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The New Long/Short Equity

High Frequency Trading Strategies

One of the benefits of high frequency trading strategies lies in their ability to produce risk-adjusted rates of return that are unmatched by anything that the hedge fund or CTA community is capable of producing.  With such performance comes another attractive feature of HFT firms – their ability to make money (almost) every day.  Of course, HFT firms are typically not required to manage billions of dollars, which is just as well given the limited capacity of most HFT strategies.  But, then again, with a Sharpe ratio of 10, who needs outside capital?  This explains why most investors have a difficult time believing the level of performance achievable in the high frequency world – they never come across such performance, because HFT firms generally have little incentive to show their results to external investors.

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By and large, HFT strategies remain the province of proprietary trading firms that can afford to make an investment in low-latency trading infrastructure that far exceeds what is typically required for a regular trading or investment management firm.  However, while the highest levels of investment performance lie beyond the reach of most investors and money managers, it is still possible to replicate some of the desirable characteristics of high frequency strategies.

Quantitative Equity Strategy

I am going to use an example our Quantitative Equity strategy, which forms part of the Systematic Strategies hedge fund.  The tables and charts below give a broad impression of the performance characteristics of the strategy, which include a CAGR of 14.85% (net of fees) since live trading began in 2013.

Value $1000
The NewEquityLSFig3

 

 

 

 

 

 

 

 

This is a strategy that is designed to produce returns on a  par with the S&P 500 index, but with considerably lower risk:  at just over 4%, the annual volatility of the strategy is only around 1/3 that of the index, while the maximum drawdown has been a little over 2% since inception.  This level of portfolio risk is much lower than can typically be achieved in an equity long/short strategy  (equity market neutral is another story, of course). Furthermore, the realized information ratio of 3.4 is in the upper 1%-tile of risk-adjusted performance amongst equity long/short strategies.  So something rather more interesting must be going on that is very different from the typical approach to long/short equity.
TheNewEquityLSFig5

 

One plausible explanation is that the strategy is exploiting some minor market anomaly that works fine for small amounts of capital, but which cannot be scaled.  But this is not the case here:  the investment universe comprises more than a hundred of the most liquid stocks in US markets, across a broad spectrum of sectors.  And while single-name investment is capped at 10% of average daily volume, this nonetheless provides investment capacity of several hundreds of millions of dollars.

Nor does the reason for the exceptional performance lie in some new portfolio construction technique:  rather, we rely on a straightforward 1/n allocation.  Again, neither is factor exposure the driver of strategy alpha:  as the factor loading table illustrates, strategy performance is largely uncorrelated with most market indices.  It loads significantly on only large cap value, chiefly because the investment universe is defined as comprising the stocks with greatest liquidity (which tend to be large cap value), and on the CBOE VIX index.  The positive correlation with market volatility is a common feature of many types of trading strategy that tend to do better in volatile markets, when short-term investment opportunities are plentiful.

FactorLoadings

While the detail of the strategy must necessarily remain proprietary, I can at least offer some insight that will, I hope, provide food for thought.

We can begin by comparing the returns for two of the stocks in the portfolio, Home Depot and Pfizer.  The charts demonstrate one of important strategy characteristic: not every stock is traded at the same frequency.  Some stocks might be traded once or twice a month; others possibly ten times a day, or more.  In other words, the overall strategy is diversified significantly, not only across assets, but also across investment horizons.  This has a considerable impact on volatility and downside risk in the portfolio.

Home Depot vs. Pfizer Inc.

HD

PFEOverall, the strategy trades an average of 40-60 times a day, or more.   This is, admittedly, towards the low end of the frequency spectrum of HFT strategies – we might describe it as mid-frequency rather than high frequency trading.  Nonetheless,  compared to traditional long/short equity strategies this constitutes a high level of trading activity which, in aggregate, replicates some of the time-diversification benefits of HFT strategies, producing lower strategy volatility.

There is another way in which the strategy mimics, at least partially, the characteristics of a HFT strategy.  The profitability of many (although by no means all) HFT strategies lies in their ability to capture (or, at least, not pay) the bid-offer spread.  That is why latency is so crucial to most HFT strategies – if your aim is to to earn rebates, and/or capture the spread, you must enter and  exit, passively, often using microstructure models to determine when to lean on the bid or offer price.  That in turn depends on achieving a high priority for your orders in the limit order book, which is a function of  latency – you need to be near the top of the queue at all times in order the achieve the required fill rate.

How does that apply here?  While we are not looking to capture the spread, the strategy does seek to avoid taking liquidity and paying the spread.  Where it can do so,  it will offset the bid-offer spread by earning rebates.  In many cases we are able to mitigate the spread cost altogether.  So, while it cannot accomplish what a HFT market-making system can achieve, it can mimic enough of its characteristics – even at low frequency – to produce substantial gains in terms of cost-reduction and return enhancement.  This is important since the transaction volume and portfolio turnover in this approach are significantly greater than for a typical equity long/short strategy.

Portfolio of Strategies vs. Portfolio of Equities

slide06But this feature, while important, is not really the heart of the matter.  Rather, the central point is this:  that the overall strategy is an assembly of individual, independent strategies for each component stock.  And it turns out that the diversification benefit of a portfolio of strategies is generally far greater than for an equal number of stocks, because the equity processes themselves will typically be correlated to a far greater degree than will corresponding trading strategies.  To take the example of the pair of stocks discussed earlier, we find that the correlation between HD and PFE over the period from 2013 to 2017 is around 0.39, based on daily returns.  By comparison, the correlation between the strategies for the two stocks over the same period is only 0.01.

This is generally the case, so that a portfolio of, say, 30 equity strategies, might reasonably be expected to enjoy a level of risk that is perhaps as much as one half that of a portfolio of the underlying stocks, no matter how constructed.  This may be due to diversification in the time dimension, coupled with differences in the alpha generation mechanisms of the underlying strategies – mean reversion vs. momentum, for example

Strategy Robustness Testing

There are, of course, many different aspects to our approach to strategy risk management. Some of these are generally applicable to strategies of all varieties, but there are others that are specific to this particular type of strategy.

A good example of the latter is how we address the issue of strategy robustness. One of the principal concerns that investors have about quantitive strategies is that they may under-perform during adverse market conditions, or even simply stop working altogether. Our approach is to stress test each of the sub-strategy models using Monte Carlo simulation and examine their performance under a wide range of different scenarios, many of which have never been seen in the historical data used to construct the models.

For instance, we typically allow prices to fluctuate randomly by +/- 30% from historical values. But we also randomize the start date of each strategy by up to a year, which reduces the likelihood of a strategy being selected simply on the strength of a lucky start. Finally, we are interested in ensuring that the performance of each sub-strategy is not overly sensitive to the specific parameter values chosen for each model. Again, we test this using Monte Carlo, assessing the performance of each sub-strategy if the parameter values of the model are varied randomly by up to 30%.

The output of all these simulation tests is compiled into a histogram of performance results, from which we select the worst 5%-tile. Only if the worst outcomes – the 1-in-20 results in the left tail of the performance distribution – meet our performance criteria will the sub-strategy advance to the next stage of evaluation, simulated trading. This gives us – and investors – a level of confidence in the ability of the strategy to continue to perform well regardless of how market conditions evolve over time.

MonteCarlo Stress test

 

An obvious question to ask at this point is: if this is such a great idea, why don’t more firms use this approach?  The answer is simple: it involves too much research.  In a typical portfolio strategy there is a single investment idea that is applied cross-sectionally to a universe of stocks (factor models, momentum models, etc).  In the strategy portfolio approach, separate strategies must be developed for each stock individually, which takes far more time and effort.  Consequently such strategies must necessarily scale more slowly.

Another downside to the strategy portfolio approach is that it is less able to control the portfolio characteristics.  For instance, the overall portfolio may, on average, have a beta close to zero; but there are likely to be times when a majority of the individual stock strategies align, producing a significantly higher, or lower, beta.  The key here is to ask the question: what matters more – the semblance of risk control, or the actual risk characteristics of the strategy?  In reality, the risk controls of traditional long/short equity strategies often turn out to be more theoretical than real.  Time and again investors have seen strategies that turn out to be downside-correlated with the market, regardless of the purported “market-neutral” characteristics of the portfolio.  I would argue that what matters far more is how the strategy actually performs under conditions of market stress, regardless of how “market neutral” or “sector neutral” it may purport to be.  And while I agree that this is hardly a widely-held view, my argument would be that one cannot expect to achieve above-average performance simply by employing standard approaches at every turn.

Parallels with Fund of Funds Investment

So, is this really a “new approach” to equity long/short? Actually, no.  It is certainly unusual.  But it follows quite closely the model of a proprietary trading firm, or a Fund of Funds. There, as here, the task is to create a combined portfolio of strategies (or managers), rather than by investing directly in the underlying assets.  A Fund of Funds will seek to create a portfolio of strategies that have low correlations to one another, and may operate a meta-strategy for allocating capital to the component strategies, or managers.  But the overall investment portfolio cannot be as easily constrained as an individual equity portfolio can be – greater leeway must be allowed for the beta, or the dollar imbalance in the longs and shorts, to vary from time to time, even if over the long term the fluctuations average out.  With human managers one always has to be concerned about the risk of “style drift” – i.e. when managers move away from their stated investment mandate, methodologies or objectives, resulting in a different investment outcomes.  This can result in changes in the correlation between a strategy and its peers, or with the overall market.  Quantitative strategies are necessarily more consistent in their investment approach – machines generally don’t alter their own source code – making a drift in style less likely.  So an argument can be made that the risk inherent in this form of equity long/short strategy is on a par with – certainly not greater than – that of a typical fund of funds.

Conclusions

An investment approach that seeks to create a portfolio of strategies, rather than of underlying assets, offers a significant advantage in terms of risk reduction and diversification, due to the relatively low levels of correlation between the component strategies.   The trading costs associated with higher frequency trading can be mitigated using passive entry/exit rules designed to avoid taking liquidity and generating exchange rebates.  The downside is that it is much harder to manage the risk attributes of the portfolio, such as the portfolio beta, sector risk, or even the overall net long/short exposure.  But these are indicators of strategy risk, rather than actual risk itself and they often fail to predict the actual risk characteristics of the strategy, especially during conditions of market stress.  Investors may be better served by an approach to long/short equity that seeks to maximize diversification on the temporal axis as well as in terms of the factors driving strategy alpha.

 

Disclaimer: past performance does not guarantee future results. You should not rely on any past performance as a guarantee of future investment performance. Investment returns will fluctuate. Investment monies are at risk and you may suffer losses on any investment.

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Pairs Trading with Copulas

Introduction

In a previous post, Copulas in Risk Management, I covered in detail the theory and applications of copulas in the area of risk management, pointing out the potential benefits of the approach and how it could be used to improve estimates of Value-at-Risk by incorporating important empirical features of asset processes, such as asymmetric correlation and heavy tails.

In this post I will take a very different tack, demonstrating how copula models have potential applications in trading strategy design, in particular in pairs trading and statistical arbitrage strategies.

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This is not a new concept – in fact the idea occurred to me (and others) many years ago, when copulas began to be widely adopted in financial engineering, risk management and credit derivatives modeling. But it remains relatively under-explored compared to more traditional techniques in this field. Fresh research suggests that it may be a useful adjunct to the more common methods applied in pairs trading, and may even be a more robust methodology altogether, as we shall see.

Recommended Background Reading

http://jonathankinlay.com/2017/01/copulas-risk-management/

http://jonathankinlay.com/2015/02/statistical-arbitrage-using-kalman-filter/

http://jonathankinlay.com/2015/02/developing-statistical-arbitrage-strategies-using-cointegration/

 

Pairs Trading with Copulas
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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.

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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
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Conditional Value at Risk Models

One of the most widely used risk measures is the Value-at-Risk, defined as the expected loss on a portfolio at a specified confidence level. In other words, VaR is a percentile of a loss distribution.
But despite its popularity VaR suffers from well-known limitations: its tendency to underestimate the risk in the (left) tail of the loss distribution and its failure to capture the dynamics of correlation between portfolio components or nonlinearities in the risk characteristics of the underlying assets.

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One method of seeking to address these shortcomings is discussed in a previous post Copulas in Risk Management. Another approach known as Conditional Value at Risk (CVaR), which seeks to focus on tail risk, is the subject of this post.  We look at how to estimate Conditional Value at Risk in both Gaussian and non-Gaussian frameworks, incorporating loss distributions with heavy tails and show how to apply the concept in the context of nonlinear time series models such as GARCH.

 

Var, CVaR and Heavy Tails

 

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Trading Market Sentiment

Text and sentiment analysis has become a very popular topic in quantitative research over the last decade, with applications ranging from market research and political science, to e-commerce.  In this post I am going to outline an approach to the subject, together with some core techniques, that have applications in investment strategy.

In the early days of the developing field of market sentiment analysis, the supply of machine readable content was limited to mainstream providers of financial news such as Reuters or Bloomberg. Over time this has changed with the entry of new competitors in the provision of machine readable news, including, for example, Ravenpack or more recent arrivals like Accern.  Providers often seek to sell not only the raw news feed service, but also their own proprietary sentiment indicators that are claimed to provide additional insight into how individual stocks, market sectors, or the overall market are likely to react to news.  There is now what appears to be a cottage industry producing white papers seeking to demonstrate the value of these services, often accompanied by some impressive pro-forma performance statistics for the accompanying strategies, which include long-only, long/short, market neutral and statistical arbitrage.

For the purpose of demonstration I intend to forego the blandishments of these services, although many are no doubt are excellent, since the reader is perhaps unlikely to have access to them.  Instead, in what follows I will focus on a single news source, albeit a highly regarded one:  the Wall Street Journal.  This is, of course, a simplification intended for illustrative purposes only – in practice one would need to use a wide variety of news sources and perhaps subscribe to a machine readable news feed service.  But similar principles and techniques can be applied to any number of news feeds or online sites.

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The WSJ News Archive

We are going to access the Journal’s online archive, which presents daily news items in a convenient summary format, an example of which is shown below. The archive runs from the beginning of 2012 through to the current day, providing ample data for analysis.  In what follows, I am going to make two important assumptions, neither of which is likely to be 100% accurate – but which will not detract too much from the validity of the research, I hope.  The first assumption is that the news items shown in each daily archive were reported prior to the market open at 9:30 AM.  This is likely to be true for the great majority of the stories, but there are no doubt important exceptions.  Since we intend to treat the news content of each archive as antecedent to the market action during the corresponding trading session, exceptions are likely to introduce an element of look-ahead bias.  The second assumption is that the archive for each day is shown in the form in which it would have appeared on the day in question.  In reality, there are likely to have been revisions to some of the stories made subsequent to their initial publication. So, here too, we must allow for the possibility of look-ahead bias in the ensuing analysis.

fig1

 

With those caveats out of the way, let’s proceed.  We are going to be using broad market data for the S&P 500 index in the analysis to follow, so the first step is to download daily price series for the index.  Note that we begin with daily opening prices, since we intend to illustrate the application of news sentiment analysis with a theoretical day-trading strategy that takes positions at the start of each trading session, exiting at market close.

fig2

From there we calculate the intraday return in the index, from market open to close, as follows:

fig3

Text Analysis & Classification

Next we turn to the task of reading the news archive and categorizing its content.  Mathematica makes the importation of html pages very straightforward,  and we can easily crop the raw text string to exclude page headers and footers.  The approach I am going to take is to derive a sentiment indicator based on an analysis of the sentiment of each word in the daily archive.  Before we can do that we must first convert the text into individuals words, stripping out standard stop-words such as “the” and “in” and converting all the text to lower case.  Naturally one can take this pre-processing a great deal further, by identifying and separating out proper nouns, for example.  Once the text processing stage is complete we can quickly summarize the content, for example by looking at the most common words, or by representing the entire archive in the form of a word cloud.  Given that we are using the archive for the first business day of 2012, it is perhaps unsurprising that we find that “2012”, “new” and “year” feature so prominently!

fig4

 

The subject of sentiment analysis is a complex one and I only touch on it here.  For those interested in the subject I can recommend The Text Mining Handbook, by Feldman and Sanger, which is a standard work on the topic.  Here I am going to employ a machine learning classifier provided with Mathematica 11.  It is not terribly sophisticated (or, at least, has not been developed with financial applications especially in mind), but will serve for the purposes of this article.  For those unfamiliar with the functionality, the operation of the sentiment classification algorithm is straightforward enough.  For instance:

fig5

We apply the algorithm to classify each word in the daily news archive and arrive at a sentiment indicator based on the proportion of words that are classified as “positive”.  The sentiment reading for the archive for Jan-3, 2012, for example, turns out to be 67.4%:

fig6

Sentiment Index Analytics

We can automate the process of classifying the entire WSJ archive with just a few lines of code, producing a time series for the daily sentiment indicator, which has an average daily value of  68.5%  – the WSJ crowd tends to be bullish, clearly!  Note how the 60-day moving average of the indicator rises steadily over the period from 2012 through Q1 2015, then abruptly reverses direction, declining steadily thereafter – even somewhat precipitously towards the end of 2016.

fig7

 

fig8

As with most data series in investment research, we are less interested in the level of a variable, such as a stock price, than we are in the changes in level.   So the next step is to calculate the daily percentage change in the sentiment indicator and examine the correlation with the corresponding intraday return in the S&P 500 Index.  At first glance our sentiment indicator appears to have very little predictive power  – the correlation between indicator changes and market returns is negligibly small overall – but we shall later see that this is not the last word.

 

fig9

 

Conditional Distributions

Thus far the results appear discouraging; but as is often the case with this type of analysis we need to look more closely at the conditional distribution of returns.  Specifically, we will examine the conditional distribution of S&P 500 Index returns when changes in the sentiment index are in the upper and lower quantiles of the distribution. This will enable us to isolate the impact of changes in market sentiment at times when the swings in sentiment are strongest.  In the analysis below, we begin by examining the upper and lower third of the distribution of changes in sentiment:

fig10

The analysis makes clear that the distribution of S&P 500 Index returns is very different on days when the change in market sentiment is large and positive vs. large and negative. The difference is not just limited to the first moment of the conditional distribution, where the difference in the mean return is large and statistically significant, but also in the third moment.  The much larger, negative skewness means that there is a greater likelihood of a large decline in the market on days in which there is a sizable drop in market sentiment, than on days in which sentiment significantly improves.  In other words, the influence of market sentiment changes is manifest chiefly through the mean and skewness of the conditional distributions of market returns.

A News Trading Algorithm

We can capitalize on these effects using a simple trading strategy in which we increase the capital allocated to a long-SPX position on days when market sentiment improves, while reducing exposure on days when market sentiment falls.  We increase the allocation by a factor – designated the leverage factor – on days when the change in the sentiment indicator is in the upper 1/3 of the distribution, while reducing the allocation by 1/leveragefactor on days when the change in the sentiment indicator falls in lower 1/3 of the distribution.  The allocation on other days is 100%.  The analysis runs as follows:

fig13 fig14

It turns out that, using a leverage factor of 2.0, we can increase the CAGR from 10% to 21% over the period from 2012-2016 using the conditional distribution approach.  This performance enhancement comes at a cost, since the annual volatility of the news sentiment strategy is 17% compared to only 12% for the long-only strategy. However, the overall net result is positive, since the risk-adjusted rate of return increases from 0.82 to 1.28.

We can explore the robustness of the result, comparing different quantile selections and leverage factors using Mathematica’s interactive Manipulate function:

fig12

Conclusion

We have seen that a simple market sentiment indicator can be created quite easily from publicly available news archives, using a standard machine learning sentiment classification algorithm.  A market sentiment algorithm constructed using methods as straightforward as this appears to provide the capability to differentiate the conditional distribution of market returns on days when changes in market sentiment are significantly positive or negative.  The differences in the higher moments of the conditional distribution appears to be as significant as the differences in the mean.  In principle, we can use the insight provided by the sentiment indicator to enhance a long-only day-trading strategy, increasing leverage and allocation on days when changes to market sentiment are positive and reducing them on days when sentiment declines.  The performance enhancements resulting from this approach appear to be significant.

Several caveats apply.  The S&P 500 index is not tradable, of course, and it is not uncommon to find trading strategies that produce interesting theoretical results.  In practice one would be obliged to implement the strategy using a tradable market proxy, such as a broad market ETF or futures contract.  The strategy described here, which enters and exits positions daily, would incur substantial trading costs, that would be further exacerbated by the use of leverage.

Of course there are many other uses one can make of news data, in particular with firm-specific news and sentiment analytics, that fall outside the scope of this article.  Hopefully, however, the methodology described here will provide a sign-post towards further, more practically useful research.