量化全流程：配对策略的python回测
这篇文章包括了从对原始数据处理、数据检验、代码实现的一系列详细步骤，如果你没有量化交易的经验，这篇文章是一个很好的开始。
配对策略属于均值回归策略的一种，主要从两只股票的价差来盈利。这个策略在市场上存在已久，但时至今日依然奏效。
第一个使用这个策略的人是利弗莫尔，对就是《股票大作手回忆录》的主人公，他用肉眼观察同类资产的表现。
在进入这个策略之前，需要区分两个统计学概念：相关性和协整性。
相关性 Correlation：
- 相关系数(ρ)衡量变量之间线性关系的程度（注意是线性 我会通篇强调）：p=-1为完全线性负相关，p=0说明两者没有线性相关，p=1为完全线性正相关
- p=0仅仅说明俩变量间没有线性关系，不一定完全没有关系。
- 用价格还是收益率来度量资产之间的相关性呢？经验表明短期用收益率度量，长期用价格度量。
协整性 Cointegration：
- 书上这么解释：两个金融时间序列之间的比率将围绕一个恒定的均值变化。
- 书上的定义说的很绕，我给你讲：股票价格和债券价格，他们的比值倾向于收敛一个数值，这两者就有高度协整性。
- 这个恒定的数值就是配对策略的出发点，我们假设不管市场如何扰动，这个数值都会回到长期均值。
配对策略：
两只股票具有高度协整关系，那么他们的价差长期来看会比较稳定，但稳定性会因为投资者“追涨杀跌”等等的不理性交易而打破，导致价差扩大。
配对交易就从这个价差切入，分别在两只股票上建立多头和空头头寸，卖空相对高估的股票，买入相对低估的股票，等待价差收敛。
配对交易同时双向建仓，对冲掉了绝大部分市场风险，因此属于市场中性策略。
开搞：
资产选择：澳大利亚ETF（EWA）和加拿大ETF（EWC）。
先来看看他俩价格之间的相关性，一眼看上去高度相关：
用代码测试一下：
import numpy as np
np.corrcoef(Asset_1, Asset2)
输出结果是0.85，验证了高度正相关的猜想。
再来看看这两组数据的比值是否平稳，如果数据随着时间变化，有趋势性和季节性，那么数据就不平稳，对于不平稳的数据，发现其中规律就无从谈起了。
对两组数据的比值进行平稳性检验：
def stationarity(ratio, cutoff = 0.05):
Data[:, 2] = Asset_2 / Asset_1
Ratio = Data[:, 2]
a = np.ravel(ratio)
if adfuller(a)[1] < cutoff:
print(‘The series is stationary’)
print(‘p-value = ‘, adfuller(a)[1])
p-value=0.032，数据平稳。
下一步检查他们的协整性，高度协整性意味着均值回归，是执行配对策略的基础。
def cointegration(a, b):
if coint(a, b)[1] < 0.05:
print(‘The series are cointegrated’)
print(‘p-value = ‘, coint(a, b)[1])
else:
print(‘The series are NOT cointegrated’)
print(‘p-value = ‘, coint(a, b)[1])
cointegration(Asset_1, Asset_2)
协整性的p-value为0.048，说明数据高度协整，存在均值回归性质。
现在对数据的比值进行标准化处理：
for i in range(len(Data)):
try:
Data[i, 3] = (Data[i — lookback:i + 1, 2].mean())
except IndexError:
pass
# 计算标准差
for i in range(len(Data)):
Data[i, 4] = ((Data[i — lookback:i + 1, 2].std()))
# 标准化
for i in range(len(Data)):
Data[i, 5] = (Data[i, 2] — Data[i, 3]) / Data[i, 4]
然后开始回测，回测的时间为过去9年的历史行情，策略代码如下：
for i in range(len(Data)):
try:
if Data[i, 2] <= lower_barrier and Data[i — 1, 2] > lower_barrier:
Data[i + 1, 4] = -1
Data[i + 1, 5] = 1
elif Data[i, 2] >= upper_barrier and Data[i — 1, 2] < upper_barrier:
Data[i + 1, 6] = 1
Data[i + 1, 7] = -1
else:
continue
except IndexError:
pass
for i in range(len(Data)):
try:
if Data[i, 5] == 1:
Data[i + holding_period, 8] = (Data[i + holding_period, 1] — Data[i, 1])
if Data[i, 6] == 1:
Data[i + holding_period, 8] = (Data[i + holding_period, 0] — Data[i, 0])
if Data[i, 4] == -1:
Data[i + holding_period, 9] = (Data[i, 0] — Data[i + holding_period, 0])
if Data[i, 7] == -1:
Data[i + holding_period, 9] = (Data[i, 1] — Data[i + holding_period, 1])
except IndexError:
pass
回测结果：
- 总交易次数：161次
- 年化回报率：21%
- 胜率：55.9%
注意，这个策略没有把手续费和其他交易成本（比如冲击成本）考虑在内，也没有加杠杆。
最后总结一下配对策略的实现过程：
- 找到两组逻辑上相关的资产，观察一下他们的收益率或者价格曲线，对直觉上相关的两组资产进行相关性检验。
- 如果两组资产接近正相关，下一步进行价格比值或收益率比值的平稳性检验
- 平稳性满足后，进行协整性检验。
- 如果数据高度协整，就可以进行数据回测了。
这个策略在数据预处理阶段的三个概念：相关性，协整性，平稳性，在后面的策略中会是常客：
- 相关性：两个变量线性相关程度
- 协整性：两个变量的比值，是不是围绕某个定值波动
- 平稳性：不随时间变化的数据
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One downside is that resistance bands are not the type of health club equipment you should use for the the rest of your life.
At least each few years you’ll need to exchange the
final set with new resistance bands to construct muscle.
They can be utilized for a selection of workout routines, together with options that
may serve as an various to both the cardio and resistance training rowing machine.
The face pull helps goal your trapezius muscular
tissues, upper lats, and rhomboids. This is also an excellent
exercise that will help you obtain and keep an upright posture.
Incorporating a big selection of various workout routines with the normal T-Bar Row not only adds variety to
your exercise routine but additionally
ensures a complete development of your back muscular tissues.
When performing any rowing movement it’s necessary to maintain a neutral head and backbone to prevent
injury.
The TRX row is much like the inverted row in that it has you pull
your body against gravity. It also recruits the body’s stabilizer
muscles to maintain the body secure and safe. Bent-over rows are
a horizontal pulling exercise, and when you COULD do things like pull-ups and pulldowns as a substitute, these are vertical pulling workout routines, so they aren’t the best alternate options.
Glutes and hamstrings – while barbell bent-over rows are an upper body
train, your legs get in on the motion too. Working with your
erector spinae, your glutes and hamstrings must work to hold you in that all-important
bent-over row place. To improve the range of motion and effectiveness
of this motion, use smaller sized weight plates on the bar.
Browse above via every train to get all the small print – muscle tissue labored, how to
do these workout routines, equipment wanted – the complete lot.
A widespread mistake is letting your shoulders go limp and
your body fall backward in the descent. In general, there are a couple
of major bent-over row alternative classifications. For instance, basic alternate
options include the dumbbell row or inverted row.
Rear Delt row is a really efficient and practical exercise for constructing muscle and energy in the rear
deltoids and higher back. The barbell row is a free weight exercise that works all of the back muscular tissues equally, this
makes it a great different to the t-bar row. The reason why
that is such a great t-bar row various is you could regulate the issue by altering your body position relative to the handles.
The closer you are to the ground, the tougher this train turns
into. Secondary to the muscles of the again, this motion will target the biceps as nicely.
Although they don’t generate the facility or size of standard weights, they’re an excellent
addition to any again routine, and can assist you to appropriate
your form, and humility, very quickly. The seal row has emerged as a
preferred variation of the row that can function a near good substitute to
the cable row. You carry out this mendacity face down on a bench, which takes virtually all the
tension off the decrease back, and maximizes rigidity on the upper back, significantly
the traps and rear delts. The dumbbell row is a
nice way to isolate all sides of the back while also keeping the load
heavy. The dumbbell single arm row is an isolateral movement, that means you’ll
be able to control the vary of motion and pressure on either side.
As well as working your rear delts, face pulls additionally work your middle
trapezius and rhomboids. These muscles normally work together and are important for each posture and shoulder well being.
The resistance band row is a workout that doesn’t require
traditional weights but delivers efficient results whether you’re at the health club or within the comfort of your own home.
Like the T-bar row, the landmine row employs a set anchor level for one end of the barbell whereas allowing you
to row the opposite end toward your torso, delivering a
sturdy upper-body exercise.
Not only does that enhance your danger for
injury, but it’s additionally not advantageous for hypertrophy.
Having your chest supported by the bench allows you
to target the again with out involving the core and erectors and makes it a lot harder to cheat the motion. If you
wrestle with feeling your again working during a row, strive an incline dumbbell row to see should you can create
a greater mind-muscle connection. The single-arm dumbbell row could be performed
by standing together with your arm supported against a bench or dumbbell rack.
The farther you pull the dumbbell back in direction of your hip, the extra you’ll hit
your lat.
There is nothing mistaken with this, however,
for variety, it’s typically helpful to train one side at a time –
a unilateral train. While this is extra of a variation than another, it’s
still a legitimate train. That mentioned, if you are capable of do pull-ups or chin-ups, they’re each nice lat pulldown alternative workout routines.
The Smith machine row is an excellent variation to make use of rather
than the barbell row because the Smith machine offers additional stability that may permit
you to lift heavier. You can range the incline of the bench and your grip to target the
muscle tissue in your back from different angles. Lowering
the incline and tucking the elbows in will emphasize your lats.
Sitting more upright and allowing the elbows to flare will target the higher back.
This video provides a useful visual information for performing single-arm
bent-over dumbbell rows. This could be a more challenging variation,
as you have to balance the burden with your physique.
Cable machine workouts are also much less intimidating and
safer for beginners or those managing an injury. Incorporate quite lots of workouts such
as the seated cable row, inverted row, chest supported machine row, or T-bar row to maintain up diversity and problem in your exercise routine.
Using a chest supported row equipment specifically targets essential muscle groups such because the latissimus dorsi and rhomboids, minimizing any
stress on the spinal column. This culminates in not solely an environment friendly but in addition a extra
comfortable workout session concentrating on your
again.
This exercise locations you in a hip-hinged place akin to a deadlift,
effectively cultivating energy, control, and endurance
all through your legs. It is often performed for average to excessive reps, at least 8–12 reps per set, as part of an upper-body or shoulder-focused exercise.
The cable rear delt row will become more of a regular wide-grip cable
row. The meadows row is a single arm landmine row that can easily
exchange the t-bar row by permitting you to create a higher
stretch on the bottom of the motion. If you wish to goal your lats extra, you can set the incline
to a decrease angle whereas tucking your elbows through
the row. If you need to goal your upper back more, you probably can set a better incline whereas
flaring your elbows out in the course of the row.
Keep your back flat and have interaction your core as you hinge at the hips and slightly bend your knees.
From this beginning position, pull the barbell in path of your
chest, squeezing your shoulder blades collectively on the prime of the motion. Decrease the barbell again to the beginning position and repeat for
the desired number of repetitions. Chest-supported
machine rows are an excellent various to the bent-over row, offering
help for the chest and decreasing strain on the decrease again while effectively focusing on the again muscles.
It permits you to emphasize the upper again whereas relieving rigidity on the lower back,
a typical draw back to many barbell back exercises. Generally speaking, seated cable
rows provide a higher range of motion than bars or
dumbbells. Most rowing workouts need some gear to add resistance and make the movement
most effective. Some rowing workouts use minimal gear, just like the inverted body weight row.
It includes as a lot as 60% more muscle activation within the lats than the standard row, making it higher
for again growth. It also places much less strain on the lower back, as you don’t have to assist the
weight of the bar. The chest-supported machine row is a machine-based
train the place the chest is supported on a padded surface — providing great assist to the
core and backbone. The bent-over row is an iconic back
exercise with a proven track document of including energy and
thickness to the again.
Lifters also want good hamstring mobility, grip power, and technical capability to do the bent-over barbell row safely and successfully.
Lifters could seek an alternative exercise to barbell rows if they’re managing an injury, working on their hamstring mobility, have
poor grip energy, or don’t have access to a barbell.
Renegade rows are a full-body strengthener and a great various to barbell rows.
You can wrap a towel on all sides of the bar to make the grip mimic extra of a rope.
This lets you target the again muscular tissues to a greater
degree by increasing range of movement throughout.
Also, this train may be done with a snatch grip (wide grip) to
get larger vary of movement and target the higher muscles
of the back. For the needs of this text I favor the dumbbells because it can be carried out via larger vary of movement to advertise
complete back muscle activation. Too much extreme ahead
lean can put pointless strain in your decrease back.
Subsequent time you do chest supported rows, after your final set, wait 60 seconds, bring the
bench flat, drop the load 20%, after which carry out as many reps as you can of half rep
chest supported rows. Switching back to the one arm dumbbell row variations, this exercise will improve the range of motion that you’ll
have to go through on each row. Very easy on your
decrease back – in relation to lat workouts,
there are two primary motion patterns; horizontal pulls (rows) and vertical
pulls (pull-ups and pulldowns). A lot of rowing exercises involve leaning forward at the waist, which
may put lots of stress in your lower again.
If you could have access to a T-Bar Row machine, T-Bar Rows would possibly actually
be the closest various to the Barbell Row out of any of the Barbell Row
alternatives listed above. You’ll end up in the same physique place
however most machines (but not all) may also provide chest
help. Inverted Rows are top-of-the-line, and most ignored,
horizontal rows you can do in the weight room. They
place zero stress on the low again and can be modified to be good for
each newbies and challenging for superior lifters. A common mistake is rotating your shoulder again on the carry, but doing that can cause
shoulder ache and prevent you from getting the
most out of the train. For those who liked the bent-over row from the underside of their
hear and don’t need to exchange it — an incline barbell row may be
the closest alternative.
If you’re looking to add selection to your back workout
routine or if the bent-over row is inflicting discomfort or pressure in your lower again, contemplate incorporating incline
dumbbell rows. This train presents an effective various that targets the
higher back muscles, promotes overall back growth, and reduces the danger of harm.
Remember to all the time begin with a correct warm-up and consult with a fitness professional in case you
have any issues or questions. Maximize your workout routine with chest-supported dumbbell rows, a dynamic train that effectively targets your again muscle tissue.
As a personal trainer, I’ve educated dozens of individuals of their house gyms.
Pairing one arm dumbbell row options with vertical
pull movements, corresponding to pulldowns or pull-ups will make for an effective back exercise.
Many powerlifters and cross-fitters are in search of barbell row alternatives, because the
barbell row may be robust on your lower again if not accomplished correctly.
I Am going to provide you with the 9 greatest barbell row
various workout routines that I hit each time I feel like
changing my again and core workout. The pendlay row is a superb
t-bar row different for powerlifters because it targets the
precise reverse muscles of the bench press, which allows for greater stability when performing heavy presses.
Some lifters expertise decrease back pain when doing conventional bent-over rows.
This model provides one of the best decrease again help whereas additionally
permitting for a horizontal row via the full vary of motion. The
resistance band seated row uses an inexpensive loop resistance band to simulate a seated cable row.
With a band, the exercise gets harder as you pull, providing the most intense effect at full contraction. Rack pulls are a deadlift variation where you raise the
bar from the pins of an influence rack. Starting with the bar off the floor means much
less low back stress and never a lot lower physique work.
Deadlifts won’t look so much like bent-over rows, however they work nearly all of the similar muscle
tissue.
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It could be equivalent to what you see with Trenbolone, however the vascularity stays with you long
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Anavar is thought for its mild nature and low threat of side effects,
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While usually thought-about one of the milder anabolic steroids,
Anavar can nonetheless carry some risks if not used responsibly.
Anavar is generally well-tolerated and considered one of
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those seeking to make lean gains with out intense water retention or other harsh results.
As at all times, consulting a medical professional is advisable before using any anabolic substance.
The appropriate time to start PCT is after three or four days at the final injection of Trenbolone.
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Monitoring liver function, lipid profiles, and hormone levels may help determine any potential points
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Very superior customers are known to use excessive doses of
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When testosterone is converted to DHT and DHT ranges rise
an extreme amount of, it could possibly have an result on the hair follicles and regular hair
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In Distinction To males, ladies don’t need to do PCT, so there’s nothing else
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At All Times seek the guidance of a healthcare skilled earlier than beginning any new
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This depends on what your purpose is for using it
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there are not any apparent damaging results on the liver
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Deca may be the least poisonous steroid cycle.
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ability to survive the “first pass” of liver metabolism and permitting it to be ingested effectively.
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Los primeros efectos, un aumento grande y repentino de la masa muscular, aparecen 2 semanas después de comenzar
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Garantizamos el éxito de la entrega en España o en cualquier parte del mundo.
Pero vale la pena considerar que para comprar esteroides en España,
se requiere el pago completo antes de que se envíen los
pedidos. Si estás buscando esteroides anabólicos en España, Pharmax-es.com es la mejor
opción para adquirir productos de calidad y efectividad comprobada.
En nuestra tienda en línea, encontrarás una amplia variedad de esteroides que se adaptan a tus necesidades específicas, ya sea para mejorar tu rendimiento deportivo, aumentar la masa muscular o recuperarte de una lesión. Comprar esteroides en España nunca ha sido tan fácil y seguro como lo es ahora gracias a nuestra plataforma, que te garantiza productos auténticos y un proceso de compra sencillo y discreto.
En el culturismo, levantamiento de pesas, crossfit y otras disciplinas de fuerza, muchos atletas utilizan esteroides anabolizantes.
Esta es una solución probada que proporciona un rápido
crecimiento en el rendimiento físico.
Puedes pagar los esteroides anabólicos comprados en nuestra tienda mediante transferencia bancaria o Bitcoin. Top Sitio web seguro donde
comprar Anabolic Steroids On-line barato. Ofrecemos entrega
garantizada a toda Europa (incluyendo Reino Unido) y EE.UU..
Esteroides.to lleva las mejores farmacias de esteroides en el mercado – Alpha Pharma,
Unigen, British Dragon, LA Pharma, Organon. Esteroides
reales, legítimos y auténticos del mundo #1 laboratorios (Tailandia, Europa).
Aunque comprar esteroides anabólicos está prohibido en muchos países, en España no es ilegal siempre
y cuando se haga con receta médica. Hay varios proveedores de
Winstrol en España, tanto en línea como en tiendas físicas.
No pierdas la oportunidad de mejorar tu rendimiento físico con los esteroides anabólicos
de Pharmax-es.com. Con nuestra entrega rápida en España, recibirás tus productos en poco tiempo,
listos para ayudarte a alcanzar nuevas metas en tu entrenamiento
y desarrollo muscular. El culturismo es una disciplina que requiere dedicación, esfuerzo y, en muchos
casos, el uso de suplementos y esteroides anabólicos para
maximizar los resultados.
Alternativas de esteroides one hundred pc naturales, seguros y legales de Dianabol, Clenbuterol, HGH,
Anavar, Trembolona y más. No, Winstrol es una sustancia controlada en España y sólo puede ser adquirido con receta
médica. La venta ilegal de esteroides puede ser peligrosa y está penada por la ley.
Recuerda siempre consultar con un profesional de la salud antes de utilizar
cualquier tipo de esteroide anabólico y seguir las dosis recomendadas para evitar riesgos en la salud.
El precio de Winstrol en España puede variar según el proveedor
y la presentación del producto. Es importante investigar y comparar precios
antes de realizar tu compra para obtener la mejor opción de acuerdo a tus necesidades y presupuesto.
“Hay un montón de páginas net o puedes adquirirlos por Instagram.
De esta manera, puedes obtener los esteroides que necesitas sin comprometer tu presupuesto. Comprar esteroides en nuestra tienda online no solo es una opción económica, sino también segura, gracias a nuestro compromiso con la calidad y la satisfacción del cliente. Algunos físicoculturistas y atletas usan esteroides anabólicos para desarrollar músculos y mejorar el rendimiento deportivo. Pueden tomar los esteroides por vía oral, inyectarlos en los músculos o aplicar un gel o crema en la piel.
References:
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