low levels of correlation (high levels of dispersion) in the underlying stock returns processes. As correlations begin to revert to historical averages, the impact will be felt in an upsurge in index volatility, compounded by the non-linear interaction between the two factors.

December 10, 2019

Modeling Asset Processes

Introduction

Over the last twenty five years significant advances have been made in the theory of asset processes and there now exist a variety of mathematical models, many of them computationally tractable, that provide a reasonable representation of their defining characteristics.

While the Geometric Brownian Motion model remains a staple of stochastic calculus theory, it is no longer the only game in town. Other models, many more sophisticated, have been developed to address the shortcomings in the original. There now exist models that provide a good explanation of some of the key characteristics of asset processes that lie beyond the scope of models couched in a simple Gaussian framework. Features such as mean reversion, long memory, stochastic volatility, jumps and heavy tails are now readily handled by these more advanced tools.

In this post I review a critical selection of asset process models that belong in every financial engineer’s toolbox, point out their key features and limitations and give examples of some of their applications.

Modeling Asset Processes

October 15, 2019

Selling Volatility

Straddles and Strangles

July 23, 2019

Crash-Proof Investing

As markets continue to make new highs against a backdrop of ever diminishing participation and trading volume, investors have legitimate reasons for being concerned about prospects for the remainder of 2016 and beyond, even without consideration to the myriad of economic and geopolitical risks that now confront the US and global economies. Against that backdrop, remaining fully invested is a test of nerves for those whose instinct is that they may be picking up pennies in front an oncoming steamroller. On the other hand, there is a sense of frustration in cashing out, only to watch markets surge another several hundred points to new highs.

In this article I am going to outline some steps investors can take to match their investment portfolios to suit current market conditions in a way that allows them to remain fully invested, while safeguarding against downside risk. In what follows I will be using our own Strategic Volatility Strategy, which invests in volatility ETFs such as the iPath S&P 500 VIX ST Futures ETN (NYSEArca:VXX) and the VelocityShares Daily Inverse VIX ST ETN (NYSEArca:XIV), as an illustrative example, although the principles are no less valid for portfolios comprising other ETFs or equities.

Risk and Volatility

Risk may be defined as the uncertainty of outcome and the most common way of assessing it in the context of investment theory is by means of the standard deviation of returns. One difficulty here is that one may never ascertain the true rate of volatility – the second moment – of a returns process; one can only estimate it. Hence, while one can be certain what the closing price of a stock was at yesterday’s market close, one cannot say what the volatility of the stock was over the preceding week – it cannot be observed the way that a stock price can, only estimated. The most common estimator of asset volatility is, of course, the sample standard deviation. But there are many others that are arguably superior: Log-Range, Parkinson, Garman-Klass to name but a few (a starting point for those interested in such theoretical matters is a research paper entitled Estimating Historical Volatility, Brandt & Kinlay, 2005).

Leaving questions of estimation to one side, one issue with using standard deviation as a measure of risk is that it treats upside and downside risk equally – the “risk” that you might double your money in an investment is regarded no differently than the risk that you might see your investment capital cut in half. This is not, of course, how investors tend to look at things: they typically allocate a far higher cost to downside risk, compared to upside risk.

One way to address the issue is by using a measure of risk known as the semi-deviation. This is estimated in exactly the same way as the standard deviation, except that it is applied only to negative returns. In other words, it seeks to isolate the downside risk alone.

This leads directly to a measure of performance known as the Sortino Ratio. Like the more traditional Sharpe Ratio, the Sortino Ratio is a measure of risk-adjusted performance – the average return produced by an investment per unit of risk. But, whereas the Sharpe Ratio uses the standard deviation as the measure of risk, for the Sortino Ratio we use the semi-deviation. In other words, we are measuring the expected return per unit of downside risk.

There may be a great deal of variation in the upside returns of a strategy that would penalize the risk-adjusted returns, as measured by its Sharpe Ratio. But using the Sortino Ratio, we ignore the upside volatility entirely and focus exclusively on the volatility of negative returns (technically, the returns falling below a given threshold, such as the risk-free rate. Here we are using zero as our benchmark). This is, arguably, closer to the way most investors tend to think about their investment risk and return preferences.

In a scenario where, as an investor, you are particularly concerned about downside risk, it makes sense to focus on downside risk. It follows that, rather than aiming to maximize the Sharpe Ratio of your investment portfolio, you might do better to focus on the Sortino Ratio.

Factor Risk and Correlation Risk

Another type of market risk that is often present in an investment portfolio is correlation risk. This is the risk that your investment portfolio correlates to some other asset or investment index. Such risks are often occluded – hidden from view – only to emerge when least wanted. For example, it might be supposed that a “dollar-neutral” portfolio, i.e. a portfolio comprising equity long and short positions of equal dollar value, might be uncorrelated with the broad equity market indices. It might well be. On the other hand, the portfolio might become correlated with such indices during times of market turbulence; or it might correlate positively with some sector indices and negatively with others; or with market volatility, as measured by the CBOE VIX index, for instance.

Where such dependencies are included by design, they are not a problem; but when they are unintended and latent in the investment portfolio, they often create difficulties. The key here is to test for such dependencies against a variety of risk factors that are likely to be of concern. These might include currency and interest rate risk factors, for example; sector indices; or commodity risk factors such as oil or gold (in a situation where, for example, you are investing a a portfolio of mining stocks). Once an unwanted correlation is identified, the next step is to adjust the portfolio holdings to try to eliminate it. Typically, this can often only be done in the average, meaning that, while there is no correlation bias over the long term, there may be periods of positive, negative, or alternating correlation over shorter time horizons. Either way, it’s important to know.

Using the Strategic Volatility Strategy as an example, we target to maximize the Sortino Ratio, subject also to maintaining very lows levels of correlation to the principal risk factors of concern to us, the S&P 500 and VIX indices. Our aim is to create a portfolio that is broadly impervious to changes in the level of the overall market, or in the level of market volatility.

One method of quantifying such dependencies is with linear regression analysis. By way of illustration, in the table below are shown the results of regressing the daily returns from the Strategic Volatility Strategy against the returns in the VIX and S&P 500 indices. Both factor coefficients are statistically indistinguishable from zero, i.e. there is significant no (linear) dependency. However, the constant coefficient, referred to as the strategy alpha, is both positive and statistically significant. In simple terms, the strategy produces a return that is consistently positive, on average, and which is not dependent on changes in the level of the broad market, or its volatility. By contrast, for example, a commonplace volatility strategy that entails capturing the VIX futures roll would show a negative correlation to the VIX index and a positive dependency on the S&P500 index.

Tail Risk

Ever since the publication of Nassim Taleb’s “The Black Swan”, investors have taken a much greater interest in the risk of extreme events. If the bursting of the tech bubble in 2000 was not painful enough, investors surely appear to have learned the lesson thoroughly after the financial crisis of 2008. But even if investors understand the concept, the question remains: what can one do about it?

The place to start is by looking at the fundamental characteristics of the portfolio returns. Here we are not such much concerned with risk, as measured by the second moment, the standard deviation. Instead, we now want to consider the third and forth moments of the distribution, the skewness and kurtosis.

Comparing the two distributions below, we can see that the distribution on the left, with negative skew, has nonzero probability associated with events in the extreme left of the distribution, which in this context, we would associate with negative returns. The distribution on the right, with positive skew, is likewise “heavy-tailed”; but in this case the tail “risk” is associated with large, positive returns. That’s the kind of risk most investors can live with.

Source: Wikipedia

A more direct measure of tail risk is kurtosis, literally, “heavy tailed-ness”, indicating a propensity for extreme events to occur. Again, the shape of the distribution matters: a heavy tail in the right hand portion of the distribution is fine; a heavy tail on the left (indicating the likelihood of large, negative returns) is a no-no.

Let’s take a look at the distribution of returns for the Strategic Volatility Strategy. As you can see, the distribution is very positively skewed, with a very heavy right hand tail. In other words, the strategy has a tendency to produce extremely positive returns. That’s the kind of tail risk investors prefer.

Another way to evaluate tail risk is to examine directly the performance of the strategy during extreme market conditions, when the market makes a major move up or down. Since we are using a volatility strategy as an example, let’s take a look at how it performs on days when the VIX index moves up or down by more than 5%. As you can see from the chart below, by and large the strategy returns on such days tend to be positive and, furthermore, occasionally the strategy produces exceptionally high returns.

The property of producing higher returns to the upside and lower losses to the downside (or, in this case, a tendency to produce positive returns in major market moves in either direction) is known as positive convexity.

Positive convexity, more typically found in fixed income portfolios, is a highly desirable feature, of course. How can it be achieved? Those familiar with options will recognize the convexity feature as being similar to the concept of option Gamma and indeed, one way to produce such a payoff is buy adding options to the investment mix: put options to give positive convexity to the downside, call options to provide positive convexity to the upside (or using a combination of both, i.e. a straddle).

In this case we achieve positive convexity, not by incorporating options, but through a judicious choice of leveraged ETFs, both equity and volatility, for example, the ProShares UltraPro S&P500 ETF (NYSEArca:UPRO) and the ProShares Ultra VIX Short-Term Futures ETN (NYSEArca:UVXY).

Putting It All Together

While we have talked through the various concepts in creating a risk-protected portfolio one-at-a-time, in practice we use nonlinear optimization techniques to construct a portfolio that incorporates all of the desired characteristics simultaneously. This can be a lengthy and tedious procedure, involving lots of trial and error. And it cannot be emphasized enough how important the choice of the investment universe is from the outset. In this case, for instance, it would likely be pointless to target an overall positively convex portfolio without including one or more leveraged ETFs in the investment mix.

Let’s see how it turned out in the case of the Strategic Volatility Strategy.

Note that, while the portfolio Information Ratio is moderate (just above 3), the Sortino Ratio is consistently very high, averaging in excess of 7. In large part that is due to the exceptionally low downside risk, which at 1.36% is less than half the standard deviation (which is itself quite low at 3.3%). It is no surprise that the maximum drawdown over the period from 2012 amounts to less than 1%.

A critic might argue that a CAGR of only 10% is rather modest, especially since market conditions have generally been so benign. I would answer that criticism in two ways. Firstly, this is an investment that has the risk characteristics of a low-duration government bond; and yet it produces a yield many times that of a typical bond in the current low interest rate environment.

Secondly, I would point out that these results are based on use of standard 2:1 Reg-T leverage. In practice it is entirely feasible to increase the leverage up to 4:1, which would produce a CAGR of around 20%. Investors can choose where on the spectrum of risk-return they wish to locate the portfolio and the strategy leverage can be adjusted accordingly.

Conclusion

The current investment environment, characterized by low yields and growing downside risk, poses difficult challenges for investors. A way to address these concerns is to focus on metrics of downside risk in the construction of the investment portfolio, aiming for high Sortino Ratios, low correlation with market risk factors, and positive skewness and convexity in the portfolio returns process.

Such desirable characteristics can be achieved with modern portfolio construction techniques providing the investment universe is chosen carefully and need not include anything more exotic than a collection of commonplace ETF products.

July 16, 2019

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.

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.

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.

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:

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).

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:

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):

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:

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.

June 18, 2019

Trading With Indices

In this post I want to discuss ways to make use of signals from relevant market indices in your trading. These signals can add value regardless of whether you trade algorithmically or manually. The techniques described here are one of the most widely applicable in the quantitative analyst’s arsenal.

Let’s motivate the discussion by looking an example of a simple trading system trading the VIX on weekly bars. Performance results for the system are summarized in the chart and table below. The system outperforms the buy and hold return by a substantial margin, with a profit factor of over 3 and a win rate exceeding 82%. What’s not to like?

Well, for one thing, this isn’t really a trading system – because the VIX Index itself isn’t tradable. So the performance results are purely notional (and, if you didn’t already notice, no slippage or commission is included).

It is very easy to build high-performing trading system in indices – because they are not traded products, index prices are often stale and tend to “follow” the price action in the equivalent traded market.

This particular system for the VIX Index took me less than ten minutes to develop and comprises only a few lines of code. The system makes use of a simple RSI indicator to decide when to buy or sell the index. I optimized the indicator parameters (separately for long and short) over the period to 2012, and tested it out-of-sample on the data from 2013-2016.

inputs:
Price( Close ) ,
Length( 14 ) ,
OverSold( 30 ) ;

variables:
RSIValue( 0 );

RSIValue = RSI( Price, Length );
if CurrentBar > 1 and RSIValue crosses over OverSold then
Buy ( !( “RsiLE” ) ) next bar at market;

The daily system I built for the S&P 500 Index is a little more sophisticated than the VIX model, and produces the following results.

Using Index Trading Systems

We have seen that its trivially easy to build profitable trading systems for index products. But since they can’t be traded, what’s the point?

The analyst might be tempted by the idea of using the signals generated by an index trading system to trade a corresponding market, such as VIX or eMini futures. However, this approach is certain to fail. Index prices lag the prices of equivalent futures products, where traders first monetize their view on the market. So using an index strategy directly to trade a cash or futures market would be like trying to trade using prices delayed by a few seconds, or minutes – a recipe for losing money.

Nor is it likely that a trading system developed for an index product will generalize to a traded market. What I mean by this is that if you were to take an index strategy, such as the VIX RSI strategy, transfer it to VIX futures and tweak the parameters in the hope of producing a profitable system, you are likely to be disappointed. As I have shown, you can produce a profitable index trading system using the simplest and most antiquated trading concepts (such as the RSI index) that long ago ceased to offer any predictive value in actual traded markets. Index markets are actually inefficient – the prices of index products often fail to fully reflect all relevant, available information in a timely way. Such simple inefficiencies are easily revealed by indicators such as moving averages. Traded markets, by contrast, are highly efficient and, with the exception of HFT, it is going to take a great deal more than a simple moving average to provide insight into the few inefficiencies that do arise.

Strategies in index products are best thought of, not as trading strategies, but rather as a means of providing broad guidance as to the general condition of the market and its likely direction over the longer term. To take the VIX index strategy as an example, you can see that each “trade” spans several weeks. So one might regard a “buy” signal from the VIX index system as an indication that volatility is expected to rise over the next month or two. A trader might use that information to lean on the side of being long volatility, perhaps even avoiding any short volatility positions altogether for the next several weeks. Following the model’s guidance in that way would would certainly have helped many equity and volatility traders during the market sell off during August 2015, for example:

The S&P 500 Index model is one I use to provide guidance as to market conditions for the current trading day. It is a useful input to my thinking as to how aggressive I want my trading models to be during the upcoming session. If the index model suggests a positive tone to the market, with muted volatility, I might be inclined to take a more aggressive stance. If the model starts trading to the short side, however, I am likely to want to be much more cautious. Yesterday (May 16, 2016), for example, the index model took an early long trade, providing confirmation of the positive tenor to the market and encouraging me to trade volatility to the short side more aggressively.

In general, I would tend to classify index trading systems as “decision support” tools that provide a means of shading opinion on the market, or perhaps providing a means of calibrating trading models to the anticipated market conditions. However, they can be used in a more direct way, short of actual trading. For example, one of our volatility trading systems uses the trading signals from a trading system designed for the VVIX volatility-of-volatility index. Another approach is to use the signals from an index trading system as an indicator of the market regime in a regime switching model.

Designing Index Trading Models

Whereas it is profitability that is typically the primary design criterion for an actual trading system, given the purpose of an index trading system there are other criteria that are at least as important.

It should be obvious from these few illustrations that you want to design your index model to trade less frequently than the system you are intending to trade live: if you are swing-trading the eminis on daily bars, it doesn’t help to see 50 trades a day from your index system. What you want is an indication as to whether the market action over the next several days is likely to be positive or negative. This means that, typically, you will design your index system using bar frequencies at least as long as for your live system.

Another way to slow down the signals coming from your index trading system is to design it for very high accuracy – a win rate of 70%, or higher. It is actually quite easy to do this: I have systems that trade the eminis on daily bars that have win rates of over 90%. The trick is simply that you have to be prepared to wait a long time for the trade to come good. For a live system that can often be a problem – no-one like to nurse an underwater position for days or weeks on end. But for an index trading system it matters far less and, in fact, it helps: because you want trading signals over longer horizons than the time intervals you are using in your live trading system.

Since the index system doesn’t have to trade live, it means of course that the usual trading costs and frictions do not apply. The advantage here is that you can come up with concepts for trading systems that would be uneconomic in the real world, but which work perfectly well in the frictionless world of index trading. The downside, however, is that this might lead you to develop index systems that trade far too frequently. So, even though they should not apply, you might seek to introduce trading costs in order to penalize higher frequency trading systems and benefit systems that trade less frequently.

Designing index trading systems in an area in which genetic programming algorithms excel. There are two main reasons for this. Firstly, as I have previously discussed, simple technical indicators of the kind employed by GP modeling systems work well in index markets. Secondly, and more importantly, you can use the GP system to tailor an index trading system to meet the precise criteria you have in mind, such as the % win rate, trading frequency, etc.

An outstanding product that I can highly recommend in this context is Mike Bryant’s Adaptrade Builder. Builder is a superb piece of software whose power and ease of use reflects Mike’s engineering background and systems development expertise.