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 17, 2011
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!
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!
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?
"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
F=(a+b(T-t))*(1+c(T-t))
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.
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
F=(a+b(T-t))*(1+c(T-t))
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.
Thursday, November 18, 2010
Columbia Workshop on Financial Engineering
Our readers in New York may be interested in this finance workshop at Columbia University tomorrow.
I am particularly interested in the talk by Kent Daniel on "Characterizing Momentum", and by Doug Borden (of Knight Equity Markets) on "Stochastic Control Theory in High-Frequency Trading". Doug's talk can be downloaded here.
I am particularly interested in the talk by Kent Daniel on "Characterizing Momentum", and by Doug Borden (of Knight Equity Markets) on "Stochastic Control Theory in High-Frequency Trading". Doug's talk can be downloaded here.
Sunday, October 10, 2010
Data mining and artificial intelligence update
Long time readers of this blog know that I haven't found data mining or artificial intelligence techniques to be very useful for my own trading, for they typically overfit to non-recurring past patterns. (Not surprisingly, they are much more useful for driverless cars.) Nevertheless, one must keep an open mind and continues to keep tabs on new developments in this field.
To this end, here is a new paper written by an engineering student at UC Berkeley which uses "support
vector machine" together with 10 simple technical indicators to predict the SPX index, purportedly with 60% accuracy. If one includes an additional indicator which measures the number of news articles on a stock in the previous day, then the accuracy supposedly goes up to 70%.
I did not have the chance to reproduce and verify this result yet, but I invite you to try it out and share your findings here. If you do so, you may find this new data mining product called 11Ants Analytics useful. It is an Excel-based software that includes 11 machine learning algorithms including the aforementioned support vector machines. It also includes decision trees which are sometimes quite useful in automatically generating a small set of trading rules from an input set of technical indicators. (Whether those rules remain profitable in the future is another question!) If you have tried this product, I would also appreciate your comments here.
(If you are a die-hard MATLAB fan, support vector machines are available in their Bioinformatics Toolbox, and classification and decision trees in their Statistics Toolbox.)
To this end, here is a new paper written by an engineering student at UC Berkeley which uses "support
vector machine" together with 10 simple technical indicators to predict the SPX index, purportedly with 60% accuracy. If one includes an additional indicator which measures the number of news articles on a stock in the previous day, then the accuracy supposedly goes up to 70%.
I did not have the chance to reproduce and verify this result yet, but I invite you to try it out and share your findings here. If you do so, you may find this new data mining product called 11Ants Analytics useful. It is an Excel-based software that includes 11 machine learning algorithms including the aforementioned support vector machines. It also includes decision trees which are sometimes quite useful in automatically generating a small set of trading rules from an input set of technical indicators. (Whether those rules remain profitable in the future is another question!) If you have tried this product, I would also appreciate your comments here.
(If you are a die-hard MATLAB fan, support vector machines are available in their Bioinformatics Toolbox, and classification and decision trees in their Statistics Toolbox.)
Saturday, October 02, 2010
The main virtue of buying options
I realized that I have omitted the most obvious virtue of trading options instead of stocks in my last post: the much more attractive reward-risk ratio for options.
Suppose your stock strategy generated a buy signal. You can either buy the stock now, or you can buy an ATM call. If you buy the stock, you are of course benefiting from 100% of the upside potential of the stock price movement, but you are similarly exposed to 100% of the downside risk. Indeed you can lose the entire market value of the stock. If you buy the call, you will benefit from > 50% of the upside potential of the stock price, assuming that your holding period is so short that the time value will not dissipate much. As the stock price rises, so does your delta. (It increases from 0.5 to 1.) But what about the downside risk? All you can lose is the option premium, usually << 50% of the market value of the stock.
In other words, while one may be tempted to hedge a large stock position with stock index futures, there is no need to hedge an equivalent call option position. This should simplify your strategy implementation and reduce risk management costs (i.e. the probable loss on your short futures position).
Given that I am a short-term trader anyway, I can't figure out why I have been trading stocks instead of options all these years! (Aside from the caveats detailed in the previous post.)
Suppose your stock strategy generated a buy signal. You can either buy the stock now, or you can buy an ATM call. If you buy the stock, you are of course benefiting from 100% of the upside potential of the stock price movement, but you are similarly exposed to 100% of the downside risk. Indeed you can lose the entire market value of the stock. If you buy the call, you will benefit from > 50% of the upside potential of the stock price, assuming that your holding period is so short that the time value will not dissipate much. As the stock price rises, so does your delta. (It increases from 0.5 to 1.) But what about the downside risk? All you can lose is the option premium, usually << 50% of the market value of the stock.
In other words, while one may be tempted to hedge a large stock position with stock index futures, there is no need to hedge an equivalent call option position. This should simplify your strategy implementation and reduce risk management costs (i.e. the probable loss on your short futures position).
Given that I am a short-term trader anyway, I can't figure out why I have been trading stocks instead of options all these years! (Aside from the caveats detailed in the previous post.)
Saturday, September 25, 2010
Implementing stock strategies using options
There are many stock trading strategies that are quite attractive in terms of Sharpe ratios, but not very attractive in terms of returns. (Pairs trading comes to mind. But in general, any market neutral strategy suffers from this problem.) Certainly, one cannot feed a family with annualized returns in the single or low double digits, unless one already has millions of dollars of capital. One way to solve this dilemma is of course to join a proprietary trading group, where we would have access to perhaps x30 leverage. Another way is to implement a stock trading strategy using options instead, though there are a sizable number of issues to consider. (I recently brushed up on my options know-how by reading the popular "Options as a Strategic Investment".)
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Reminder: my next pairs trading workshop will take place in New York on October 26-27th.
- Using options will allow you to increase your leverage beyond the Reg T x2 leverage (or even the day trading x4 leverage) only if you buy options only, but not selling them. For example, to implement a pairs trading strategy on 2 different stocks, you would have to buy call options on the long side, and buy put options on the short side (but not sell call options). Otherwise the margin requirement for selling calls is as onerous as shorting the underlying stock itself.
- The effective leverage is computed by multiplying the delta of the option by the underlying stock price divided by the option premium. If you buy an out-of-money (OTM) option, the delta will be small (smaller than 0.5), but the option premium is small also. Vice versa for an in-the-money (ITM) option. So you would have to find the optimal strike price so that the effective leverage is maximized. I personally choose to buy an at-the-money (ATM) call or slightly ITM call without actually computing the optimized strike, but perhaps you have reached a different conclusion?
- Naturally, the shorter the time-to-expiration, the cheaper the option and higher the effective leverage. Additionally, for ITM options, their deltas increase as we get closer to expiration, which also contributes to higher effective leverage. However, the time-to-expiration must of course be longer than the expected holding period of your position, otherwise you would incur the transaction cost of rolling over to the further-month options.
- The discussion of finding the right strike price based on its delta is moot if your brokerage's API does not provide you with delta for your automated trading system. In theory, Interactive Brokers's API provide deltas for whole options chains, and quant2ib's MATLAB API will pass these on to your MATLAB exeuction program too. However, I have not been successful in retrieving deltas using quant2ib's API. If you have encountered a similar problem, and perhaps have found the reason/cure for this, please let me know. For now, I am reduced to assuming that all my near ATM calls for different stocks have the same delta, and I increase this common value from 0.5 to close to 1 as time passes.
- Options don't have MOO, LOO, MOC or LOC order types. If one uses market orders to buy at the open or close, one would incur significant transaction costs due to the much wider bid-ask spread compared to stocks. I try to use limit orders on options orders as much as possible.
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Reminder: my next pairs trading workshop will take place in New York on October 26-27th.
Sunday, August 22, 2010
Phantom quotes
Have you ever got the feeling that your market orders are often filled at prices worse than the NBBO displayed on your trading screen? Apparently, this may be the result of deliberate manipulation of the market by high frequency traders. These HF traders submit thousands of quotes per second to the NYSE ("quote stuffing") and then cancel them within 50 ms. This slows down the exchange data queue so much that by the time a quote is transmitted to you, it is stale already, even if your trading server is collocated at the exchange. (Checking the time stamp of the quote is of no help: the time stamp is based on the time the quote enters the queue, not when it exits the queue.)
If you can no longer believe in the quotes, is there any integrity left in the market? Much as I think that HFT may be useful liquidity providers, I can't see how this specific practice could be good for anyone over the long term.
(Hat tip: Jim Liew of Alpha Quant Club.)
If you can no longer believe in the quotes, is there any integrity left in the market? Much as I think that HFT may be useful liquidity providers, I can't see how this specific practice could be good for anyone over the long term.
(Hat tip: Jim Liew of Alpha Quant Club.)
Saturday, August 14, 2010
What are we to do with Sharpe ratio?
I wrote several times before how useless Sharpe ratio is for certain types of strategies: see here and here. Not only is a high Sharpe ratio quite useless in telling you what damage extreme events can do to your equity, a low Sharpe ratio is also quite useless in telling you what spectacular gain your strategy might enjoy in the event of a catastrophe. I came across another brilliant example of the latter category in the best-selling book "The Big Short", where the author tells of the story of the fund manager Mike Burry.
Mike Burry started buying credit default swaps in 2005, essentially an insurance policy on mortgage-backed securities, betting that there will be widespread defaults on mortgages. Of course, we now know how this story would turn out: Mike Burry made $750 million in 2007 alone. But there was nothing but pain for the fund manager and his investors in 2005-2006, since they had to pay an annual premium of 8% of the portfolio. Investors who measured the performance of this strategy using Sharpe ratio, without knowing the details of the strategy itself, would be quite justified to think that it was an utter disaster prior to 2007. And indeed, many of them lost no time in trying to pull out their investments.
So what are we to do with Sharpe ratio, with its inherent reliance on Gaussian distributions? Clearly, it is useful for measuring high frequency strategies which you can count on to generate consistent returns every day, but which has limited catastrophic risks. But it is less useful for measuring statistical arbitrage strategies that hold positions over multiple days, since there may well be substantial hidden catastrophic risks in these strategies that would not be revealed by their track record and standard deviation of returns alone. As for strategies that are designed to benefit from catastrophes, such as Mike Burry's CDS purchases or Nassim Taleb's options purchases, it is completely useless. If I were to allocate my assets over different hedge funds, I would be sure to include some funds in the first category to generate cash flows for my daily needs, as well as funds in the last category to benefit from the infrequent black-swan events. As for the funds in the middle category, I am increasingly losing my enthusiasm.
Mike Burry started buying credit default swaps in 2005, essentially an insurance policy on mortgage-backed securities, betting that there will be widespread defaults on mortgages. Of course, we now know how this story would turn out: Mike Burry made $750 million in 2007 alone. But there was nothing but pain for the fund manager and his investors in 2005-2006, since they had to pay an annual premium of 8% of the portfolio. Investors who measured the performance of this strategy using Sharpe ratio, without knowing the details of the strategy itself, would be quite justified to think that it was an utter disaster prior to 2007. And indeed, many of them lost no time in trying to pull out their investments.
So what are we to do with Sharpe ratio, with its inherent reliance on Gaussian distributions? Clearly, it is useful for measuring high frequency strategies which you can count on to generate consistent returns every day, but which has limited catastrophic risks. But it is less useful for measuring statistical arbitrage strategies that hold positions over multiple days, since there may well be substantial hidden catastrophic risks in these strategies that would not be revealed by their track record and standard deviation of returns alone. As for strategies that are designed to benefit from catastrophes, such as Mike Burry's CDS purchases or Nassim Taleb's options purchases, it is completely useless. If I were to allocate my assets over different hedge funds, I would be sure to include some funds in the first category to generate cash flows for my daily needs, as well as funds in the last category to benefit from the infrequent black-swan events. As for the funds in the middle category, I am increasingly losing my enthusiasm.
Friday, July 30, 2010
Pair trading technologies update
Pair trading was invented two decades ago, but automating its implementation has only recently become fashionable with independent traders. But once the spotlight is on, innovations come fast and furious. Here are a number of recent developments that I find interesting:
1. I mentioned previously the software called quant2ib. It is an API which allows us to get market data and send orders from a Matlab program to Interactive Brokers (IB). I have used it extensively for our trading, and it is as reliable as IB's native API. Their latest version now includes functions for constructing a "combo" security. This combo security can be pairs of stocks, ETF's, futures, etc. (with the notable exception of currencies), and the API allows you to get market data as well as to submit orders on a combo. This is a huge improvement because you can now automatically trade a pair of securities as one unit by submitting limit orders on the combo. (Previously, you would have had to submit market order on at least one side of the pair, and this would have required your program to continuously monitor the market prices and send orders when appropriate. Or else you had to give up using the API and manually enter a "generic combo" limit order in IB's TWS.)
2. Alphacet Discovery also has the ability to send limit orders on pairs, due to its partnership with Knight Trading. Besides, based on a demo that I have recently seen, they also now have great pairs portfolio and execution reporting functionality. (Full disclosure: I used to consult for them.)
3. IB itself has released a "Scale Trader" algorithm that can be applied to combos (see 1. above. Hat tip: Mohamed.) I can't explain this better than their press release: "... ScaleTrader algorithm allows clients to create conditions under which a long position in one stock is built while simultaneously creating an offsetting short position in the other. The ScaleTrader is named because investors can 'scale-in' to market weakness by setting orders to buy as the market moves lower. Similarly, sell orders can be 'scaled' into when a market is rising. The ScaleTrader algorithm can be programmed to buy the spread and subsequently take profit by selling the spread if the difference reaches predetermined levels set by the user." In other words, it allows us to automatically implement the "parameterless trading" or the "averaging-in" strategy that I blogged about previously without any programming on our part!
Speaking of pair trading, I will be teaching my first New York workshop in October. (My editor inevitably picks touristy locations for these workshops. My London workshop takes place across the street from the Tower of London, my New York workshop is across from the new World Trade Center, and my Hong Kong workshop is in the "Golden Mile" shopping district of Tsim Sha Tsui.)
1. I mentioned previously the software called quant2ib. It is an API which allows us to get market data and send orders from a Matlab program to Interactive Brokers (IB). I have used it extensively for our trading, and it is as reliable as IB's native API. Their latest version now includes functions for constructing a "combo" security. This combo security can be pairs of stocks, ETF's, futures, etc. (with the notable exception of currencies), and the API allows you to get market data as well as to submit orders on a combo. This is a huge improvement because you can now automatically trade a pair of securities as one unit by submitting limit orders on the combo. (Previously, you would have had to submit market order on at least one side of the pair, and this would have required your program to continuously monitor the market prices and send orders when appropriate. Or else you had to give up using the API and manually enter a "generic combo" limit order in IB's TWS.)
2. Alphacet Discovery also has the ability to send limit orders on pairs, due to its partnership with Knight Trading. Besides, based on a demo that I have recently seen, they also now have great pairs portfolio and execution reporting functionality. (Full disclosure: I used to consult for them.)
3. IB itself has released a "Scale Trader" algorithm that can be applied to combos (see 1. above. Hat tip: Mohamed.) I can't explain this better than their press release: "... ScaleTrader algorithm allows clients to create conditions under which a long position in one stock is built while simultaneously creating an offsetting short position in the other. The ScaleTrader is named because investors can 'scale-in' to market weakness by setting orders to buy as the market moves lower. Similarly, sell orders can be 'scaled' into when a market is rising. The ScaleTrader algorithm can be programmed to buy the spread and subsequently take profit by selling the spread if the difference reaches predetermined levels set by the user." In other words, it allows us to automatically implement the "parameterless trading" or the "averaging-in" strategy that I blogged about previously without any programming on our part!
Speaking of pair trading, I will be teaching my first New York workshop in October. (My editor inevitably picks touristy locations for these workshops. My London workshop takes place across the street from the Tower of London, my New York workshop is across from the new World Trade Center, and my Hong Kong workshop is in the "Golden Mile" shopping district of Tsim Sha Tsui.)
Saturday, May 29, 2010
The Quants
Once in a while, a book about trading written for the general public contains some useful nuggets even for professionals. Fortune's Formula was one. It introduced me to the world of Kelly's formula, Universal Portfolios, and the maximization of compounded growth rate. The Quants, by WSJ reporter Scott Patterson, is another. (Hat tip to my partner Steve for telling me about it.)
What is the most important take-away in The Quants? No, it is not that you should learn to become a master poker player or chess player before hoping to make it big, though you would think that given Patterson's exhaustive coverage of poker games played by the top quants. Among my own professional acquaintances, trader-poker-players are still a minority.
The most important take-away is what ex-employees said about Renaissance Technologies: "there is no secret formula for the fund's success, no magic code discovered decades ago by geniuses .... Rather, Madallion [Fund]'s team of ninety or so Ph.D.'s are constantly working to improve the fund's systems, ..."
In other words, though you may not have 90 Ph.D.'s at your disposal, you can still work on continuously improving/refining your strategies, improving the engineering of your trading environment, and increasing the diversity of your strategies. And though you may still not archive 60-70% annualized returns every year, you will nevertheless enjoy stable returns year after year.
By the way, it is good to see my ex-colleagues Lalit Bahl, Vincent and Stephen Della Pietra mentioned in the book, all of whom left IBM to join Renaissance many years ago, and who are extraordinarily nice and friendly guys, quite in contrast to the norm on Wall Street.
What is the most important take-away in The Quants? No, it is not that you should learn to become a master poker player or chess player before hoping to make it big, though you would think that given Patterson's exhaustive coverage of poker games played by the top quants. Among my own professional acquaintances, trader-poker-players are still a minority.
The most important take-away is what ex-employees said about Renaissance Technologies: "there is no secret formula for the fund's success, no magic code discovered decades ago by geniuses .... Rather, Madallion [Fund]'s team of ninety or so Ph.D.'s are constantly working to improve the fund's systems, ..."
In other words, though you may not have 90 Ph.D.'s at your disposal, you can still work on continuously improving/refining your strategies, improving the engineering of your trading environment, and increasing the diversity of your strategies. And though you may still not archive 60-70% annualized returns every year, you will nevertheless enjoy stable returns year after year.
By the way, it is good to see my ex-colleagues Lalit Bahl, Vincent and Stephen Della Pietra mentioned in the book, all of whom left IBM to join Renaissance many years ago, and who are extraordinarily nice and friendly guys, quite in contrast to the norm on Wall Street.
Saturday, May 22, 2010
A HFT primer
As a follow-up of my previous discussions on high frequency trading, I have invited guest blogger Jennifer Groton to share with us a quick survey of various common HFT strategies used by equities and FX traders.
==
High frequency trading strategies are under fire. The recent trading spike in our national exchanges was duly noted as a short-circuit waiting to happen and drew immediate industry criticism of auto-trading robots. Before a witch-hunt ensues, perhaps a review of the common HFT strategies in stocks and Forex is in order.
High-frequency firms employ a wide variety of low-margin trading strategies that are implemented by professional market intermediaries who have invested heavily in technology. These firms claim that they make markets more efficient by enhancing liquidity and transparent price discovery to the benefit of investors. The Forex market’s unique combination of high liquidity and low volatility make it an ideal environment for deploying HFT strategies, although many of the ideas and technology are from the equity markets. The basic strategies fall into three categories: market-making, trending or predictive, and classic arbitrage.
Market-making strategies tend to focus on a single stock or currency pair. Many firms in this area have been described as engaging in "rebate-capture trading", a reference to the credits that firms get for providing liquidity on most market centers.
The second group consists of mean-reversion and trending strategies. These utilize technical indicators for stocks or forex indicators for currencies, and seek to generate more return from individual trades.
The last group may involve a cross-section of trades from multiple markets. The classic arbitrage strategy is a form of the “carry trade” that uses the prices of a domestic bond, a bond denominated in a foreign currency, the spot price of the currency, and the price of a forward contract on the currency. If the market prices are sufficiently different from those implied in the model to cover transactions costs, then four transactions can be made to guarantee a risk-free profit.
High frequency trading is attributed with generating over 70% of the volume of trades on our equity markets. Similar statistics are not available for forex markets, but speculating disguised as commercially necessary trades have been reported to be over two-thirds of the volume. Liquidity and pricing transparency are the benefits offered by its advocates, but regulators and other market participants who disagree with this positive assessment are presently discounting these benefits. Transaction taxes and time limits on orders have been proposed to mitigate the perceived risk created by HFT firms, but the wheels of Washington move slowly, even in crisis. For the time being, there is no indication that their participation will be discontinued.
==
High frequency trading strategies are under fire. The recent trading spike in our national exchanges was duly noted as a short-circuit waiting to happen and drew immediate industry criticism of auto-trading robots. Before a witch-hunt ensues, perhaps a review of the common HFT strategies in stocks and Forex is in order.
High-frequency firms employ a wide variety of low-margin trading strategies that are implemented by professional market intermediaries who have invested heavily in technology. These firms claim that they make markets more efficient by enhancing liquidity and transparent price discovery to the benefit of investors. The Forex market’s unique combination of high liquidity and low volatility make it an ideal environment for deploying HFT strategies, although many of the ideas and technology are from the equity markets. The basic strategies fall into three categories: market-making, trending or predictive, and classic arbitrage.
Market-making strategies tend to focus on a single stock or currency pair. Many firms in this area have been described as engaging in "rebate-capture trading", a reference to the credits that firms get for providing liquidity on most market centers.
The second group consists of mean-reversion and trending strategies. These utilize technical indicators for stocks or forex indicators for currencies, and seek to generate more return from individual trades.
The last group may involve a cross-section of trades from multiple markets. The classic arbitrage strategy is a form of the “carry trade” that uses the prices of a domestic bond, a bond denominated in a foreign currency, the spot price of the currency, and the price of a forward contract on the currency. If the market prices are sufficiently different from those implied in the model to cover transactions costs, then four transactions can be made to guarantee a risk-free profit.
High frequency trading is attributed with generating over 70% of the volume of trades on our equity markets. Similar statistics are not available for forex markets, but speculating disguised as commercially necessary trades have been reported to be over two-thirds of the volume. Liquidity and pricing transparency are the benefits offered by its advocates, but regulators and other market participants who disagree with this positive assessment are presently discounting these benefits. Transaction taxes and time limits on orders have been proposed to mitigate the perceived risk created by HFT firms, but the wheels of Washington move slowly, even in crisis. For the time being, there is no indication that their participation will be discontinued.
Saturday, May 08, 2010
Are flash orders to be blamed for Dow's 1,000 points drop?
Before the smoke is clear, fingers are already pointing at flash orders. See these two NYT pieces here and here. Our reader Madan has convinced me previously that flash orders can indeed be used to front-run other traders, but until more evidence comes in, I am yet to be convinced that they are the main culprit. Couldn't old-fashioned automated momentum programs accomplished the same thing after an initial erroneous transaction price and/or quote was reported? Perhaps you know of discussions elsewhere on the blogosphere that bring more light to the issue?
Sunday, May 02, 2010
An additional ETF pair
Many of you know that there are a number of dependable commodity-related ETF pairs that remain cointegrated ever since I mentioned them in 2006: IGE-EWC, IGE-EEM, IGE-EWA, EWA-EWC, etc. (Their latest zScores are available here to my book's readers and to Premium Content subscribers.) A recent visit to a client in South Africa prompted me to add a new one: EWA-EZA.
It is worth noting that for those country ETF pairs that cointegrate, their underlying currency cross-rates are often stationary as well. Now, there are several advantages in trading currency cross rates instead of ETF pairs. When trading a stationary cross rate, you can enter a limit order to enter and exit, but trading pairs of ETF's involve market orders on at least one side. Also, ETF's can sometimes be hard-to-borrow, and their margin requirements are much more onerous than that of currencies. However, the one major disadvantage in trading cross rates is that they are not always available on your brokerage. For example, based on the cointegration of EWA and EZA you would think that trading AUDZAR would be quite profitable. And you would be right, theoretically, except that AUDZAR is not available for trading on Interactive Brokers. If you know of a good Forex brokerage that have many emerging markets cross-rates for trading, especially those of Latin American countries, please let the rest of us know!
It is worth noting that for those country ETF pairs that cointegrate, their underlying currency cross-rates are often stationary as well. Now, there are several advantages in trading currency cross rates instead of ETF pairs. When trading a stationary cross rate, you can enter a limit order to enter and exit, but trading pairs of ETF's involve market orders on at least one side. Also, ETF's can sometimes be hard-to-borrow, and their margin requirements are much more onerous than that of currencies. However, the one major disadvantage in trading cross rates is that they are not always available on your brokerage. For example, based on the cointegration of EWA and EZA you would think that trading AUDZAR would be quite profitable. And you would be right, theoretically, except that AUDZAR is not available for trading on Interactive Brokers. If you know of a good Forex brokerage that have many emerging markets cross-rates for trading, especially those of Latin American countries, please let the rest of us know!
Saturday, April 17, 2010
How do you limit drawdown using Kelly formula?
As many of you know, I am a fan of Kelly formula because it allows us to maximize long-term growth of equity while minimizing the probability of ruin. However, what Kelly formula wont' prevent is a deep drawdown, though we are assured that the drawdown won't be as much as 100%! This is unsatisfactory to many traders and especially fund managers, since a deep drawdown is psychologically painful and may cause you to panic and shut down a strategy prematurely.
There is an easy way, though, that you can use Kelly formula to limit your drawdown to be much less than 100%. Suppose the optimal Kelly leverage of your strategy is determined to be K. And suppose you only allow a maximum drawdown (measured from the high watermark, as usual) to be D%. Then you can simply set aside D% of your initial total account equity for trading, and apply a leverage of K to this sub-account to determine your portfolio market value. The other 1-D% of the account will be sitting in cash. You can then be assured that you won't lose all of the equity of this sub-account, or equivalently, you won't suffer a drawdown of more than D% in your total account. If your trading strategy is profitable and the total account equity reaches a new high watermark, then you can reset your sub-account equity so that it is again D% of the total equity, moving some cash back to the "cash" account. Otherwise, you continue to keep the equity in the cash account separate from the equity of the trading sub-account.
Notice that because of this separation of accounts, this scheme is not equivalent to just using a leverage of L=K*D% on your total account equity. Indeed, some of you may be too nervous to use the full K as leverage, and prefer to use a leverage L smaller than K. (In fact, the common wisdom is that, due to estimation errors, it is never advisable to set L to be more than K/2, i.e. half-Kelly.) The problem with using a L that is too small is that, besides not achieving maximum growth, the portfolio market value will be unresponsive to gains or losses and will remain relatively constant. Using the scheme I suggested above will cure this problem as well, because you can apply a higher leverage L_sub to the sub-account (e.g. use L_sub = L/D%) as long as L_sub < K, so that the portfolio market value is much more sensitive to your P&L while still ensuring the drawdown will not exceed D%.
Has anyone tried this scheme in their actual trading? If so, I would be interested in hearing your experience and see if practice is as good as theory.
There is an easy way, though, that you can use Kelly formula to limit your drawdown to be much less than 100%. Suppose the optimal Kelly leverage of your strategy is determined to be K. And suppose you only allow a maximum drawdown (measured from the high watermark, as usual) to be D%. Then you can simply set aside D% of your initial total account equity for trading, and apply a leverage of K to this sub-account to determine your portfolio market value. The other 1-D% of the account will be sitting in cash. You can then be assured that you won't lose all of the equity of this sub-account, or equivalently, you won't suffer a drawdown of more than D% in your total account. If your trading strategy is profitable and the total account equity reaches a new high watermark, then you can reset your sub-account equity so that it is again D% of the total equity, moving some cash back to the "cash" account. Otherwise, you continue to keep the equity in the cash account separate from the equity of the trading sub-account.
Notice that because of this separation of accounts, this scheme is not equivalent to just using a leverage of L=K*D% on your total account equity. Indeed, some of you may be too nervous to use the full K as leverage, and prefer to use a leverage L smaller than K. (In fact, the common wisdom is that, due to estimation errors, it is never advisable to set L to be more than K/2, i.e. half-Kelly.) The problem with using a L that is too small is that, besides not achieving maximum growth, the portfolio market value will be unresponsive to gains or losses and will remain relatively constant. Using the scheme I suggested above will cure this problem as well, because you can apply a higher leverage L_sub to the sub-account (e.g. use L_sub = L/D%) as long as L_sub < K, so that the portfolio market value is much more sensitive to your P&L while still ensuring the drawdown will not exceed D%.
Has anyone tried this scheme in their actual trading? If so, I would be interested in hearing your experience and see if practice is as good as theory.
Saturday, February 27, 2010
Conference on the sociology of quantitative finance
A new conference called Psi-Q will be held in London this June, featuring luminaries in the academic quantitative finance world, as well as risk and fund managers from various banks and hedge funds. Example topics:
- How did shared beliefs, practices, ways of calculating, and technical systems impact evaluation of asset-backed securities and CDOs before and during the credit crises?
- Was that Lucky or Good? Creating a framework for skill attribution in finance, business management and other risky endeavors.
- The “backing out” phenomena observed in options markets: how traders use models to imply independent variables consistent with market observed pricing, and where enough traders can be wrong about the expected results and the backed-out positions can send the wrong message.
Thursday, February 18, 2010
Pairs Trading Workshop in Hong Kong
For my readers in Asia, I will be conducting a pairs trading workshop in Hong Kong on March 10-11. This workshop is organized by the Technical Analyst magazine and is similar to the one I gave in London last year.
However, I have added a few useful insights based on audience feedback. As always, no prior knowledge of Matlab or advanced statistics is assumed. The numerous in-class exercises should be sufficient to bring your Matlab programming skills up to speed.
However, I have added a few useful insights based on audience feedback. As always, no prior knowledge of Matlab or advanced statistics is assumed. The numerous in-class exercises should be sufficient to bring your Matlab programming skills up to speed.
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