Trading VXX with nearest neighbors prediction

An experienced trader knows what behavior to expect from the market based on a set of indicators and their interpretation. The latter is often done based on his memory or some kind of model. Finding a good set of indicators and processing their information poses a big challenge. First, one needs to understand what  factors are correlated to future prices. Data that does not have any predictive quality only intorduces noise and complexity, decreasing strategy performance. Finding good indicators is a science on its own, often requiring deep understandig of the market dynamics. This part of strategy design can not be easily automated. Luckily, once a good set of indicators has been found, the traders memory and 'intuition' can be easily replaced with a statistical model, which will likely to perform much better as computers do have flawless memory and can make perfect statistical estimations.

Regarding volatility trading, it took me quite some time to understand what influences its movements. In particular, I'm interested in variables that predict future returns of VXX and  XIV. I will not go into full-length explanation here, but just present a conclusion : my two most valuable indicators for volatility are the term structure slope and current volatility premium.
My definition of these two is:

• volatility premium = VIX-realizedVol
• delta (term structure slope) = VIX-VXV

VIX & VXV are the forward 1 and 3 month implied volatilities of the S&P 500. realizedVol here is a 10-day realized volatility of SPY, calculated with Yang-Zhang formula. delta  has been often discussed on VixAndMore blog, while premium is well-known from option trading.

It makes sense to go short volatility when premium  is high and futures are in contango (delta  < 0). This will cause a tailwind from both the premium and daily roll along the term structure in VXX. But this is just a rough estimation. A good trading strategy would combine information from both premium and delta to come with a prediction on trading direction in VXX.

I've been struggling for a very long time to come up with a good way to combine the noisy data from both indicators. I've tried most of the 'standard' approaches, like linear regression, writing a bunch of 'if-thens' , but all with a very minor improvements compared to using only one indicator. A good example of such 'single indicator' strategy with simple  rules can be found on TradingTheOdds blog . Does not look bad, but what can be done with multiple indicators?

I'll start with some out-of-sample VXX data that I got from MarketSci. Note that this is simulated data, before VXX was created. 

The indicators for the same period are plotted below:

If we take one of the indicators (premium in this case) and plot it against future returns of VXX, some correlation can be seen, but the data is extremely noisy:

Still, it is clear that negative premium is likely to have positive VXX returns on the next day.
Combining both premium and delta into one model has been a challenge for me, but I always wanted to do a statistical approximation. In essence, for a combination of (delta,premium), I'd like to find all historic values that are closest to the current values and make an estimation of the future returns based on them. A couple of times I've started writing my own nearest-neighbor interpolation algorithms, but every time I had to give up... until I came across the scikit nearest neighbors regression. It enabled me to quickly build a predictor based on two inputs and the results are so good, that I'm a bit worried that I've made a mistake somewhere...

Here is what I did:

1. create a dataset of [delta,premium] -> [VXX next day return] (in-of-sample)
2. create a nearest-neighbor predictor based on the dataset above
3. trade strategy (out-of-sample) with the rules:
• go long if predicted return > 0
• go short if predicted return <0

The strategy could not be simpler...

The results seem extremely good and get better when more neigbors are used for estimation.

First, with 10 points, the strategy is excellent in-sample, but is flat out-of-sample (red line in figure below is the last point in-sample)

Then, performance gets better with 40 and 80 points:

In the last two plots, the strategy seems to perform the same in- and out-of-sample. Sharpe ratio is around 2.3.
I'm very pleased with the results and have the feeling that I've only been scratching the surface of what is possible with this technique.

Simple backtesting module

My search of an ideal backtesting tool (my definition of 'ideal' is described in the earlier 'Backtesting dilemmas' posts) did not result in something that I could use right away. However, reviewing the available options helped me to understand better what I really want. Of the options I've looked at, pybacktest was the one I liked most because of its simplicity and speed. After going through the source code,  I've got some ideas to make it simpler and a bit more elegant. From there, it was only a small step to writing my own backtester, which is now available in the TradingWithPython library.

I have chosen an approach where the backtester contains functionality which all trading strategies share and that often gets copy-pasted. Things like calculating positions and pnl, performance metrics and making plots.

Strategy specific functionality, like determining entry and exit points should be done outside of the backtester. A typical workflow would be:
find entry and exits -> calculate pnl and make plots with backtester -> post-process strategy data

At this moment the module is very minimal (take a look at the source here), but in the future I plan on adding profit and stop-loss exits and multi-asset portfolios.

Usage of the backtesting module is shown in this example notebook

Boosting performance with Cython

Even with my old pc (AMD Athlon II, 3GB ram), I seldom run into performance issues when running vectorized code. But unfortunately there are plenty of cases where that can not be easily vectorized, for example the drawdown function. My implementation of such was extremely slow, so I decided to use it as a test case for speeding things up. I'll be using the SPY timeseries with ~5k samples as test data. Here comes the original version of my drawdown function (as it is now implemented in the TradingWithPython library)

def drawdown(pnl):
    """
    calculate max drawdown and duration

    Returns:
        drawdown : vector of drawdwon values
        duration : vector of drawdown duration
    """
    cumret = pnl

    highwatermark = [0]

    idx = pnl.index
    drawdown = pd.Series(index = idx)
    drawdowndur = pd.Series(index = idx)

    for t in range(1, len(idx)) :
        highwatermark.append(max(highwatermark[t-1], cumret[t]))
        drawdown[t]= (highwatermark[t]-cumret[t])
        drawdowndur[t]= (0 if drawdown[t] == 0 else drawdowndur[t-1]+1)

    return drawdown, drawdowndur

%timeit drawdown(spy)
1 loops, best of 3: 1.21 s per loop

Hmm 1.2 seconds is not too speedy for such a simple function. There are some things here that could be a great drag to performance, such as a list *highwatermark* that is being appended on each loop iteration. Accessing Series by their index should also involve some processing that is not strictly necesarry. Let's take a look at what happens when this function is rewritten to work with numpy data

def dd(s):
#    ''' simple drawdown function '''
    
    highwatermark = np.zeros(len(s))
    drawdown = np.zeros(len(s))
    drawdowndur = np.zeros(len(s))

 
    for t in range(1,len(s)):
        highwatermark[t] = max(highwatermark[t-1], s[t])
        drawdown[t] = (highwatermark[t]-s[t])
        drawdowndur[t]= (0 if drawdown[t] == 0 else drawdowndur[t-1]+1)
       
     
    return drawdown , drawdowndur

%timeit dd(spy.values)
10 loops, best of 3: 27.9 ms per loop

Well, this is much faster than the original function, approximately 40x speed increase. Still there is much room for improvement by moving to compiled code with cython Now I rewrite the dd function from above, but using optimisation tips that I've found on the cython tutorial . Note that this is my first try ever at optimizing functions with Cython.

%%cython
import numpy as np
cimport numpy as np

DTYPE = np.float64
ctypedef np.float64_t DTYPE_t

cimport cython
@cython.boundscheck(False) # turn of bounds-checking for entire function
def dd_c(np.ndarray[DTYPE_t] s):
#    ''' simple drawdown function '''
    cdef np.ndarray[DTYPE_t] highwatermark = np.zeros(len(s),dtype=DTYPE)
    cdef np.ndarray[DTYPE_t] drawdown = np.zeros(len(s),dtype=DTYPE)
    cdef np.ndarray[DTYPE_t] drawdowndur = np.zeros(len(s),dtype=DTYPE)

    cdef int t
    for t in range(1,len(s)):
        highwatermark[t] = max(highwatermark[t-1], s[t])
        drawdown[t] = (highwatermark[t]-s[t])
        drawdowndur[t]= (0 if drawdown[t] == 0 else drawdowndur[t-1]+1)
        
    return drawdown , drawdowndur

%timeit dd_c(spy.values)
10000 loops, best of 3: 121 µs per loop

Wow, this version runs in 122 microseconds, making it ten thousand times faster than my original version! I must say that I'm very impressed by what the Cython and IPython teams have achieved! The speed compared with ease of use is just awesome!
 P.S. I used to do code optimisations in Matlab using pure C and .mex wrapping, it was all just pain in the ass compared to this.

Backtesting dilemmas: pyalgotrade review

Ok, moving on to the next contestant: PyAlgoTrade

First impression: actively developed, pretty good documentation, more than enough feautures ( TA indicators, optimizers etc) . Looks good, so I went on with the installation which also went smoothly.

The tutorial seems to be a little bit out of date, as the first command yahoofinance.get_daily_csv() throws an error about unknown function. No worries, the documentation is up to date and I find that the missing function is now renamed to yahoofinance.download_daily_bars(symbol,year,csvFile). The problem is that this function only downloads data for one year instead of everything from that year to current date. So pretty useless.
After I downloaded the data myself and saved it to csv, I needed to adjust the column names because apparently pyalgotrade expects Date,Adj Close,Close,High,Low,Open,Volume to be in the header. That is all minor trouble.

Following through to performance testing on an SMA strategy that is provided in the tutorial. My dataset consists of 5370 days of SPY:

%timeit myStrategy.run()
1 loops, best of 3: 1.2 s per loop

That is actually pretty good for an event-based framework.

But then I tried searching documentation for functionality needed to backtest spreads and multiple asset portfolios and just could not find any. Then I tried to find a way to feed pandas DataFrame as an input to a strategy and it happens to be not possible, which is again a big disappointment. I did not state it as a requirement in the previous post, but now I come to realisation that pandas support is a must for any framework that works with time series data. Pandas was a reason for me to switch from Matlab to Python and I never want to go back.

Conclusion pyalgotrade does not meet my requrement for flexibility. It looks like it was designed with classic TA in mind and single instrument trading. I don’t see it as a good tool for backtesting strategies that involve multiple assets, hedging etc.

Backtesting dilemmas

A quantitative trader faces quite some challenges on a way to a successful trading strategy. Here I’ll discuss a couple dilemmas involved in backtesting. A good trading simulation must :

1. Be good approximation of the real world. This one is of course the most important requirement .
2. Allow unlimited flexibility: the tooling should not stand in the way of testing out-of-the-box ideas. Everything that can be quantified should be usable.
3. Be easy to implement & maintain. It is all about productivity and being able to test many ideas to find one that works.
4. Allow for parameter scans, walk-forward testing and optimisations. This is needed for investigating strategy performance and stability depending on strategy parameters.

The problem with satisfying all of the requirements above is that #2 and #3 are conflicting ones. There is no tool that can do everything without the cost of high complexity (=low maintainablity). Typically, a third party point-and-click tool will severely limit freedom to test with custom signals and odd portfolios, while at the other end of the spectrum a custom-coded diy solution will require tens or more hours to implement with high chances of ending up with cluttered and unreadable code. So in attempt to combine the best of both worlds, let’s start somewehere in the middle: use an existing backtesting framework and adapt it to our taste.
In the following posts I’ll be looking at three possible candidates I’ve found:

• Zipline is widely known and is the engine behind Quantopian
• PyAlgotrade seems to be actively developed and well-documented
• pybacktest is a light-weight vector-based framework with that might be interesting because of its simplicity and performance.

I’ll be looking at suitability of these tools benchmarking them against a hypothetical trading strategy. If none of these options fits my requirements I will have to decide if I want to invest into writing my own framework (at least by looking at the available options I’ll know what does not work) or stick with custom code for each strategy.
First one for the evaluation is Zipline.
My first impression of Zipline and Quantopian is a positive one. Zipline is backed by a team of developers and is tested in production, so quality (bugs) should be great. There is good documentation on the site and an example notebook on github .
To get a hang of it, I downloaded the exampe notebook and started playing with it. To my disappointment I quickly run into trouble at the first example Simplest Zipline Algorithm: Buy Apple. The dataset has only 3028 days, but running this example just took forever. Here is what I measured:

dma = DualMovingAverage()
%timeit perf = dma.run(data)

1 loops, best of 3: 52.5 s per loop

I did not expect stellar performance as zipline is an event-based backtester, but almost a minute for 3000 samples is just too bad. This kind of performance would be prohibitive for any kind of scan or optimization. Another problem would arise when working with larger datasets like intraday data or multiple securities, which can easily contain hundreds of thousands of samples.
Unfortunately, I will have to drop Zipline from the list of useable backtesters as it does not meet my requirement #4 by a fat margin.
In the following post I will be looking at PyAlgotrade.
Note: My current system is a couple of years old, running an AMD Athlon II X2 @2800MHZ with 3GB of RAM. With vector-based backtesting I’m used to calculation times of less than a second for a single backtest and a minute or two for a parameter scan. A basic walk-forward test with 10 steps and a parameter scan for 20x20 grid would result in a whooping 66 hours with zipline. I’m not that paitient.

Starting IPython notebook from windows file exlorer

I organize my IPython notebooks by saving them in different directories. This brings however an inconvenience, because to access the notebooks I need to open a terminal and type 'ipython notebook --pylab=inline'  each and every time. I'm sure the ipython team will solve this in the long run, but in the meantime there is a pretty descent way to quickly access the notebooks from the file explorer.

All you need to do is add a context menu that starts ipython server in your desired directory:

A quick way to add the context item is by running this registry patch.  (Note: the patch assumes that you have your python installation located in C:\Anaconda . If not, you’ll need to open the .reg file in a text editor and set the right path on the last line).

Instructions on adding the registry keys manually can be found on Frolian's blog.

Leveraged ETFs in 2013, where is your decay now?

Many people think that leveraged etfs in the long term underperform their benchmarks. This is true for choppy markets, but not in the case of trending conditions, either up or down. Leverage only has effect on the most likely outcome, not on the expected outcome. For more background please read this post.

2013 has been a very good year for stocks, which trended up for most of the year. Let's see what would happen if we shorted some of the leveraged etfs exactly a year ago and hedged them with their benchmark. 
Knowing the leveraged etf behavior  I would expect that leveraged etfs outperformed their benchmark, so the strategy that would try to profit from the decay would lose money.

I will be considering these pairs:

SPY 2 SSO -1 
SPY -2 SDS -1
QQQ 2 QLD -1
QQQ -2 QID -1
IYF -2 SKF -1

Each leveraged etf is held short (-1 $) and hedged with an 1x etf. Notice that to hedge an inverse etf a negative position is held in the 1x etf.

Here is one example: SPY vs SSO. 
Once we normalize the prices to 100$ at the beginning of the backtest period (250 days) it is apparent that  the 2x etf outperforms 1x etf.

 Now the results of  the backtest on the pairs above:

All the 2x etfs (including inverse) have outperformed their benchmark over the course of 2013. According to expectations, the strategy exploiting 'beta decay' would not be profitable.

I would think that playing leveraged etfs against their unleveraged counterpart does not provide any edge, unless you know the market conditions beforehand (trending or range-bound).  But if you do know the coming market regime, there are much easier ways to profit from it. Unfortunately, nobody has yet been really succesful at predicting the market regime at even the very short term.


Full source code of the calculations is available for the subscribers of the Trading With Python course. Notebook #307

Putting a price tag on TWTR

Here is my shot at Twitter valuation. I'd like to start with a disclaimer: at this moment a large portion of my portrolio consists of short TWTR position, so my opinion is rather skewed. The reason I've done my own analysis is that my bet did not work out well, and Twitter made a parabolic move in December 2013. So the question that I'm trying to answer here is "should I take my loss or hold on to my shorts?".

At the time of writing, TWTR trades around $64 mark, with a market cap of 34.7 B$. Up till now the company has not made any profit, loosing 142M$ in 3013 after making 534M$ in revenues. The last two numbers give us yearly company spendings of 676M$.

Price derived from user value

Twitter can be compared with  with Facebook, Google and LinkedIn to get an idea of user numbers and their values. The table below summarises user numbers per company and a value per user derived from the market cap. (source for number of users: Wikipedia, number for Google is based on number of unique searches)

	users [millions]	user value [$]
FB	1190	113
TWTR	250	139
GOOG	2000	187
LNKD	259	100

It becomes apparent that the market valuation per user is very similar for all of the companies, however my personal opinion is that:

• TWTR is currently more valuable per user thatn FB or LNKD. This is not logical as both competitors have more valuable personal user data at their disposal. 
• GOOG has been excelling at extracting ad revenue from its users. To do that, it has a set of highly diversified offerings, from search engine to Google+ , Docs and Gmail. TWTR has nothing resembling that, while its value per user is only 35% lower thatn that of Google.
• TWTR has a limited room to grow its user base as it does not offer products comparable to FB or GOOG offerings. TWTR has been around for seven years now and most people wanting an accout have got their chance. The rest just does not care.
• TWTR user base is volatile and is likely to move to the next hot thing when it will become available.

I think the best reference here would be LNKD, which has a stable niche in the professional market. By this metric TWTR would be overvalued. Setting user value at 100$ for TWTR would produce a fair TWTR price of 46 $.

Price derived from future earnings

There is enough data available of the future earnings estimates. One of the most useful ones I've found is here.

Using those numbers while subtracting company spendings, which I assume to remain constant , produces this numbers:

	banks	independents
2013	-51	-43
2014	292	462
2015	612	1120

Net income in M$

With an assumption that a healthy company will have a final PE ratio of around 30, we can calculate share prices:

	banks	independents	average
2013	-2.81	-2.37	-2.59
2014	16.08	25.45	20.76
2015	33.71	61.69	47.70

TWTR price in $ based on PE=30

Again, average price estimate is around 46-48 $ mark which is what it was around the IPO. Current price of 64$  is around 36% too high to be reasonable.

Conclusion

Based on available information, optimistic valuation of TWTR should be in the 46-48 $ range. There are no clear reasons it should be trading higher and many operational risks to trade lower.

My guess is that during the IPO enough professionals have reviewed the price, setting it at a fair price level. What happened next was an irrational market move not justified by new information. Just take a look at the bullish frenzy on stocktwits,  with people claiming things like 'this bird will fly to $100'. Pure emotion, which never works out well.

The only thing that rests me now is to put my money where my mouth is and stick to my shorts. Time will tell.