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457Figure 30.1:is mostly down or flat. In addition it has a large drawdown duration of 318 days during mid-2014 to mid-2015 and a large maximum daily drawdown of 17.23%, compared to 13.04% for thebenchmark.Despite this it does admit a Sharpe ratio of 1.12 compared to 0.75 for the benchmark, but theperformance is not significant enough to justify a full production implementation of the strategy.30.5.3 Sentiment on S&P500 Energy StocksThe base quantity of shares used for each ticker is 5,000.The energy stocks mix performs quite differently to the collection of tech stocks. It is very
458Figure 30.2:volatile, posting months with large gains and other months with large losses. Its maximumdaily drawdown is extensive at 27.49%, which single-handedly eliminates it from any furtherconsideration as a reasonable quantitative strategy. In addition the strategy seems to lose alleffectiveness after mid-2014, when it drops underwater and remains flat through 2015.It has a poor Sharpe ratio at 0.63 compared to the benchmark of 0.75. Hence this is not aviable strategy that would be taken forward in its current form.30.5.4 Sentiment on S&P500 Defence StocksThe base quantity of shares used for each ticker is 2,000.
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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
Page 419 and 420: 406if all(self.latest_prices > -1.0
Page 421 and 422: 408It also changes the FixedPositio
Page 423 and 424: 410’--testing/--no-testing’, de
Page 425 and 426: 412• Asset Selection - Choosing a
Page 427 and 428: 414if self.R is not None:self.R = s
Page 429 and 430: 416)self.events_queue.put(SignalEve
Page 431 and 432: 418@click.option(’--testing/--no-
Page 433 and 434: 420• Short-Term Trend - Predict m
Page 435 and 436: 422It takes the CSV file path as an
Page 437 and 438: 424produce a final truth column whe
Page 439 and 440: 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
Page 449 and 450: 436):lookforward_minutes=5,up_down_
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: 456sentiment_handler = SentdexSenti
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 and 492: 47831.5 Strategy Results31.5.1 Tran
Page 493 and 494: 480Figure 31.3: Trend Following Reg
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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