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479The underlying strategy is designed to capture short-term trends in the SPY ETF. It posts aSharpe Ratio of 0.37, which means it is taking on a substantial amount of volatility in order togenerate the returns. In fact the benchmark has an almost identical Sharpe ratio. The maximumdaily drawdown is slightly larger than the benchmark, but it produces a slight increase in CAGRat 6.41% compared to 5.62%.In essence the strategy performs about as well as the buy-and-hold benchmark. This is tobe expected given how it behaves. It is a lagged filter and, despite making 41 trades, does notnecessarily avoid the large downward moves. The major question is whether a regime filter willimprove the strategy or not.31.5.3 HMM Regime Detection FilterFigure 31.3 displays the tearsheet for the "with HMM filter" strategy.Note that this application of the regime filter is out-of-sample. That is, no returns dataused within the backtest were used in the training of the Hidden Markov Model.The regime detection filter strategy produces rather different results. Most notably it reducesthe strategy maximum daily drawdown to approximately 24% compared to that produced bythe benchmark of approximately 56%. This is a big reduction in "risk". However the Sharperatio does not increase too heavily at 0.48 because the strategy still endures a lot of associatedvolatility to obtain those returns.The CAGR does not see a vast improvement at 6.88% compared to 6.41% of the previousstrategy but its risk has been reduced somewhat.Perhaps a more subtle issue is that the number of trades has been reduced from 41 to 31.While the trades eliminated were large downward moves (and thus beneficial) it does mean thatthe strategy is making less "positively expected bets" and so has less statistical validity.In addition the strategy did not trade at all from early 2008 to mid 2009. Thus the strategyeffectively remained in drawdown from the previous high watermark through this period. Themajor benefit, of course, is that it did not lose money when many others would have!A production implementation of such a strategy would likely periodically retrain the HiddenMarkov Model as the estimated state transition probabilities are very unlikely to be stationary.In essence, the HMM can only predict state transitions based on previous returns distributionsit has seen. If the distribution changes (i.e. due to some new regulatory environment) then themodel will need to be retrained to capture its behaviour. The rate at which this needs to becarried out is, of course, the subject of potential future research!31.6 Full Code# regime_hmm_train.pyfrom __future__ import print_functionimport datetimeimport pickleimport warnings
480Figure 31.3: Trend Following Regime Detection with HMMfrom hmmlearn.hmm import GaussianHMMfrom matplotlib import cm, pyplot as pltfrom matplotlib.dates import YearLocator, MonthLocatorimport numpy as npimport pandas as pdimport seaborn as snsdef obtain_prices_df(csv_filepath, end_date):"""
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ContentsI Introduction 11 Introduct
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38.2 Correlation . . . . . . . . .
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513.2 The Kalman Filter . . . . . .
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719 Support Vector Machines . . . .
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928 Kalman Filter-Based Pairs Tradi
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Limit of Liability/Disclaimer ofWar
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Part IIntroduction1
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4The aim of this book is to provide
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61.3 How Is The Book Laid Out?The b
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81.5 How Does This Book Differ From
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101.7.1 AlternativesThere are many
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Chapter 2Introduction to Bayesian S
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15Table 2.1: Comparison of Frequent
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172.2 Applying Bayes’ Rule for Ba
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19the next chapter. At this stage,
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21# Create and plot a Beta distribu
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Chapter 3Bayesian Inference of a Bi
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25• The fairness of the coin does
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273.4.3 Multiple Flips of the CoinN
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29x = np.linspace(0, 1, 100)params
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31Hence, all we need to do is re-ar
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33Figure 3.3: The prior and posteri
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Chapter 4Markov Chain Monte CarloIn
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374.2.1 Markov Chain Monte Carlo Al
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39We discussed the fact that we cou
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41Finally we specify the Metropolis
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43we do not need to compute 100,000
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45x, stats.beta.pdf(x, alpha, beta)
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Chapter 5Bayesian Linear Regression
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49non-informative priors.• Poster
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51# Use a linear model (y ~ beta_0
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53# Use the No-U-Turn Samplerstep =
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55plt.show()We can see the sampled
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57"""Calculates the Markov Chain Mo
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Chapter 6Bayesian Stochastic Volati
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61plt.show()Figure 6.1: Different r
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63( )yilog ∼ t(ν, 0, exp(−2s i
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656.3.2 Model Specification in PyMC
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67Figure 6.5: Overlay of samples fr
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69plt.xlabel(’Time’)plt.ylabel(
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Part IIITime Series Analysishttps:/
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74• Seasonal Variation - Many tim
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767.5 How Does This Relate to Other
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78Definition 8.1.1. Expectation. Th
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808.2 CorrelationCorrelation is a d
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82Definition 8.3.4. Stationary in t
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84Figure 8.2: Correlogram plotted i
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868.6 Next StepsNow that we’ve di
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88• Use our knowledge of time ser
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909.3.2 CorrelogramWe can also plot
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929.4.2 CorrelogramThe autocorrelat
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94created the difference series, we
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96there are a few that are marginal
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9810.1 How Will We Proceed?In this
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10010.4.1 RationaleIn the previous
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10210.4.4 Simulations and Correlogr
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104Figure 10.2: Realisation of AR(1
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10610.4.5 Financial DataAmazon Inc.
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108Figure 10.6: Correlogram of Firs
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110> plot(gspcrt)Figure 10.8: First
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112model, as well as the conditiona
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114Figure 10.10: Realisation of MA(
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116Coefficients:ma1 intercept-0.729
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118> require(quantmod)> getSymbols(
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120> amznrt.maCall:arima(x = amznrt
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122Figure 10.16: Residuals of MA(1)
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124Figure 10.18: Residuals of MA(3)
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12610.6.3 RationaleTo date we have
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128Figure 10.20: Correlogram of an
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130Figure 10.22: Correlogram of an
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132Figure 10.23: Correlogram of the
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134Notice that there are some signi
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136I would like to thank you for be
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138Figure 11.1: Plot of simulated A
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140> amzn = diff(log(Cl(AMZN)))As i
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142We fit an ARIMA model by looping
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144being able to create strategy in
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14611.5.2 Why Does This Model Volat
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148ɛ t = σ t w t (11.17)σ 2 t =
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1502.5 % 97.5 %a0 0.1786255 0.21726
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152Figure 11.10: Residuals of an AR
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Figure 11.13: Squared residuals of
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156mean, but due to its stationarit
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158x t = pz t + w x,t (12.1)y t = q
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160Figure 12.3: Plot of x t and y t
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162> layout(1:2)> plot(badcomb, typ
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164We then created two subsequent s
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166Figure 12.6: Backward-adjusted c
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168Coefficients:(Intercept) ewaAdj3
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170> plot(rdsaAdj, rdsbAdj,xlab="RD
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172set.seed(123)## SIMULATED DATA##
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174plot(comb1$residuals, type="l",x
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176> q <- 0.6*z + rnorm(10000)> r <
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178Figure 12.12: Plot of s t , the
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180EWA.Adjusted.l2 EWC.Adjusted.l2
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182library("quantmod")library("tser
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184
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186• Smoothing - Estimating the p
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18813.2.1 A Bayesian ApproachRecall
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190E[y t+1 |D t ] = E[Ft+1θ T t +
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192of our linear regression. The ne
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194Figure 13.1: Scatterplot of the
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196Figure 13.2: Time-varying slope
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198delta = 1e-5trans_cov = delta /
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200
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202"risk manager". They will be use
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204Figure 14.1: Two-state Markov Ch
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206Figure 14.2: Hidden Markov Model
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208> bull_var <- 0.1> bear_mean <-
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210historical financial data.14.3.3
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212The same process will now be car
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214install.packages(’quantmod’)
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216
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Chapter 15Introduction to Machine L
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22115.3.1 Linear RegressionAn eleme
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223While seemingly not a traditiona
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Chapter 16Supervised LearningSuperv
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227ŷ = ˆf(x) = argmax z∈R p(y =
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Chapter 17Linear RegressionIn this
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231if __name__ == "__main__":# Set
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23317.3 Maximum Likelihood Estimati
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235To simplify the notation the lat
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237Once the full dataset is created
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239if __name__ == "__main__":# Set
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241))lr_model.coef_[0]# Create a sc
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Chapter 18Tree-Based MethodsIn this
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245Figure 18.2: The resulting parti
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24718.3 Decision Trees for Classifi
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249In quantitative finance applicat
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251(a) Grow a tree ˆf b with k spl
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253tslag["Lag%s" % str(i+1)] = ts["
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255The same approach is carried out
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257seen whether it is feasible to p
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259amzn = create_lagged_series("AMZ
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Chapter 19Support Vector MachinesIn
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263• Non-Probabilistic - Since th
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265The key point here is that it is
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267classification. Overfitting mean
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269Figure 19.6: Addition of a singl
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27119.8 Support Vector MachinesThe
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273p∑K(x i , x k ) = (1 + x ij x
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Chapter 20Model Selection andCross-
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277This motivates the concept of a
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279Figure 20.1: Various estimates o
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281error for a particular model est
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283Figure 20.3: Amazon, Inc. - Pric
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28520.2.5 Python ImplementationWe a
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287At this stage we have the necess
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289..import pylab as plt....def plo
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291fold = 0# Loop over the k-foldsf
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293Figure 20.5: Test MSE curves for
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295return tsretdef validation_set_p
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297model = Pipeline([("polynomial_f
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299X = lags[["Lag1", "Lag2", "Lag3"
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Chapter 21Unsupervised LearningThe
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303parameters of the model, θ.Conv
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Chapter 22Clustering MethodsIn this
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3072. Iterate the following until c
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309]# Generate a list of the 2D clu
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311clustered using K-Means and then
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313ax.set_axis_bgcolor((1,1,0.9))ax
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315ClusterTomorrow to contain tomor
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317Figure 22.4: 3D scatterplot of n
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319# Apply the K-Means Algorithm fo
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321# up days and red for down daysc
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323sp500["ClusterMatrix"] = list(zi
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Chapter 23Natural Language Processi
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327The Reuters 21578 dataset can be
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329for export as shippers are now e
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331tungtung-oilveg-oilwheatwoolwpiy
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333in order to minimise memory usag
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335’The Tokyo Grain Exchange said
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337for t in d[0]:if t in topics:d_t
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339This would mean that we are givi
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341partitions into the training and
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3430.660194174757[[21 0 0 0 2 3 0 0
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345self.encoding = encodingdef _res
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347"""topics = open("data/all-topic
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Part VQuantitative Trading Techniqu
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352While vectorised backtests are s
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354• Backtest - Encapsulates the
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356The second strategy provides a 3
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35825.4.1 MonthlyLiquidateRebalance
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360"""Size the order to reflect the
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362Figure 25.1: US Equities/Bonds 6
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364five years relative to US equiti
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366# Use the monthly liquidate and
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368import datetimefrom qstrader imp
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37026.2 Strategy ImplementationTo i
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372final.order[1],final.order[3]),
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374> spIntersect = merge( spArimaGa
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376enters what looks to be more a s
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378# Output the CSV file to "foreca
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380
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382natural gas.The hypothesis prese
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384## Carry out linear regression o
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38627.5 Python QSTrader Implementat
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388that arrive out of order in the
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390if self.invested is not None:if
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392take into account commission dif
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394adf.test(comb$residuals, k=1)# c
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396def go_short_units(self):"""Go s
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398from qstrader.trading_session.ba
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400default=’’,help=’Pickle (.
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402Hence we can "long the spread" i
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404class KalmanPairsTradingStrategy
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406if all(self.latest_prices > -1.0
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408It also changes the FixedPositio
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410’--testing/--no-testing’, de
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412• Asset Selection - Choosing a
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414if self.R is not None:self.R = s
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416)self.events_queue.put(SignalEve
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418@click.option(’--testing/--no-
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420• Short-Term Trend - Predict m
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422It takes the CSV file path as an
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424produce a final truth column whe
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426bias-variance trade-off of the m
Page 441 and 442: 428used by the machine learning mod
Page 443 and 444: 430IQFeedIntradayCsvBarPriceHandler
Page 445 and 446: 432’--filename’,default=’’,
Page 447 and 448: Figure 29.2: Tearsheet for Random F
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Page 451 and 452: 438#ts["UpDown"] = down_tot & up_to
Page 453 and 454: 440events_queue - A handle to the s
Page 455 and 456: 442from intraday_ml_strategy import
Page 457 and 458: 444if __name__ == "__main__":main()
Page 459 and 460: 446sentiment.In recent years there
Page 461 and 462: 448Ticker Name Period LinkMSFT Micr
Page 463 and 464: 450self.statistics.update(event.tim
Page 465 and 466: 452if self.end_date is not None:sen
Page 467 and 468: 454a sent_sell corresponding exit t
Page 469 and 470: 456sentiment_handler = SentdexSenti
Page 471 and 472: 458Figure 30.2:volatile, posting mo
Page 473 and 474: 460fication by adding many more sto
Page 475 and 476: 462events_queue = queue.Queue()csv_
Page 477 and 478: 464def main(config, testing, ticker
Page 479 and 480: 466In quantitative trading this pro
Page 481 and 482: 468self.tickers[ticker]["timestamp"
Page 483 and 484: 470df["Adj Close"][mask],".", lines
Page 485 and 486: 472from qstrader.event import (Sign
Page 487 and 488: 474class RegimeHMMRiskManager(Abstr
Page 489 and 490: 476# If in the undesirable regime,
Page 491: 47831.5 Strategy Results31.5.1 Tran
Page 495 and 496: 482ax.grid(True)plt.show()if __name
Page 497 and 498: 484elif short_sma < long_sma and se
Page 499 and 500: 486elif action == "SLD":if self.inv
Page 501 and 502: 488backtest = Backtest(price_handle
Page 503 and 504: 490holding an instrument representi
Page 505 and 506: 492rolling_sharpe_s = np.sqrt(self.
Page 507 and 508: 494In order to use the annualised r
Page 509 and 510: 496Figure 32.2: Aluminum Smelting S
Page 511 and 512: 498
Page 513 and 514: 500[18] Wikipedia: Viterbi algorith
Page 515 and 516: 502[56] Investor, S. Regime detecti
Page 517: 504[92] Sinclair, E. Volatility Tra
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