Tuesday, December 27, 2011

Risk indicators

During the financial crisis of 2008, I wrote about how I watched some risk indicators such as the VIX or the TED spread  to decide what leverage I should use for my trading strategies. It turns out that this procedure is just as critical for the current crisis that began in August 2011. In fact, more than leverage-determinants, they can be used as the all-important variable that determines whether a certain strategy should be run at all. (What's the point of running a model that you think will lose money with low leverage?)

There are now more than a few of these risk indicators to pick from. Besides the VIX and the TED, there are the VSTOXX (EURO STOXX 50 Volatility), the VXY (JPMorgan G7 Volatility Index), the EM-VXY (JPMorgan Emerging Market Volatility Index), the ETF's ONN and OFF, and probably many more that I haven't heard of yet. 

A lot of academic research has been done on whether we can devise "regime switching" models based on some complicated pattern-recognition algorithms to decide whether a market is in a certain "regime" which favors this or that particular model or parameter set. And often, these regime switching models rely on the recognition of some complicated set of patterns in the historical price series. Sorry to say, I have not found any of these complex regime switching model to have any real out-of-sample predictive power. On the other hand, my research shows that some of the aforementioned simple risk indicators will indeed prevent some trading models from falling off the cliff.

But which of these indicators are applicable to which model? This is not so obvious. For example, you might think that the EM-VXY would be an ideal leading indicator for Forex trading models that involve emerging market currencies, but I have found that it is only a contemporaneous (and thus useless) indicator to mine. Another example, I said during the 2008 financial crisis that VIX seems to be a useless contemporaneous indicator for equities trading models, but strangely, it is a good leading indicator for FX models. In contrast, the TED spread that everyone were obsessed about in 2008 shot up to over 300 bps then, but never went beyond 100 bps this time around. So really only rigorous backtesting can guide us here.

What risk indicators do you use? And have you really backtested their efficacies? Your comments would be very welcome here.

Friday, November 11, 2011

Trading platform and EC2 revisited

Recently I opened a discussion on the various software platforms which allow the programmers among us to build trading strategies easily. Here is one other addition: Quantopian. It is only in alpha stage, but I did get a preview of its features:

1) You can code in Python, which is an easier language to learn than Java, but no less powerful. In fact, I know of a superb programmer who uses Python to backtest HF strategies.

2) It is web-based, which means you can take advantage of collocation on a server much more stable than your own desktops. (For those who worry about the confidentiality of your strategies, the founder indicated to me that they can run an image of the software on an Amazon EC2 account that you owned so they won't have access to your codes. As for the confidentiality of codes residing on EC2 itself, please see below*.)

3) It is event-driven (or for those who like the latest jargon: CEP-enabled), like all the Java API's that I discussed in the previous article.

4) They have 1-min US equities data for backtesting. Tick-level data will be available soon.

5) Toolboxes for common technical indicators, mathematical algorithms, etc. will be available soon.

6) They will run a competition for trading models which makes it easier for independent traders to become trading advisers to others, or to raise money for their own funds.

Unfortunately, live walk-forward testing is not yet available.

* Some readers have wondered whether it is safe to run their trading models on Amazon's EC2. Won't Amazon's employees have access to their wildly profitable strategies? The answer is no: Amazon's security policy:

Guest Operating System: Virtual instances are completely controlled by the customer. Customers have full root access 
or administrative control over accounts, services, and applications. AWS does not have any access rights to customer 
instances and cannot log into the guest OS....

Thanks to a reader OL from France who provided me with this info. He also told me that: 

"So, I finally deployed my momentum strategy on a Linux instance of EC2 (which is free btw).
I wrote it based on the java demo application provided by Interactive Brokers and some parts of Algoquant.
So far, I use a European instance of EC2 which alas doesn't have the best latency to IB US servers (90 ms) but still better than my bedroom connection. 
A test ping from a US instance to IB US servers results in only 15 ms ..."

So there you go: Java+Algoquant+IB+EC2=profit.

Friday, September 30, 2011

Stop loss, profit cap, survivorship bias, and black swans

I have long espoused the view that we should not impose stop-losses on mean-reverting strategies, nor profit caps on momentum strategies. My view on the latter has not changed, but it has evolved on the former.

My original reason for opposing stop-losses on mean-reverting strategy is this. Say you believe your specific price series is mean-reverting, and say you have entered into a long position when the price is low. Now, however, the price gets much lower, and you are suffering a large unrealized loss. Well, based on your mean-reverting belief, you should buy more instead of liquidating! Indeed, if you backtest the effect of stop-losses on mean-reverting strategies, you will almost inevitably find that they decrease the overall returns and even Sharpe ratios.

But what this simplistic view ignored is 1) survivorship bias, and 2) black swan events. (Hat tip: Ben, who prompted me to consider these two issues.)

1) We normally would only trade those price series with a mean-reverting strategy only if we see that the prices did eventually revert. No one would bother to trade those price series that used to mean-revert, but suddenly stopped doing so. But saying that stop-losses are harmful to mean-reverting strategies is ignoring the fact that some mean-reverting will stop working altogether and would not survive our strategies selection process.

2) Let's define black swan events as those that did not occur in your backtest period. For example, let's say you never had a loss of 20% in a single day. So if you backtest a stop-loss of 20%, it will have no effect whatsoever on your backtest performance. However, no one can say for sure that it won't occur in the future. So if you or your investors simply cannot tolerate a 20% loss, you should impose this as a stop-loss. (After all, your brokerage has already imposed a stop-loss of 100% on you whether you like it or not.)

We can in fact turn point 2) around when deciding what stop-loss to use: a stop-loss should be loose enough so that it should have no effect on the backtest performance, and of course tight enough so that it will not result in the demise of your trading career.

There is also the issue of whether to use stop-loss on the intraday drawdown, or to use it on the multiple-day drawdown. I would argue that only intraday stop-loss is important to prevent a black-swan loss. In practice, when a strategy has a string of non-catastrophic losses occurring over multiple days, resulting in a large, unprecedented, drawdown, the trader will typically re-examine the strategy, taking into account this most recent performance and tweak the strategy so that it could theoretically be avoided. This is almost like a multi-day stop-loss strategy, as we stop an old strategy and start a new, modified, one. (Though the modified strategy might still recommend that you keep holding the current position!)

Now why am I still holding dear to the principle that one should not impose profit-caps on momentum strategies? Why, the possibility of black swan events again! But this time, any black swan can only result in unprecedented one-day gain instead of loss, since we should always have stop-losses on momentum strategies. We certainly don't want to impose a profit-cap to rule out this possibility!

Sunday, September 18, 2011

More on automated trading platforms

The ideal software platform for automating backtesting and executing your algorithmic trading strategies depends mainly on your level of programming expertise and your budget. If you are a competent programmer in, say, Java or C#, there is nothing to prevent you from utilizing the API offered (usually for free) by many brokerages to automate execution. And of course, it is also easy for you to write a separate backtesting program utilizing historical data. However, even for programmer-traders, there are a couple of inconveniences in developing these programs from scratch:

A) Every time we change brokerages, we have to re-write parts of the low-level functions that utilize the brokerage's API;

B) The automated trading program cannot be used to backtest unless a simulator is built to feed the historical data into the program as if they were live. To reduce bugs, it is better to have the same code that both backtests and trades live.

This is where a number of open-source algorithmic trading development platforms come in. These platforms all assume that the user is a Java programmer. But they eliminate the hassles A) and B) above as they serve as the layer that shield you from the details of the brokerage's API, and let you go from backtesting to live trading mode with a figurative turn of a key. I have taken a tour of one such platforms Marketcetera, and will highlight some features here:

1) It has a trading GUI with features similar to that of IB's TWS. This will be useful if your own brokerage's GUI is dysfunctional.

2) Complex Event Processing (CEP) is available as a module. CEP is essentially a way for you to easily specify what kind of market/pricing events should trigger a trading action. For e.g., "BUY if ask price is below 20-min moving average." Of course, you could have written this trading rule in a callback function, but to retrieve the 20-min MA on-demand could be quite messy. CEP solves that data retrieval problem for you by storing only those data that is needed by your registered trading rules.

3) It can use either FIX or a brokerage's API for connection. Available brokerage connectors include Interactive Brokers and Lime Brokerage.

4) It offers a news feed, which can be used by your trading algorithms to trigger trading actions if you use Java's string processing utilities to parse the stories properly.

5) The monthly cost ranges from $3,500 - $4,500.

If Marketcera is beyond your budget, you can check out AlgoTrader. It has advantages 1)-3) but not 4) listed above, and is completely free. I invite readers who have tried these or other similar automated trading platforms to comment their user experience here.

P.S. For those of us who use Matlab to automate our executions, a reader pointed out there is a new product MATTICK that allows you to send order via the FIX protocol which should let us trade with a great variety of brokerages.

Saturday, July 23, 2011

Sorry, your return is too high for us

I enjoyed reading Richard Wilson's The Hedge Fund Book (Richard also runs the Hedge Fund Blogger site). To be clear: it is purely marketing-oriented. It doesn't tell you how to find a successful trading strategy, but its focus is to tell you how to market your fund to investors once you have a successful strategy. To that end, it does a pretty good job in conveying what might be conventional wisdom to seasoned fund managers. (For e.g., don't bother to market to institutional investors if your AUM is less than $100M.) The book is filled with quite engaging interviews with fund managers, fund marketers, and other fund service providers (including our very own administrator Fund Associates). If Scott Patterson's The Quants is about the gods of hedge funds, this book is for and about the mortals.

One paragraph in the book stood out: "I've worked closely on the third-party marketing and capital introduction/prime brokerage side of the business, and I often see both types of firms deny clients service [to funds with high returns and high risk] ... Nobody wants to be associated with a manager aiming at 30 percent a month returns."

Maybe not aiming at, but what's wrong with achieving a 30 percent a month returns? I have actually met institutional investors who don't want to look at a fund that actually achieved double-digit monthly returns. Presumably that's because they believe that a high return automatically implies high risk, and also presumably a high leverage as well.  I would argue that there are 2 reasons not to completely dismiss such funds out-of-hand:

1) Leverage should not be determined arbitrarily, but should be based on the minimum of what's dictated by half-Kelly (see my extensive discussions of Kelly formula on this blog and in my book) and what's dictated by the maximum single-day drawdown seen historically or in VaR simulations. And if this minimum still turns out to be higher than what most institutional investors are comfortable with, one should be bold enough to adopt it in your fund.

2) As an investor, there is an easy way to control leverage and risk: just apply Constant Proportion Portfolio Insurance (a concept also discussed elsewhere on this blog). For example, if the fund manager tells you the fund employs a constant 10x leverage (as dictated by the risk analysis outlined in 1) and you are only comfortable with 5x leverage, just invest half your capital into the fund, and keep the other half as cash in your bank account! Going forward, if the fund loses money, your effective leverage would have decreased to below 5x. Say you invested $1M into the fund, and kept $1M in the bank. And say the fund lost $0.5M. Your total equity is now $1.5M, and the fund manager is supposed to trade a $0.5M*10=$5M portfolio. Your effective leverage is now only 3.33x, well within your tolerance. Now if instead, the fund made money, you can immediately withdraw some of the profits to keep your effective leverage at 5x. So, say the fund made $0.5M. Your equity is now $2.5M, and the fund manager is supposed to trade a $1.5M*10=$15M portfolio. If you don't withdraw, this would increase your effective leverage to 6x. But if you immediately withdraw $0.25M, then the fund manager will trade a $1.25M*10=$12.5M portfolio, giving you an effective leverage of the desired 5x.

If you are an investor in hedge funds, please let us know what you think of this scheme in the comments section!

Monday, July 18, 2011

The social utility of hedge funds

There is an article in the New Yorker magazine profiling Bridgewater Associates, the world's biggest global macro hedge fund. Inevitably, we come to the awkward question: "If hedge-fund managers are playing a zero-sum game, what is their social utility?"

I thought about this question a lot in the past, and I used to agree with many others that the social utility of hedge funds, or trading in general, is to provide liquidity to the markets. And a good economic case can be made that the more liquid a market is, the higher the utility it is to all participants. However, based on recent experience of flash crash and other unfortunate mishaps, we find out that traders typically do not provide liquidity when it is needed most! So this answer becomes quite unsatisfactory.

In trying to come up with a better reply, I though it is curious that few people asked "What is the purpose of having a Department of Defence?" since wars between nations are typically also zero-sum games, yet we greatly honour those who serve in the armed forces (in contrast to our feelings for hedge fund managers).

To me, clearly the answer with the best moral justification is that, in both cases, there is great social utility in defending either your clients' comfortable retirement from financial meltdown (e.g. due to governmental or corporate mismanagement), or in defending your country from foreign aggression. More specifically, the purpose of hedge funds is to reduce long-term volatility in your clients' net worth. (I would like to say "reduce risks to your clients' net worth", but that would be a bit too optimistic!) 

I emphasize long-term volatility, because of course trading generates a lot of daily or hourly volatility in your clients' equity. But I do not believe that such short-term volatility affects ones' life goals. On the other hand, a 3-or-more-year drawdown in a typical buy-and-hold portfolio can wreck havoc with many lives.

If one day, the markets become so quiescent that few hedge funds can generate higher Sharpe ratio than a buy-and-hold portfolio (as indeed seems to be the case with the US equities markets these days), then yes, most hedge fund managers should just quit, instead of hogging intellectual resources from our best universities.

Sunday, July 03, 2011

Hedge fund transparency and "barometers"

Jim Liew of Alpha Quant Club recently posted an interesting article about the increasing demand for transparency of hedge fund strategies by institutional investors, so much so that they are essentially willing to invest only in managed accounts with real-time trades and positions updates. This is, of course, bad for fund managers, since not only can the investor reverse-engineer the simpler strategies from such knowledge, they can also piggy-back on the trades, thus paying a much smaller portion of their profits as performance fee. One might be tempted to think that since the investors are going to reverse-engineer the product anyway, why not just make it as simple and as generic as possible, and charge a much lower fee than the usual 2-20 (which hopefully will attract a much larger investor base), so that the main value to the investor is just convenience and not the originality of the strategy?

In fact, Jim wants to do just that. He proposes to construct hedge fund "barometers", essentially prototypical hedge fund strategies running in managed accounts. This would work well if these barometers have large enough capacities such that the performance can hold up even when a large number of investors sign up. From the investors' point of view, this is a trade-off between investing in a truly outstanding, high-performance strategy while paying a large fee and losing "transparency", versus just investing in a generic strategy that may still outperform the broad market. For some institutional investors, this might just be the bargain they are looking for.

Friday, June 17, 2011

When cointegration of a pair breaks down

I have written a lot in the past about the cointegration of ETF pairs, and how this condition can lead to profitable pairs trading. However, as every investment advisor could have told you, past cointegration is no guarantee of future cointegration. Often, cointegration for a pair breaks down for an extended period, maybe as long as a half a year or more. Naturally, trading this pair during this period is a losing proposition, but abandoning such a pair completely is also unsatisfactory, since cointegration often mysteriously returns after a while.

A case in point is the ETF pair GLD-GDX. When I first tested it in 2006, it was an excellent candidate for pair trading, and I not only traded it in my personal portfolio, but we traded it in our fund too. Unfortunately, it went haywire in 2008. We promptly abandoned it, only to see the strategy recovered sharply in 2007.

So the big question is: how do we know whether the loss of cointegration is temporary, and how do we know when to resume trading a pair?

To answer the first question, it is often necessary to go beyond the technicals, and delve into the fundamentals of pair. Take GLD-GDX as the example. When I taught my pairs trading workshop in South Africa, several  portfolio managers in attendance told me that there are 2 reasons why gold spot price diverged from gold miners' stock prices. Firstly, due to the sharp increase in oil prices during the first half of 2008, it costs the gold miners a lot more in energy to extract the gold from the ground, hence the gold miners' income lags behind the rise in gold prices. Secondly, many gold miners hedge their exposure to fluctuating gold prices with derivatives. Hence when gold price rise beyond a certain limit, the gold miners cease to benefit from this rise. Recently, the Economist magazine published an article that essentially confirms this view. But further confirmation can be gained by introducing oil (future) price into the cointegration equation. If you do that, and if you trade this triplet of GLD-GDX-USO, you will find that it is profitable throughout the entire period from 2006-2010. If you find trading a triplet too complicated, you can at least backtest a trading filter such that you will cease to trade GLD-GDX whenever USO goes beyond (above, and maybe below too) a certain band. If you have done all these backtests, you will have a plan in place to tell you when to resume trading this pair. But even if you haven't done this backtest, and you find that you need to stop trading a pair because of cumulating losses, you should at least continue paper trading it to see when it is turning around!

(By the way, if you think trading ETF pairs offers too low returns due to the low leverage allowed, consider the single stock futures on ETF's trading on the OneChicago exchange. Certainly the future on GDX is available there, while you might just trade the futures GC and CL directly on CME. There is, of course, the usual caveat that applies to futures pairs trading: the switch from contango to backwardation and vice versa can ruin many a pairs-trading strategy, even if the spot prices remain cointegrating. But that's a story for another time.)

Thursday, June 02, 2011

Even more on news driven trading

News driven trading is even more in vogue today than when I last mentioned it, judging from the increasing number of vendors (e.g. Ravenpack, Sensobeat, Recorded Future, etc.) and researchers pitching their wares. Not only are traditional financial and economic news deemed important, but researchers have found even blog posts (at least those on Seeking Alpha) and Twitter (Hat tip: Satya and William) to be predictive of stock prices.

One key ingredient to success in this type of trading is of course the ability to gain access to breaking news ahead of other traders. On the macroeconomic news front, the MIT Billion Prices project has spun off a company called PriceStats to deliver daily consumer product price index to subscribers. PriceStats compiles this index by continuously scanning online retailers' websites, and hopefully provides a preview of the official CPI numbers. Whether this is useful for futures and currencies traders is of course subject to their rigorous backtests, though the chart displayed on their website does suggest that the daily price index is a leading indicator of the CPI.

There is an important caveat to using news trading: not all news are equal. So another key ingredient to success is to carefully differentiate between the different types of news and backtest their predictive abilities separately. For example, I recall some research has indicated that an analyst downgrade of a stock from a "hold" to a "sell" rating has more impact than from "buy" to "hold" rating.

My own experience with news driven trading is that for all this trouble, the trading opportunities are relatively few compared to pure price driven trading, the consistency of success is low, and finally the profitability lifespan is short. If you have better experience, do share it with us.

Tuesday, May 17, 2011

A platform, a shareware site, and some courses for quant traders

I mentioned in various places that Alphacet Discovery is an industrial strength integrated platform for backtesting and implementing quantitative trading strategies. But of course, it has many competitors, one of which is a relatively new company called Deltix. Deltix has the distinction of offering a full Matlab interface, which is convenient if you are already a Matlab programmer. (Full disclosure: I previously have a consulting relationship with Alphacet, but have none with Deltix.)

There is also a new website for sharing trading strategy software called Quantonomics. In the words of its founder Joshua, the goal is to "connect programmers and stock traders". Joshua also told me that he will create a custom application on his site for any of you readers as a gift!

A colleague of mine in Singapore, Dr. Li Haksun, who was previously a quant with UBS and BNP Paribas, is offering a course on quantitative trading strategy in July. It covers more theoretical concepts than my own courses: e.g. hidden markov model, stochastic control, and Kalman filters are included.

And of course, my own workshops on Backtesting and Statistical Arbitrage will be offered again in London next week.

Tuesday, May 10, 2011

Time-of-day effects in FX trading

As I mentioned in a previous post, one of the main ingredients of success in constructing a profitable momentum trading strategy in Forex (and futures) is to pay attention to the entry and exit times. I haven't seen any good momentum strategy that has "time-translation invariance", i.e. works without reference to a fixed time of the day. The fixed time can refer to a benchmark level of the market (e.g. the previous close), or it can be the entry or exit time.  (This is in contrast to mean-reverting strategies where the reference price can often be just a moving average.) A recent research paper (Hat tip: William) points to another example of such time-of-day effects in FX markets: a currency typically depreciates during its local trading hours.

Saturday, April 23, 2011

The many facets of linear regression

Many years ago, a portfolio manager asked me in a phone interview: "Do you believe that linear or nonlinear models are more powerful in building trading models?" Being a babe-in-the-woods, I did not hesitate in answering "Nonlinear!" Little did I know that this is the question that separate the men from the boys in the realm of quantitative trading. Subsequent experiences showed me that nonlinear models have mostly been unmitigated disasters in terms of trading profits. As Max Dama said in a recent excellent article on linear regression: "...when the signal to noise ratio is .05:1, ... there’s not much point in worrying about [higher order effects]". One is almost certain to overfit a nonlinear model to non-recurring noise.

Until recently, I have used linear regression mainly in finding hedge ratios between two instruments in pair trading, or more generally in finding the weightings (in number of shares) of individual stocks in a basket in some form of index arbitrage. Of course, others have found linear algebra useful in principal component analysis and more generally factor analysis as well. But thanks to a number of commenters on this blog as well as various private correspondents, I have begun to apply linear regression more directly in trading models.

One way to directly apply linear regression to trading is to use it in place of moving averages. Using moving average implicitly assumes that there is no trend in a price series, that the mean of the prices will remain the same. This of course may not be true. So using linear regression to project the current equilibrium price is sometimes more accurate than just setting it equal to a moving average. I have found that in some cases, this equilibrium price results in better mean-reverting models: e.g. short an instrument when its current price is way above the equilibrium price. Of course, one can also use linear regression in a similar way in momentum models: e.g. if the current price is way above the equilibrium price, consider this a "breakout" and buy the instrument. 

Max in his article referenced above also pointed out a more sophisticated version of linear regression, commonly called "weighted least squares regression" (WLS). WLS is to linear regression what exponential moving average (EMA) is to simple moving average (SMA): it gives more weights to recent data points. Indeed I have found that EMA often gives better results than SMA in trading. However, so far I have not found WLS to be better than simple least squares. Max also referenced an article which establishes the equivalence between weighted least squares and Kalman filter. Now Kalman filter is a linear model that is very popular among quantitative traders. The nice feature about Kalman filter is that there is very few free parameters: the model will adapt itself to the means and covariances of the input time series gradually. And furthermore, it can do so one-step at a time (or in technical jargon, using an "online" algorithm) : i.e., there is no need to separate the data into "training" and "test" sets, and no need to define a "lookback" period unlike moving averages. It makes use of "hidden states" much like Hidden Markov Models (HHM), but unlike HHM, Kalman filter is faithfully linear.

I haven't used Kalman filter much myself, but I would welcome any comments from our readers on its usage. Also, if you know of other ways to use linear regression in trading, do share with us here!

Friday, March 11, 2011

Momentum strategies in futures and forex

I have long found that it is easier to find good (i.e. high Sharpe ratio) mean-reverting strategies than good momentum strategies. Partly, that is because I was mainly a stock trader instead of a futures/currencies trader, and individual stocks mean-revert most of the time. There are exceptions, such as after special corporate events such as earnings announcements, and I have tested momentum strategies based on these events. But the success of even these event-driven strategies has been uneven, especially since more traders become aware of them.

Now that I am focusing more on trading futures and currencies, I have gradually been introduced to the world of momentum investing. There is a good book in this area that deserves to be better known: Joe Duffy's The Ultimate Trading Robot, which is an almost step-by-step guide to constructing futures trending strategies that rely on prices alone. Another example would be the London Breakout strategy mentioned by our reader Bernd in the comments here. After studying these examples, I realized why my previous, rather desultory, search for momentum strategies in the futures and FX markets had been in vain: the overnight gap in these markets seems critical. For futures, the overnight gap is obvious, but in the case of the London Breakout strategy, for example, the trader has the task defining for herself what the optimal closing and opening times are in order to compute the gap. Intraday trend without an overnight breakout does not seem persistent enough to be traded profitably. I also wonder if there is a more elegant (i.e. mathematical) way to quantify such breakout phenomena without using the traditional technical indicators.

If you know of ideas for good momentum strategies, you are most welcome to share and discuss them here!

Tuesday, January 25, 2011

High frequency trading ideas

I just started reading Larry Harris' book "Trading and Exchanges" (thanks to Max Dama's glowing book review) and already a couple of potential high frequency trading techniques stood out:

"Quote matching" - a technique whereby front-runners place a limit buy order just a cent (for stocks) higher than the best bid price. If the order is filled, they then place a limit sell order just a cent lower than the best ask. Assuming the best bid-ask quotes don't move, the worst they can do is to lose 1 cent by selling the share back to the best bidder, while the most profit they can make is the bid-ask spread plus rebates for providing liquidity minus 2 cents by having the sell long limit order filled. This could work out quite profitably if the bid-ask spread is wide. But of course, the best bid-ask do change constantly, so front-runners would need to cancel and correct their limit orders constantly, and the optimal algorithm for doing this could get quite complicated. Meanwhile, if you are a bona fide liquidity provider, you would have to avoid providing this free option to the front-runners by constantly monitoring who is in front of you. As usual, this chess game can quickly degenerate into an HFT arms race.

"Manipulation of stop orders" - a.k.a. "gunning the market", a technique whereby the market gunners buy aggressively so as to trigger large buy stop orders that they believe are in place at a higher price. When these buy stop orders are filled, the prices are driven higher still, and these manipulators then sell their position profitably.

One of my old momentum strategies was a victim of these market gunners, and after that sad experience I refused to use stop orders any more, at least for stocks. However, here is a question for our knowledgeable readers: can other traders actually see what stop orders there are on an order book (whether for stocks, futures, or Forex markets)? And if so, would a trading robot that simulates stop orders by sending out buy market orders when the stop price is touched work better than manually placing a buy stop order on the order book?

Wednesday, January 05, 2011

Shorting the VIX calendar spread

Lately there were a few interesting discussions in the blogosphere on the profitability of shorting the VXX-VXZ spread. (See Quantum Blog and The Speculator's Ball.) For background, VXX is an ETN that tracks the first and second month of the VIX future, which in turn tracks the VIX volatility index, which in turn tracks the volatility of SPX. VXZ is the ETN that tracks the 4th - 7th months of the VIX future. During the period 2009-2010, there were 2 different reasons why shorting this "calendar spread" was profitable:

1) The VIX futures were/are in contango: i.e. the back months' futures are more expensive than the front months'.
2) The volatility of SPX was decreasing with time.

However, some traders seem to think that either one of these conditions is enough to ensure the profitability of shorting a calendar spread.  It is not. (Otherwise, life as a futures trader would be too easy!)

To see this, let's resort to a simplistic linear approximation to a model of futures prices. From John Hull's book on derivatives, section 3.12, the price of  a future which matures at time T is

F(t, T)=E(ST)exp(c(T-t)),

where E(ST) is the expected value of the spot price at maturity, c is a constant, and t is the current time. If the futures are in contango, then c > 0.

If we assume that abs(c) is small, and T-t is also small (i.e. not too far from maturity), and that the expected value of the spot price changes slowly, we can linearize this formula as


If the market expects the future spot price to increase, then b > 0.

After a few simple algebraic steps, you can verify that the calendar spread's price is proportional to

F(t, T1)-F(t, T2) ~ bct

where T1 < T2 (i.e. F(t, T1) is the front month's price, and F(t, T2) the back month's).

This is a satisfyingly illustrative result. It says that shorting this calendar spread will be profitable if

A) futures are in contango and the expected spot price in the future is decreasing; or else
B) futures are in backwardation and the expected spot price in the future is increasing.

So what is the situation today? Will it still be profitable to short this spread? As our fellow bloggers have pointed out, VIX futures are still in contango, but the market is expecting volatility to increase in the future over the last month or so. So this may no longer be a profitable trade anymore.