Signal Processing and Sample Frequency – www.jonathankinlay.com

The Importance of Sample Frequency

Too often we apply a default time horizon for our trading, whether it below (daily, weekly) or higher (hourly, 5 minute) frequency.  Sometimes the choice is dictated by practical considerations, such as a desire to avoid overnight risk, or the (lack of0 availability of low-latency execution platform.

But there is an alternative approach to the trade frequency decision that often yields superior results in terms of trading performance.    The methodology derives from signal processing and the idea essentially is to use Fourier transforms to help identify the cyclical behavior of the strategy alpha and hence determine the best time-frames for sampling and trading.  I wrote about this is a previous blog post, in which I described how to use principal components analysis to investigate the factors driving the returns in various pairs trading strategies.  Here I want to take a simpler approach, in which we use Fourier analysis to select suitable sample frequencies.  The idea is simply to select sample frequencies where the signal strength appears strongest, in the hope that it will lead to superior performance characteristics in what strategy we are trying to develop.

Signal Decomposition for S&P500 eMini Futures

Let’s take as an example the S&P 500 emini futures contract. The chart below shows the continuous ES futures contract plotted at 1-minute intervals from 1998. At the bottom of the chart I have represented the signal analysis as a bar chart (in blue), with each bar representing the amplitude at each frequency. The white dots on the chart identify frequencies that are spaced 10 minutes apart.  It is immediately evident that local maxima in the spectrum occur around 40 mins, 60 mins and 120 mins.  So a starting point for our strategy research might be to look at emini data sampled at these frequencies.  Incidentally, it is worth pointing out that I have restricted the session times to 7AM – 4PM EST, which is where the bulk of the daily volume and liquidity tend to occur.  You may get different results if you include data from the Globex session.

Emini Signal

This is all very intuitive and unsurprising: the clearest signals occur at frequencies that most traders typically tend to trade, using hourly data, for example. Any strategy developer is already quite likely to consider these and other common frequencies as part of their regular research process.  There are many instances of successful trading strategies built on emini data sampled at 60 minute intervals.

Signal Decomposition for US Bond Futures

Let’s look at a rather more interesting example:  US (30 year) Bond futures. Unlike the emini contract, the spectral analysis of the US futures contract indicates that the strongest signal by far occurs at a frequency of around 47 minutes.  This is decidedly an unintuitive outcome – I can’t think of any reason why such a strong signal should appear at this cycle length, but, statistically it does. 

US Bond futures

Does it work?  Readers can judge for themselves:  below is an example of an equity curve for a strategy on US futures sampled at 47 minute frequency over the period from 2002.  The strategy has performed very consistently, producing around $25,000 per contract per year, after commissions and slippage.

US futures EC

Conclusion

While I have had similar success with products as diverse as Corn and VIX futures, the frequency domain approach is by no means a panacea:  there are plenty of examples where I have been unable to construct profitable strategies for data sampled at the frequencies with very strong signals. Conversely, I have developed successful strategies using data at frequencies that hardly registered at all on the spectrum, but which I selected for other reasons.  Nonetheless, spectral analysis (and signal processing in general) can be recommended as a useful tool in the arsenal of any quantitative analyst.

Posted in Commodity Futures, eMini Futures, Fourier Transforms, Futures, Signal Processing | Tagged , , , , | Comments Off on Signal Processing and Sample Frequency – www.jonathankinlay.com

Trading Strategy Design – www.jonathankinlay.com

In this post I want to share some thoughts on how to design great automated trading strategies – what to look for, and what to avoid.

For illustrative purposes I am going to use a strategy I designed for the ever-popular S&P500 e-mini futures contract.

The overall equity curve for the strategy is show below.

@ES Equity Curve

This is often the best place to start.  What you want to see, of course, is a smooth, upward-sloping curve, without too many sizable drawdowns, and one in which the strategy continues to make new highs.  This is especially important in the out-of-sample test period (Jan 2014- Jul 2015 in this case).  You will notice a flat period around 2013, which we will need to explore later.  Overall, however, this equity curve appears to fit the stereotypical pattern we hope to see when developing a new strategy.

Let’s move on look at the overall strategy performance numbers.

STRATEGY PERFORMANCE CHARACTERISTICS

@ES Perf Summary(click to enlarge)

 1. Net Profit
Clearly, the most important consideration.  Over the 17 year test period the strategy has produced a net profit  averaging around $23,000 per annum, per contract.  As a rough guide, you would want to see a net profit per contract around 10x the maintenance margin, or higher.

2. Profit Factor
The gross profit divided by the gross loss.  You want this to be as high as possible. Too low, as the strategy will be difficult to trade, because you will see sustained periods of substantial losses.  I would suggest a minimum acceptable PF in the region of 1.25.  Many strategy developers aim for a PF of 1.5, or higher.

3. Number of Trades
Generally, the more trades the better, at least from the point of view of building confidence in the robustness of strategy performance.  A strategy may show a great P&L, but if it only trades once a month it is going to take many many years of performance data to ensure statistical significance.  This strategy, on the other hand, is designed to trade 2-3 times a day.  Given that, and the length of the test period, there is little doubt that the results are statistically significant.

Profit Factor and number of trades are opposing design criteria – increasing the # trades tends to reduce the PF.  That consideration sets an upper bound on the # trades that can be accommodated, before the profit factor deteriorates to unacceptably low levels.  Typically, 4-5 trades a day is about the maximum trading frequency one can expect to achieve.

4. Win Rate
Novice system designers tend to assume that you want this to be as high as possible, but that isn’t typically the case.  It is perfectly feasible to design systems that have a 90% win rate, or higher, but which produce highly undesirable performance characteristics, such as frequent, large drawdowns.  For a typical trading system the optimal range for the win rate is in the region of 40% to 66%.  Below this range, it becomes difficult to tolerate the long sequences of losses that will result, without losing faith in the system.

5. Average Trade
This is the average net profit per trade.  A typical range would be $10 to $100.  Many designers will only consider strategies that have a higher average trade than this one, perhaps $50-$75, or more.  The issue with systems that have a very small average trade is that the profits can quickly be eaten up by commissions. Even though, in this case, the results are net of commissions, one can see a significant deterioration in profits if the average trade is low and trade frequency is high, because of the risk of low fill rates (i.e. the % of limit orders that get filled).  To assess this risk one looks at the number of fills assumed to take place at the high or low of the bar.  If this exceeds 10% of the total # trades, one can expect to see some slippage in the P&L when the strategy is put into production.

6. Average Bars
The number of bars required to complete a trade, on average.  There is no hard limit one can suggest here – it depends entirely on the size of the bars.  Here we are working in 60 minute bars, so a typical trade is held for around 4.5 hours, on average.   That’s a time-frame that I am comfortable with.  Others may be prepared to hold positions for much longer – days, or even weeks.

Perhaps more important is the average length of losing trades. What you don’t want to see is the strategy taking far longer to exit losing trades than winning trades. Again, this is a matter of trader psychology – it is hard to sit there hour after hour, or day after day, in a losing position – the temptation to cut the position becomes hard to ignore.  But, in doing that you are changing the strategy characteristics in a fundamental way, one that rarely produces a performance improvement.

What the strategy designer needs to do is to figure out in advance what the limits are of the investor’s tolerance for pain, in terms of maximum drawdown, average losing trade, etc, and design the strategy to meet those specifications, rather than trying to fix the strategy afterwards.

7. Required Account Size
It’s good to know exactly how large an account you need per contract, so you can figure out how to scale the strategy.  In this case one could hope to scale the strategy up to a 10-lot in a $100,000 account.  That may or may not fit the trader’s requirements and again, this needs to be considered at the outset.  For example, for a trader looking to utilize, say, $1,000,000 of capital, it is doubtful whether this strategy would fit his requirements without considerable work on the implementations issues that arise when trying to trade in anything approaching a 100 contract clip rate.

8. Commission
Always check to ensure that the strategy designer has made reasonable assumptions about slippage and commission.  Here we are assuming $5 per round turn.  There is no slippage, because the strategy executes using limit orders.

9. Drawdown
Drawdowns are, of course, every investor’s bugbear.  No-one likes drawdowns that are either large, or lengthy in relation to the annual profitability of the strategy, or the average trade duration.  A $10,000 max drawdown on a strategy producing over $23,000 a year is actually quite decent – I have seen many e-mini strategies with drawdowns at 2x – 3x that level, or larger.  Again, this is one of the key criteria that needs to be baked into the strategy design at the outset, rather than trying to fix later.

 ANNUAL PROFITABILITY

Let’s now take a look at how the strategy performs year-by-year, and some of the considerations and concerns that often arise.

@ES Annual1. Performance During Downturns
One aspect I always pay attention to is how well the strategy performs during periods of high market stress, because I expect similar conditions to arise in the fairly near future, e.g. as the Fed begins to raise rates.

Here, as you can see, the strategy performed admirably during both the dot com bust of 1999/2000 and the financial crisis of 2008/09.

2. Consistency in the # Trades and % Win Rate
It is not uncommon with low frequency strategies to see periods of substantial variation in the # trades or win rate.  Regardless how good the overall performance statistics are, this makes me uncomfortable.  It could be, for instance, that the overall results are influenced by one or two exceptional years that are unlikely to be repeated.  Significant variation in the trading or win rate raise questions about the robustness of the strategy, going forward.  On the other hand, as here, it is a comfort to see the strategy maintaining a very steady trading rate and % win rate, year after year.

3. Down Years
Every strategy shows variation in year to year performance and one expects to see years in which the strategy performs less well, or even loses money. For me, it rather depends on when such losses arise, as much as the size of the loss.  If a loss occurs in the out-of-sample period it raises serious questions about strategy robustness and, as a result, I am very unlikely to want to put such a strategy into production. If, as here, the period of poor performance occurs during the in-sample period I am less concerned – the strategy has other, favorable characteristics that make it attractive and I am willing to tolerate the risk of one modestly down-year in over 17 years of testing.

INTRA-TRADE DRAWDOWNS

Many trades that end up being profitable go through a period of being under-water.  What matters here is how high those intra-trade losses may climb, before the trade is closed.  To take an extreme example, would you be willing to risk $10,000 to make an average profit of only $10 per trade?  How about $20,000? $50,000? Your entire equity?

The Maximum Average Excursion chart below shows the drawdowns on a trade by trade basis.  Here we can see that, over the 17 year test period, no trade has suffered a drawdown of much more than $5,000.  I am comfortable with that level. Others may prefer a lower limit, or be tolerant of a higher MAE.

MAE

Again, the point is that the problem of a too-high MAE is not something one can fix after the event.  Sure, a stop loss will prevent any losses above a specified size.  But a stop loss also has the unwanted effect of terminating trades that would have turned into money-makers. While psychologically comfortable, the effect of a stop loss is almost always negative  in terms of strategy profitability and other performance characteristics, including drawdown, the very thing that investors are looking to control.

 CONCLUSION
I have tried to give some general guidelines for factors that are of critical importance in strategy design.  There are, of course, no absolutes:  the “right” characteristics depend entirely on the risk preferences of the investor.

One point that strategy designers do need to take on board is the need to factor in all of the important design criteria at the outset, rather than trying (and usually failing) to repair the strategy shortcomings after the event.

 

 

 

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My Big Fat Greek Vacation – www.jonathankinlay.com

LEARNING TO TRUST A TRADING SYSTEM

One of the most difficult decisions to make when running a systematic trading program is SystemTradingknowing when to override the system.  During the early 2000’s when I was running the Caissa Capital fund, the models would regularly make predictions on volatility that I and our head Trader, Ron Henley, a former option trader from the AMEX, disagreed with.  Most times, the system proved to have made the correct decision. My take-away from that experience was that, as human beings, even as traders, we are not very good at pricing risk.

My second take-away was that, by and large, you are better off trusting the system, rather than second-guessing its every decision.  Of course, markets can change and systems break down; but the right approach to assessing this possibility is to use statistical control procedures to determine formally whether or not the system has broken down, rather than going through a routine period of under-performance (see:  is your strategy still working?)

GREEK LESSONS

So when the Greek crisis blew up in June my first instinct was not to start looking grexit jisawimmediately for the escape hatch.  However, as time wore on I became increasingly concerned that the risk of a Grexit or default had not abated.  Moreover, I realized that there was really nothing comparable in the data used in the development of the trading models that was in any way comparable to the scenario facing Greece, the EU and, by a process of contagion, US markets.  Very reluctantly, therefore, I came to the decision that the smart way to play the crises was from the sidelines.  So we made the decisions to go 100% to cash and waited for the crisis to subside.

A week went by. Then another.  Of course, I had written to our investors explaining what we intended to do, and why, so there were no surprises.  Nonetheless, I felt uncomfortable not making money for them.  I did my best to console myself with the principal rule of money management: first, do not lose money.  Of course we didn’t – but neither did we make much money, and ended June more or less flat.

COMEBACK

After the worst of the crisis was behind us, I was relieved to see that the models appeared almost as anxious as I was to make up for lost time.  One of the features of the system is

poker2that it makes aggressive use of leverage. Rather like an expert poker player, when it judges the odds to be in its favor, the system will increase its bet size considerably; at other times it will hunker down, play conservatively, or even exit altogether.  Consequently, the turnover in the portfolio can be large at times.  The cost of trading high volume can substantial, especially in some of the less liquid ETF products, where the bid/ask spread can amount to several cents.  So we typically aim to execute passively, looking to buy on the bid and sell on the offer, using execution algos to split our orders up and randomize them. That also makes it tougher for HFT algos to pick us off as we move into and out of our positions.

So, in July, our Greek “vacation” at an end, the system came roaring back, all guns blazing. It quickly moved into some aggressive short volatility positions to take advantage of the elevated levels in the VIX, before reversing and gong long as the index collapsed to the bottom of the monthly range.

A DOUBLE-DIGIT MONTHLY RETURN: +21.28%

The results were rather spectacular:  a return of +21.28% for the month, bringing the totalMonthly Pct Returns return to 38.25% for 2015 YTD.

In the current low rate environment, this rate of return is extraordinary, but not entirely unprecedented: the strategy has produced double-digit monthly returns several times in the past, most recently in August last year, which saw a return of +14.1%.  Prior, to that, the record had been +8.90% in April 2013.

Such outsized returns come at a price – they have the effect of increasing strategy volatility and hence reducing the Sharpe Ratio.   Of course, investors worry far less about upside volatility than downside volatility (or simi-variance), which is why the Sortino Ratio is in some ways a more appropriate measure of risk-adjusted performance, especially for strategies like ours which has very large kurtosis.

VALUE OF $1000Since inception the compound annual growth rate (CAGR) of the strategy has been 45.60%, while the Sharpe Ratio has maintained a level of around 3 since that time.

Most of the drawdowns we have seen in the strategy have been in single digits, both in back-test and in live trading.  The only exception was in 2013, where we experienced a very short term decline of -13.40%, from which the strategy recovered with a couple of days.

In the great majority of cases, drawdowns in VIX-related strategies result from bad end-of-day “marks” in the VIX index.  These can arise for legitimate reasons, but are often

Sharpecaused by traders manipulating the index, especially around option expiration. Because of the methodology used to compute the VIX, it is very easy to move the index by 5bp to 10bp, or more, by quoting prices for deep OTM put options as expiration nears.  This can be critically important to holders of large VIX option positions and hence the temptation to engage in such manipulation may be irresistible.

For us, such market machinations are simply an annoyance, a cost of doing business in the VIX.  Sure, they inflate drawdowns and strategy volatility, but there is not much we can do about them, other wait patiently for bad “marks” to be corrected the following day, which they almost always are.

Looking ahead over the remainder of the year, we are optimistic about the strategy’s opportunities to make money in August, but, like many traders, we are apprehensive about Ann Returnsthe consequences if the Fed should decide to take action to raise rates in September.  We are likely to want to take in smaller size through the ensuing volatility, since either a long- or short-vol positions carries considerable risk in such a situation.  As and when a rate rise does occur, we anticipate a market correction of perhaps 20% or more, accompanied by surge in market volatility.  We are likely to see the VIX index reach the 20’s or 30’s, before it subsides.  However, under this scenario, opportunities to make money on the short side will likely prove highly attractive going into the final quarter of the year.  We remain hopeful of achieving a total return in the region of 40% to 50%, or more in 2015.

STRATEGY PERFORMANCE REPORT Jan 2012 – Jul 2015

Monthly Returns

 

 

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Making Money with High Frequency Trading

There is no standard definition of high frequency trading, nor a single type of strategy associated with it. Some strategies generate returns, not by taking any kind of view on market direction, but simply by earning Exchange rebates. In other cases the strategy might try to trade ahead of the news as it flows through the market, from stock to stock (or market to market).  Perhaps the most common and successful approach to HFT is market making, where one tries to earn (some fraction of) the spread by constantly quoting both sides of the market.  In the latter approach, which involves processing vast numbers of order messages and other market data in order to decide whether to quote (or pull a quote), latency is of utmost importance.  I would tend to argue that HFT market making owes its success as much, or more, to computer science than it does to trading or microstructure theory.

By contrast, Systematic Strategies’s approach to HFT has always been model-driven.  We are unable to outgun firms like Citadel or Getco in terms of their speed of execution; so, instead, we focus on developing theoretical models of market behavior, on the assumption that we are more likely to identify a source of true competitive advantage that way.  This leads to slower, less latency-sensitive strategies (the models have to be re-estimated or recomputed in real time), but which may nonetheless trade hundreds of times a day.

A good example is provided by our high frequency scalping strategy in Corn futures, which trades around 100-200 times a day, with a win rate of over 80%.

Corn Monthly PNL EC

 

One of the most important considerations in engineering a HFT strategy of this kind is to identify a suitable bar frequency.  We find that our approach works best using data at frequencies of 1-5 minutes, trading at latencies of around 1 millisec, whereas other firms are reacting to data tick-by-tick, with latencies measured in microseconds.

Often strategies are built using only data derived from with a single market, based on indicators involving price action, pattern trading rules, volume or volatility signals.  In other cases, however, signals are derived from other, related markets: the VXX-ES-TY complex would be a typical example of this kind of inter-market approach.

When we build strategies we often start by using a simple retail platform like TradeStation or MultiCharts.  We know that if the strategy can make money on a platform with retail levels of order and market data latency (and commission rates), then it should perform well when we transfer it to a production environment, with much lower latencies and costs.  We might be able to trade only 1-2 contracts in TradeStation, but in production we might aim to scale that up to 10-15 contract per trade, or more, depending on liquidity.  For that reason we prefer to trade only intraday, when market liquidity is deepest; but we often find sufficient levels of liquidity to make trading worthwhile 1-2 hours before the open of the day session.

Generally, while we look for outside money for our lower frequency hedge fund strategies, we tend not to do so for our HFT strategies.  After all, what’s the point?  Each strategy has limited capacity and typically requires no more than a $100,000 account, at most.  And besides, with Sharpe Ratios that are typically in double-digits, it’s usually in our economic interest to use all of the capacity ourselves.  Nor do we tend to license strategies to other trading firms.  Again, why would we?  If the strategies work, we can earn far more from trading rather than licensing them.

We have, occasionally, developed strategies for other firms for markets in which we have no interest (the KOSPI springs to mind).  But these cases tend to be the exception, rather than the rule.

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Why do Investors Invest in Venture Capital Funds?

VC ImageToo Cool for School?

Startups and Venture Capital are red hot right now. And very cool. If that isn’t a contradiction. Perusing the Business Insider list of “The 38 coolest startups in Silicon Valley”, one is struck by the sheer ingenuity of some ideas. And the total stupidity of others.

Innovation is hard. I have been doing for over 30 years in systematic trading and it never gets any easier. Ideas with great theoretical underpinnings sometimes just don’t work. Others look great in backtest, but fail to transition successfully into production. Some strategies work great for a while, then performance fades as market conditions change. What makes innovation so challenging in the arena of investment management is the competition: millions of very smart minds looking at the same data and trying to come up with something new, often using very similar approaches.

Innovation in the real world is just as challenging, but in a different way. It’s easier in the beginning – you have a whole world of possibilities to play with and so it should be less challenging to come up with something new. But innovation is much more difficult than it first appears. If your idea has any value, chances are someone has already thought of it. They may be developing it now. Or they may have tried to develop the concept and found flaws in it that you have yet to discover.

Innovation Is Hard

I have made a few attempts at innovation in the real world. The first was a product called Easypaycard, a concept that a friend of mine came up with at the start of the internet era. The idea was that you could use the card to send money to anyone, anywhere in the world, via the internet, even if they didn’t have a bank account. Aka Paypal. Couldn’t get anyone interested in that idea.

Then there was a product called Web Telemetrics: a microchip that you could place on any object (or person) and track it on an interactive online map, that would provide not only location, but also other readings like temperature, stress and, in the case of a person, heart rate, etc. Bear in mind, this was in 1999, long before Google maps and location services like Apple’s “find my phone”. I thought it was a rather ingenious concept. The VCs didn’t agree – in the final competition they allocated the money to a company selling women’s shirts online. After that I decided to call it quits, for a while.

There matters stood until 2013, when I came up with a consumer electronics product called Adflik. This contained some quite clever circuitry and machine learning algorithms to detect commercials, when it would switch to the next commercial-free station in your playlist of channels. I thought the product concept was great, but I seriously under-estimated the ad-tolerance of the average American. Only one other person agreed with me! Successful product innovation is tough.

You would think that after three total failures I would hang up my boots. It’s not as though my work in investment research is uncreative, or unrewarding. But I find the idea of developing a physical product, or even an electronic product like an iPhone app, compelling.

 Venture Capital Returns

When you ask a venture capitalist about all this, he is likely to respond, rather haughtily, that his business is not about innovation, but rather to produce a return for his investors. Looking at some of the “hottest” startups, however, suggests to me that we are right back where we were in 1999. That gives me serious cause for concern about the returns that VC funds are likely to produce going forward, especially when interest rates start to rise.

For example, the business model for one of these firms is a grocery delivery service: after you have selected your very expensive groceries from Whole Foods, they will shop and deliver your order to you for an extra $3.99. Sounds like a nice idea, but a $2Bn valuation? Ludicrous. That business is going to evaporate in a puff of smoke at the first sign of a recession, or market correction, which could be right around the corner.

So how good are VC’s at producing investment returns? I did a little digging. What I found was that, while in general the VC fund industry is happy to trumpet its returns, it is almost totally silent about the other half of the investment equation: risk. As for something like a Sharpe Ratio – what that?

To answer I dug up some data from Cambridge Associates on their US Venture Capital Index, which measures quarterly pooled end-to-end net returns to Limited Partners. The index data runs from 1981 to Q2 2014, which is plentiful enough to perform a credible analysis on. Here is what I found:

CAGR (1981-Q2 2-14) : 13.85%

Annual SD: 20.35%

Sharpe Ratio: 0.68

Impressive? Not at all. Any half-decent hedge fund should have a Sharpe Ratio of at least 1. Our own Volatility ETF strategy, for example, has a Sharpe of over 3. We are currently running several high frequency strategies with double-digit Sharpe Ratios.

Note that in computing the Sharpe Ratio, I have ignored the risk free rate of return, which at times during the 1980’s was in double digits. So, if anything, the actual risk adjusted performance is likely significantly lower than stated here.

 VC Funds vs Hedge Funds

Why does this matter? Simple – if you gave me a risk budget equivalent to the VC Index, i.e. a standard deviation of 20% per annum, our volatility strategy would have produced a CAGR of over 60%, for the same degree of investment risk. A high frequency strategy operating at the same risk levels would produce returns north of 200% annually!

Of course, just as with hedge funds, the Cambridge Associates index is an “average” of around 1400 VC funds, some of which will have outperformed the benchmark by a significant margin. Still, the aggregate performance is not exactly stellar.

But it gets worse. Look at the chart of the compounded index returns over the period from 1981:

Source: Cambridge Associates

The key point to note is that the index has yet to regain the levels is achieved 15 years ago, before the dot com bust. If VC funds operated high water marks, as most hedge funds do, the overwhelming majority of them would gone out of business many years ago.

So Why Invest in VC Funds?

Given their unimpressive aggregate performance, why do investors invest in VC funds? One answer might lie in the relatively low correlations with other asset classes. For example, over the period from 1981, the correlation between the VC index and the S&P 500 index has averaged only 0.34.

Again, however, if low correlation to the market is the issue, investors can do better by a judicious choice of hedge fund strategy, such as equity market neutral, for example, which typically has a market correlation very close to zero.

Nor is the absolute level of returns a factor: plenty of hedge funds measure their performance in terms of absolute returns. And if investors’ appetite for return is great enough to accommodate a 20% annual volatility, there is no difficulty borrowing at very low margin rates to leverage up the return.

One rational reason for investors’ apparently insatiable appetite for VC funds is capacity: unlike many hedge funds, there is no problem finding investments capable of absorbing multiple $billions, given the global pretensions, rapid burn rates and negligible cash flows of many of these new ventures. But, of course, capacity is only an advantage when the investment itself is sound.

Plowing vast sums into grocery collection services, or online women’s-wear stores, may appear a genius idea to some. But for the rest of us, as the inestimable Lou Reed put it, “other people, they gotta work”.

 

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Volatility ETF Strategy June 2015: -0.13% +13.99% YTD Sharpe 2.68 YTD

HIGHLIGHTS

  • 2015 YTD: + 13.99%
  • CAGR over 40%
  • Sharpe ratio in excess  of 3
  • Max drawdown -13.40%
  • Liquid, exchange-traded ETF assets
  • Fully automated, algorithmic execution
  • Monthly portfolio turnover
  • Managed accounts with daily MTM
  • Minimum investment $250,000
  • Fee structure 2%/20%

VALUE OF $1000

 

 

 

 

 

 

NOTES FOR JUNE 2015

We went to cash in the latter half of June in view of the uncertainties over the situation in Greece.

STRATEGY DESCRIPTION

The Systematic Strategies Volatility ETF  strategy uses mathematical models to quantify the relative value of ETF products based on the CBOE S&P500 Volatility Index (VIX) and create a positive-alpha long/short volatility portfolio. The strategy is designed to perform robustly during extreme market conditions, by utilizing the positive convexity of the underlying ETF assets. It does not rely on volatility term structure (“carry”), or statistical correlations, but generates a return derived from the ETF pricing methodology.

The net volatility exposure of the portfolio may be long, short or neutral, according to market conditions, but at all times includes an underlying volatility hedge. Portfolio holdings are adjusted daily using execution algorithms that minimize market impact to achieve the best available market prices.

 

PERFORMANCE

The strategy is designed to produce consistent returns in the range of 25% to 40% annually, with annual volatility of around 10% and Sharpe ratio in the region of 2.5 to 3.5.

Ann Returns

RISK CONTROL

Our portfolio is not dependent on statistical correlations and is always hedged. We never invest in illiquid securities. We operate hard exposure limits and caps on volume participation.

Sharpe

 

 

 

 

 

OPERATIONS
We operate fully redundant dual servers operating an algorithmic execution platform designed to minimize market impact and slippage.  The strategy is not latency sensitive.

MONTHLY RETURNS     (Click to Enlarge)

Monthly Returns

 

 

 

PERFORMANCE STATISTICS

PERFORMANCE STATS

 

 

 

 

 

 

 

 

 

 

 

 

(Click to Enlarge)

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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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)

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.

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High Frequency Trading Strategies

Most investors have probably never seen the P&L of a high frequency trading strategy.  There is a reason for that, of course:  given the typical performance characteristics of a HFT strategy, a trading firm has little need for outside capital.  Besides, HFT strategies can be capacity constrained, a major consideration for institutional investors.  So it is amusing to see the reaction of an investor on encountering the track record of a HFT strategy for the first time.  Accustomed as they are to seeing Sharpe ratios in the range of 0.5-1.5, or perhaps as high as 1.8, if they are lucky, the staggering risk-adjusted returns of a HFT strategy, which often have double-digit Sharpe ratios, are truly mind-boggling.

By way of illustration I have attached below the performance record of one such HFT strategy, which trades around 100 times a day in the eMini S&P 500 contract (including the overnight session).  Note that the edge is not that great – averaging 55% profitable trades and profit per contract of around half a tick – these are some of the defining characteristics of HFT trading strategies.  But due to the large number of trades it results in very substantial profits.  At this frequency, trading commissions are very low, typically under $0.1 per contract, compared to $1 – $2 per contract for a retail trader (in fact an HFT firm would typically own or lease exchange seats to minimize such costs).

Fig 2 Fig 3 Fig 4

 

Hidden from view in the above analysis are the overhead costs associated with implementing such a strategy: the market data feed, execution platform and connectivity capable of handling huge volumes of messages, as well as algo logic to monitor microstructure signals and manage order-book priority.  Without these, the strategy would be impossible to implement profitably.

Scaling things back a little, lets take a look at a day-trading strategy that trades only around 10 times a day, on 15-minute bars.  Although not ultra-high frequency, the strategy nonetheless is sufficiently high frequency to be very latency sensitive. In other words, you would not want to try to implement such a strategy without a high quality market data feed and low-latency trading platform capable of executing at the 1-millisecond level.  It might just be possible to implement a strategy of this kind using TT’s ADL platform, for example.

While the win rate and profit factor are similar to the first strategy, the lower trade frequency allows for a higher trade PL of just over 1 tick, while the equity curve is a lot less smooth reflecting a Sharpe ratio that is “only” around 2.7.

Fig 5 Fig 6 Fig 7

 

The critical assumption in any HFT strategy is the fill rate.  HFT strategies execute using limit or IOC orders and only a certain percentage of these will ever be filled.  Assuming there is alpha in the signal, the P&L grows in direct proportion to the number of trades, which in turn depends on the fill rate.  A fill rate of 10% to 20% is usually enough to guarantee profitability (depending on the quality of the signal). A low fill rate, such as would typically be seen if one attempted to trade on a retail trading platform, would  destroy the profitability of any HFT strategy.

To illustrate this point, we can take a look at the outcome if the above strategy was implemented on a trading platform which resulted in orders being filled only when the market trades through the limit price.  It isn’t a pretty sight.

 

Fig 8

The moral of the story is:  developing a HFT trading algorithm that contains a viable alpha signal is only half the picture.  The trading infrastructure used to implement such a strategy is no less critical.  Which is why HFT firms spend tens, or hundreds of millions of dollars developing the best infrastructure they can afford.

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Designing a Scalable Futures Strategy

I have been working on a higher frequency version of the eMini S&P 500 futures strategy, based on 3-minute bar intervals, which is designed to trade a couple of times a week, with hold periods of 2-3 days.  Even higher frequency strategies are possible, of course, but my estimation is that a hold period of under a week provides the best combination of liquidity and capacity.  Furthermore, the strategy is of low enough frequency that it is not at all latency sensitive – indeed, in the performance analysis below I have assumed that the market must trade through the limit price before the system enters a trade (relaxing the assumption and allowing the system to trade when the market touches the limit price improves the performance).

The other important design criteria are the high % of profitable trades and Kelly f (both over 95%).  This enables the investor to employ money management techniques, such a fixed-fractional allocation for example, in order to scale the trade size up from 1 to 10 contracts, without too great a risk of a major drawdown in realized P&L.

The end result is a strategy that produces profits of $80,000 to $100,000 a year on a 10 contract position, with an annual rate of return of 30% and a Sharpe ratio in excess of 2.0.

Furthermore, of the 682 trades since Jan 2010, only 29 have been losers.

Annual P&L (out of sample)

Annual PL

 

Equity Curve

EC

Strategy Performance

Perf 1

What’s the Downside?

Everything comes at a price, of course.  Firstly, the strategy is long-only and, by definition, will perform poorly in falling markets, such as we saw in 2008.  That’s a defensible investment thesis, of course – how many $billions are invested in buy and hold strategies? – and, besides, as one commentator remarked, the trick is to develop multiple strategies for different market regimes (although, sensible as that sounds, one is left with the difficulty of correctly identifying the market regime).

The second drawback is revealed by the trade chart below, which plots the drawdown experienced during each trade.  The great majority of these drawdowns are unrealized, and in most cases the trade recovers to make a profit.  However, there are some very severe cases, such as Sept 2014, when the strategy experienced a drawdown of $85,000 before recovering to make a profit on the trade.

For most investors, the agony of risking an entire year’s P&L just to make a few hundred dollars would be too great.

It should be pointed out that the by the time the drawdown event took place the strategy had already produced many hundreds of thousands of dollars of profit.  So, one could take the view that by that stage the strategy was playing with “house money” and could well afford to take such a risk.

One obvious “solution” to the drawdown problem is to use some kind of stop loss. Unfortunately, the effect is simply to convert an unrealized drawdown into a realized loss.  For some, however, it might be preferable to take a hit of $40,000 or $50,000 once every few years, rather than suffer the  uncertainty of an even larger potential loss.  Either way, despite its many pleasant characteristics, this is not a strategy for investors with weak stomachs!

Trade

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Investing in Leveraged ETFs – Theory and Practice

May. 5, 2015 11:48 AM ET  |  44 comments  |  Includes: DUSTERXERYFASFAZGDXNUGTSPXLSPXSTNATZA

Summary

  • Leveraged ETFs suffer from decay, or “beta slippage.” Researchers have attempted to exploit this effect by shorting pairs of long and inverse leveraged ETFs.
  • The results of these strategies look good if you assume continuous compounding, but are often poor when less frequent compounding is assumed.
  • In reality, the trading losses incurred in rebalancing the portfolio, which requires you to sell low and buy high, overwhelm any benefit from decay, making the strategies unprofitable in practice.
  • A short levered ETF strategy has similar characteristics to a short straddle option position, with positive Theta and negative Gamma, and will experience periodic, large drawdowns.
  • It is possible to develop leveraged ETF strategies producing high returns and Sharpe ratios with relative value techniques commonly used in option trading strategies.

Decay in Leveraged ETFs

Leveraged ETFs continue to be much discussed on Seeking Alpha.

One aspect in particular that has caught analysts’ attention is the decay, or “beta slippage” that leveraged ETFs tend to suffer from.

Seeking Alpha contributor Fred Picard in a 2013 article (“What You Need To Know About The Decay Of Leveraged ETFs“) described the effect using the following hypothetical example:

To understand what is beta-slippage, imagine a very volatile asset that goes up 25% one day and down 20% the day after. A perfect double leveraged ETF goes up 50% the first day and down 40% the second day. On the close of the second day, the underlying asset is back to its initial price:

(1 + 0.25) x (1 – 0.2) = 1

And the perfect leveraged ETF?

(1 + 0.5) x (1 – 0.4) = 0.9

Nothing has changed for the underlying asset, and 10% of your money has disappeared. Beta-slippage is not a scam. It is the normal mathematical behavior of a leveraged and rebalanced portfolio. In case you manage a leveraged portfolio and rebalance it on a regular basis, you create your own beta-slippage. The previous example is simple, but beta-slippage is not simple. It cannot be calculated from statistical parameters. It depends on a specific sequence of gains and losses.

Fred goes on to make the point that is the crux of this article, as follows:

At this point, I’m sure that some smart readers have seen an opportunity: if we lose money on the long side, we make a profit on the short side, right?

Shorting Leveraged ETFs

Taking his cue from Fred’s article, Seeking Alpha contributor Stanford Chemist (“Shorting Leveraged ETF Pairs: Easier Said Than Done“) considers the outcome of shorting pairs of leveraged ETFs, including the Market Vectors Gold Miners ETF (NYSEARCA:GDX), the Direxion Daily Gold Miners Bull 3X Shares ETF (NYSEARCA:NUGT) and the Direxion Daily Gold Miners Bear 3X Shares ETF (NYSEARCA:DUST).

His initial finding appears promising:

Therefore, investing $10,000 each into short positions of NUGT and DUST would have generated a profit of $9,830 for NUGT, and $3,900 for DUST, good for an average profit of 68.7% over 3 years, or 22.9% annualized.

At first sight, this appears to a nearly risk-free strategy; after all, you are shorting both the 3X leveraged bull and 3X leveraged bear funds, which should result in a market neutral position. Is there easy money to be made?

Fig 3

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