Introduction to Quantitative/Algorithmic trading: from
Technical Analysis to Statistical Arbitrage
PQFC trading Seminar part II
Xiaoguang Wang
PhD Candidate, Department of Statistics
Purdue University
April 21, 2014
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Important Disclosures
The following presentation is for educational purpose only.
All symbols and trading ideas discussed in the presentation are for
demonstration only and are not recommendations.
Active trading is not suitable for everyone.
Past performance does not guarantee future results.
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Outline
1
Introduction to Quantitative Trading
2
Quantitative Trading using Technical Analysis
Technical Indicator
Algorithm design and implementation
3
Optimizing your quantitative trading strategies
Back testing
4
Quantitative Trading using more advanced tools
Statistical Arbitrage
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What is Quantitative Trading?
Trading strategies based on quantitative analysis which rely on
mathematical computations and number crunching to identify trading
opportunities.
The process consists of thorough examination of vast databases
searching for repeating patternspersistent occurrences of a
phenomenon, correlations among liquid assets.
Price and volume are two of the more common data inputs used in
quantitative analysis as the main inputs to mathematical models.
It is generally used by financial institute and hedge funds. Nowadays,
quantitative trading is also commonly used by individual investors.
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Main types of quantitative trading strategies
High frequency trading
Algorithmic trading using technical analysis
Liquidity trading (such as Convertible arbitrage)
Statistical arbitrage
Mean-reverting
Pair trading (long & short; cointegration; Equity risk-neutral)
Volatility trading/arbitrage
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Steps to construct a quantitative trading strategy
Strategy Identification: Finding a strategy, exploiting an edge and
deciding on trading frequency
Strategy Backtesting: Obtaining data, analyzing strategy
performance and removing biases
Execution System: Linking to a brokerage, automating the trading
and minimizing transaction costs
Risk Management: Optimal capital allocation, ”bet size”/Kelly
criterion and trading psychology
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Technical Analysis
Philosophy of Technical Analysis:
Market action discounts everything.
Prices move in trends: A trend in motion is more likely to continue
than to reverse. (An adaptation of Newtons first law of motion.)
History repeats itself.
A trend is assumed to be in effect until it gives definite signals that it
has reversed.
The market is more psychological than logical.
(To know more information about technical analysis basics, please go to
my website.)
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Main types of technical indicators
Trend detective indicators: Moving Average systems, Bollinger Bands,
parabolic SAR, Commodity Channel Index, ZigZag
Oscillation indicators: MACD, RSI, RVI, Stochastic Oscillator,
Williams percent range
Volume indicators: Volumes, On balance volume, Accumulation,
Distribution.
Others: Pivot system, Fibonacci retracement system.
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Moving Average
Simple Moving Average (SMA): the unweighted mean of the previous
n data.
pM + pM−1 + · · · + pM−(n−1)
SMA =
n
Weighted Moving Average (WMA): weights decrease in arithmetical
progression
WMAM =
npM + (n − 1)pM−1 + · · · + 2pM−n+1 + pM−n+1
n + (n − 1) + · · · + 2 + 1
Exponential Moving Average (EMA): weights decrease exponentially
S1 = Y1
for t > 1,
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Moving average system
A Moving Average Crossover System refers to plotting multiple
moving average indicators of different periods on one price chart.
A Moving Average Envelop system plots two bands around a moving
average, staggered by a specific percentage rate.
The two main principals for trading strategies based on a moving average
system are:
Moving average indicators of important periods (such as
20,60,100,200) offer support or resistance for price process.
Short-period (fast) moving average indicator up-crosses long-period
(slow) moving average indicator indicating the beginning or speed-up
of uptrend, and vice verse.
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Moving Average Crossover
Crossover between price and
indicator
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Crossover between MAs
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Moving Average Envelope
in the chart below, a 5% envelope is placed around a 25-day moving
average. Notice how the move often reverses direction after approaching
one of the levels. A price move beyond the band can signal a period of
exhaustion, and traders will watch for a reversal toward the center average.
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Bollinger bands
Drawback of MA envelope: the bandwidth is fixed regardless of the price
dynamics, while volatility of price is stochastic.
Improvement: Bollinger Band, which consists of:
an N-period moving average (MA)
an upper band at K times an N-period standard deviation above the
moving average (MA + Kσ)
a lower band at K times an N-period standard deviation below the
moving average (MA Kσ)
Typical values for N and K are 20 and 2, respectively. The default choice
for the average is a simple moving average. Usually the same period is
used for both the middle band and the calculation of standard deviation.
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Bollinger bands
S&P 500 with 20-day, two-standard-deviation Bollinger Bands, %b and
bandwidth.
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MACD
The Moving Average Convergence Divergence (MACD) technique is a
trend-following momentum indicator which combines two exponential
averages of past prices into two lines: the MACD line and the signal line.
The MACD line is constructed as the difference between two exponential
moving averages computed using last m and n closing prices (n > m).
1
1
EMALt−1 , EMAL0 = P0
EMALt = Pt + 1 −
n
n
1
1
EMASt = Pt + 1 −
EMASt−1 , EMAS0 = P0
m
m
MACDt = EMASt − EMALt ,
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MACD - cont.
The signal line, SLt is a k-period exponential moving average of the
MACD line
1
1
SLt−1 , SL0 = 0
SLt = MACDt + 1 −
k
k
Taking the difference between the MACD and the signal line we obtain the
MACD-Histogram (MACDH) indicator, which highlights variations in the
spread between the fast and the slow lines
MACDHt = MACDt − SLt
The most popular parameters in the MACD and MACDH computations
are m = 12, n = 26, k = 9.
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MACD - signal line crossover
The chart above shows IBM with its 12-day EMA (green), 26-day EMA
(red) and the 12,26,9 MACD in the indicator window. There were eight
signal line crossovers in six months: four up and four down.
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MACD - center line crossover
The chart above shows Pulte Homes (PHM) with at least four centerline
crosses in nine months. The resulting signals worked well because strong
trends emerged with these centerline crossovers.
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MACD - center line crossover
Above is a chart of Cummins Inc (CMI) with seven centerline crossovers in
five months. In contrast to Pulte Homes, these signals would have resulted
in numerous whipsaws because strong trends did not materialize after the
crossovers.
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MACD - center line crossover
This chart shows 3M (MMM) with a bullish centerline crossover in late
March 2009 and a bearish centerline crossover in early February 2010.
This signal lasted 10 months. In other words, the 12-day EMA was above
the 26-day EMA for 10 months. This was one strong trend.
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MACD - Divergences
The MACD turned up with a bullish divergence with a signal line crossover
in early December. Google confirmed a reversal with resistance breakout.
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MACD - Divergences
Above we see Gamestop (GME) with a large bearish divergence from
August to October. On the price chart, notice how broken support turned
into resistance on the throwback bounce in November (red dotted line).
This throwback provided a second chance to sell or sell short.
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MACD - Divergences
This chart shows the S&P 500 ETF (SPY) with four bearish divergences
from August to November 2009. Despite less upside momentum, the ETF
continued higher because the uptrend was strong. Its MACD (momentum)
may have been less positive (strong) as the advance extended, but it was
still largely positive.
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MACD - Conclusions
Brings together momentum and trend in one indicator
Chartists looking for more sensitivity may try a shorter short-term
moving average and a longer long-term moving average.
MACD(5,35,5) is more sensitive than MACD(12,26,9) and might be
better suited for weekly charts.
The MACD is not particularly good for identifying overbought and
oversold levels. MACD does not have any upper or lower limits to
bind its movement.
MACD Line is calculated using the actual difference between two
moving averages. This means MACD values are dependent on the
price of the underlying security. The MACD values for a $20 stocks
may range from -1.5 to 1.5, while the MACD values for a $100 may
range from -10 to +10.
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Stochastic Oscillator
Developed by George C. Lane in the late 1950s, the Stochastic Oscillator
is a momentum indicator that shows the location of the close relative to
the high-low range over a set number of periods.
According to an interview with Lane, the Stochastic Oscillator ”doesn’t
follow price, it doesn’t follow volume or anything like that. It follows the
speed or the momentum of price. As a rule, the momentum changes
direction before price.” As such, bullish and bearish divergences in the
Stochastic Oscillator can be used to foreshadow reversals. This was the
first, and most important, signal that Lane identified. Lane also used this
oscillator to identify bull and bear set-ups to anticipate a future reversal.
Because the Stochastic Oscillator is range bound, is also useful for
identifying overbought and oversold levels.
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Stochastic Oscillator: Calculation
%K=(Current Close-Lowest Low)/(Highest High-Lowest Low)*100
%D = 3-day SMA of %K
Lowest Low = lowest low for the look-back period
Highest High = highest high for the look-back period
%K is multiplied by 100 to move the decimal point two places
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Stochastic Oscillator: Three types
Fast Stochastic Oscillator:
Fast %K = %K basic calculation
Fast %D = 3-period SMA of Fast %K
Slow Stochastic Oscillator:
Slow %K = Fast %K smoothed with 3-period SMA
Slow %D = 3-period SMA of Slow %K
The Full Stochastic Oscillator is a fully customizable version of the
Slow Stochastic Oscillator. Users can set the look-back period, the
number of periods to slow %K and the number of periods for the %D
moving average.
The default parameters: Fast Stochastic Oscillator (14,3), Slow Stochastic
Oscillator (14,3) and Full Stochastic Oscillator (14,3,3).
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Stochastic Oscuallator: Three types
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Stochastic Oscuallator: Overbought/Oversold
Yahoo! (YHOO) with the Full Stochastic Oscillator (20,5,5).
A longer look-back period (20 days versus 14) and longer moving averages
for smoothing (5 versus 3) produce a less sensitive oscillator with fewer
signals.
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Stochastic Oscuallator: Overbought/Oversold with
adjustments
Crown Castle (CCI) with the Full Stochastic Oscillator (20,5,5).
Overbought readings were ignored because the bigger trend was up.
Trading in the direction of the bigger trend improves the odds.
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Stochastic Oscuallator: Overbought/Oversold
It is sometimes necessary to increase sensitivity to generate signals.
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Stochastic Oscuallator: Divergences
International Gaming Tech (IGT) with a bullish divergence in
February-March 2010
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Stochastic Oscuallator: Divergences
Kohls (KSS) with a bearish divergence in April 2010
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Stochastic Oscuallator: Bull Bears Set-up
Network Appliance (NTAP) with a bull set-up in June 2009
A set-up is not a signal. The set-up foreshadows a tradable low in the near
future. NTAP declined below its June low and the Stochastic Oscillator
moved below 20 to become oversold. Traders could have acted when the
Stochastic Oscillator moved above its signal line, above 20 or above 50.
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Stochastic Oscuallator: Bull Bears Set-up
Motorola (MOT) with a bear set-up in November 2009
Notice that the Stochastic Oscillator did not make it back above 80 and
turned down below its signal line in mid December.
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RSI
Developed J. Welles Wilder, the Relative Strength Index (RSI) is a
momentum oscillator that measures the speed and change of price
movements.
RSI oscillates between zero and 100.
Traditionally, and according to Wilder, RSI is considered overbought
when above 70 and oversold when below 30.
Signals can also be generated by looking for divergences, failure
swings and centerline crossovers. RSI can also be used to identify the
general trend.
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RSI: Calculations
RSI = 100 −
100
1 + RS
RS = Average Gain/Average Loss
The very first calculations for average gain and average loss are simple 14
period averages.
First Average Gain = Sum of Gains over the past 14 periods / 14.
First Average Loss = Sum of Losses over the past 14 periods / 14
The second, and subsequent, calculations are based on the prior averages
and the current gain loss:
Average Gain = [(previous Average Gain) x 13 + current Gain] / 14.
Average Loss = [(previous Average Loss) x 13 + current Loss] / 14.
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Algorithm Designs
Before optimizing or improving your trading strategies using quantitative
methods, you need to first translate your trading ideas into clear
algorithms ready to be implemented.
The algorithm can be simple or complicated depending on your trading
ideas.
A simple example:
current time t.
If positiont−1 ≥ 0 and RSIt−1 > 70 and RSIt < 70, then close buying
positions and short sell 1 more share.
If positiont−1 ≤ 0 and RSIt−1 < 30 and RSIt > 30, then close
shorting positions and buy 1 more share
t = t + 1.
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Another example: range-breakthrough
Trading idea: after price process stays quietly in a very narrow range for a
significant period of time, the price break out the range in one direction
with strong motivation. Then we expect the price continue to follow this
direction and build up a trend. Things to think about for algorithm design:
How to define ”narrow”?
What is ”a significant period of time”?
What is ”strong motivation”?
When to close the position?
How to set up stop-loss?
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Range-breakthrough example: paramerization
To solve those questions above, we can introduce some parameters whose
values can be determined by users or after doing back testing on historical
data.
Illustrations:
Narrow parameter: range width W
Period of time: at least N days
Strong motivation: Price closing above or below the range for more
than the amount X .
Conditions to realize your profits: for long positions, once
Closet < Closet−1 and Closet−1 < Closet−2 . For short positions, vice
verse.
Stop-Loss parameter: Stop positions once the floating P&L is below
Y dollars.
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Range-breakthrough example: Algorithm
range = False
If High(N) − Low (N) ≤ W , then range = True and UB = High(N),
LB = Low (N).
If Positiont == 0 and range = True and Closet − UB > X , then buy
1 share at market and set range = False.
If Positiont == 0 and range = True and LB − Closet > X , then
short 1 share at market and set range = False.
If profits < Y then close current positions.
If Positiont > 0 and Closet < Closet−1 and Closet−1 < Closet−2 , sell
to cover.
If Positiont < 0 and Closet > Closet−1 and Closet−1 > Closet−2 , buy
to cover.
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Algorithm Implementations
After designing the algorithms, the next step is to implement the
algorithm with a specific programming language. Popular choices are:
Excel VBA, C++, Matlab, or some platform-based language, such as
Meta Trader 4 (5), TradeStation, etc.
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Meta Trader 4
Register and download the software for free:
http://www.metatrader4.com/
Programming Language: MQL4 or MQL5
http://www.mql4.com/
MQL4 Documentation and reference
Back test: Ctrl + R
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Optimize trading strategies
Once you implement the trading algorithms with a programming language,
you are able to run the algorithm over historical data to evaluate its quality.
In most cases, the results of your trading algorithm without optimization
might look not very exciting. But do not just think that your trading idea
does bot work out and throw it away.
The problems might come from inappropriate set-up of parameter values,
or related to the trading product you use, or the inappropriate time period
you use when testing.
And most of the issues above (and much more than that) can be solved by
optimizing your strategy.
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Steps to optimize trading strategies
Do back-testing and optimize important parameters.
Pay attention to the situations of Maximum Drawdown and
Maximum Consecutive Loss. Add some filter steps to avoid those
extremely bad situations.
Back test your algorithm on different time periods, to evaluate its
stability and finally settle down parameter values.
Do forward-testing of the optimized algorithm for a significant period
of time before you put your real money on it.
After you formally take use of the algorithm with real money, you still
need to evaluate the algorithm with the new coming data from time
to time to check if the market situations change greatly or not.
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Important things to remember
The time period you use should be long enough to guarantee the
statistical significance of your testing results. But keep in mind that
newer data should have higher importance.
Do not just maximize your balance. There are still many other
important factors in evaluating trading strategies, such as:
Balance
Maximum Drawdown
Consecutive maximum loss
percentage of wins
Sharp ratio, percentage of maximum profits over total profits
Margin level required
Try your algorithm on similar products, on different time periods.
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Back-testing example illustration with MetaTrade 4:
Moving Average trading system
The trading idea of the MA system to be tested is very simple: open
positions when price crossover with the MA line of a given period N. And
close positions when price crossovers the MA of another period M.
You can download this trading strategy online from the link below:
http://articles.mql4.com/download/11538
There are many other well-designed trading strategy you may download
from the MQL4 community. Some of them are very good candidates after
some slight adjustments. You can try to evaluate and improve those
strategies by yourself!
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MA strategy example - cont.
After running the algorithm, the results look very disappointing. As shown
in the graph above, we keep losing money, consistently..
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MA strategy example - cont
Now let’s see how optimization can make bad things good.
As shown above, we set up the parameter optimization ranges based on
the underlying product we test on, i.e. the EURUSD 1 hour data.
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MA strategy example - cont
From the optimization results, we choose the one that performs the best
considering both profits and maximum drawdown as shown above. Note
that the total number of trades is also relatively large, which gives us more
confidence from the statistical sense.
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MA strategy example -cont
The parameter values corresponding to the optimal case are as below:
Stop Loss = 1290
Take Profit = 370
MA open period = 13
MA close period = 40
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MA strategy example - cont
Now we use the optimized parameter values as input and run the
algorithm again.
As shown above, now the algorithm turns out to be a very good one.
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MA strategy example - cont
Further look into the statistical details of the trading algorithm, we find
that this algorithm looks pretty good in all kinds of perspectives.
And you can even further improve this trading strategy by looking at on
price chart the trade which realized the consecutive maximum loss. And
you notice that it is because the algorithm keeps sending short sell orders
several times in an uptrend market. Then you can try to avoid this
problem by adding a filter. For example, use a smoother MA line as a filter
line and do not go short while price is above this MA line.
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Forward test can be totally different
After this simple example, you might think that designing trading strategy
is very easy given that such a simple MA system can turn out to be so
good. But before being too optimistic, let me remind you several things:
Past performance can not GUARANTEE future results!
Try your optimized algorithm on a different time period to see if it
still works well.
Back testing ignored the execution time delay, transaction fees,
potential market liquidity issue and many other factors that can
matter a lot in real-time trading.
So use your optimized algorithm to do a forward-testing for a
significant period of time before putting money on it.
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More accurate tools
Technical analysis has already been well-known in the market.
Meanwhile, opportunities left using simple technical tools to make
money become fewer and fewer.
You can use what you learn in your MATH courses or STAT courses
to design more accurate trading algorithms.
Brain storm:
Moving average is just a simple time-series model. Then why not use
other time series models?
Stochastic Oscillator or RSI tries to measure the volatility of price
process, then why not use better model to estimator volatility more
accurately?
While trying to improve the probability of winning in your algorithms,
have you ever thought about using probability distributions of all kinds
of random events in the market? What you need is just an event with
high probability.
Why always analyzing one asset price process? How about create a
new (swap) process by combining several asset prices together?
Can we design some indicators representing fundamental factors?
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What is Statistical Arbitrage?
In academic literature, ”statistical arbitrage” is opposed to
(deterministic) arbitrage. In deterministic arbitrage, a sure profit can
be obtained from being long some securities and short others. In
statistical arbitrage, there is a statistical mispricing of one or more
assets based on the expected value of these assets. In other words,
statistical arbitrage conjectures statistical mispricings of price
relationships that are true in expectation, in the long run when
repeating a trading strategy.
Among those who follow the hedge fund industry, ”statistical
arbitrage” refers to a particular category of hedge funds (other
categories include global macro, convertible arbitrage, and so on). In
this narrower sense, statistical arbitrage is often abbreviated as Stat
Arb or StatArb. According to Andrew Lo, StatArb ”refers to highly
technical short-term mean-reversion strategies involving large
numbers of securities, very short holding periods (measured in days to
seconds), and substantial computational, trading, and information
technology infrastructure”.
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Main types of StatArb
Mean-reverting
Pair trading (long & short; cointegration; Equity risk-neutral)
Volatility trading/arbitrage
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StatArb: Improvements of technical analysis
Many statistical arbitrage strategies can be considered as improvements on
technical analysis based strategies:
StatArb says that it’s better to do mean-reverting strategies on a
stationary process (go and read your time series textbook about the
definition of stationarity)
StatArb says that volatility process is stochastic which can be
modeled pretty well with a nonlinear time series model (such as
GARCH).
StatArb says that modeling of some stochastic quantity is the first
step to generate trading ideas.
StatArb says that you should take use of the statistics you learn to do
everything instead of thinking naively. For example: what does
”significant” mean in statistics? Why not use cross-validation when
doing back-testing?
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Two homework assignments for you
Combine the S&P 500 index future and the Gold future into a
stationary process; verify the process you designed is stationary; then
use mean-reverting idea to design trading strategies (you can
calculate RSI on the stationary process to generate mean-reverting
trading signals; or you can design a new tool to measure the price
deviation from the mean); optimize your trading strategy by
back-testing (use cross-validation)
Use USDJPY hourly data from 2010 - 2013 to estimator weekly
realized volatility series; fit a time-series model on the volatility series;
generate trading ideas based on the time series model predictions;
optimize your trading strategy by back-testing (use cross-validation)
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Conclusion
Investing your time and efforts is more important than investing your
money!
Thank you!
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