[SOLVED] algorithm COMP226 Assignment 2: Strategy Development

COMP226 Assignment 2: Strategy Development

COMP226 Assignment 2: Strategy

Development

The latest version of this document can be found here:

https://www2.csc.liv.ac.uk/~rahul/teaching/comp226/_downloads/a2.pdf

Continuous
Assessment Number

2 (of 2)

Weighting 10%

Assignment Circulated 13:00 Thursday 30 March 2017

Deadline 12:00 Monday 8 May 2017

Submission Mode Electronic only

Learning Outcomes
Assessed

This assignment will address the following learning outcomes:

Understand the spectrum of computer-based trading
applications and techniques, from profit-seeking trading
strategies to execution algorithms.

Be able to design trading strategies and evaluate critically
their historical performance and robustness.

Understand the common pitfalls in developing trading
strategies with historical data.

Understand methods for measuring risk and diversification
at the portfolio level.

Summary of
Assessment

The goal of this assignment is to implement and optimize a
well-defined trading strategy within the backtester_v4.2
framework. The assignment will be assessed via the testing of 6
functions that you need to implement. The input and output
behaviour of each function is fully specified and a code template
is provided as a starting point.

In addition to addressing the learning outcomes above, another
purpose of this assignment is for students to familiarize
themselves with the backtester framework that will also be used
in COMP396.

Marking Criteria Individual marks are attributed for each of 6 functions that
should be implemented. If all 6 function implementations pass
all the automated tests then a mark of 100% will be achieved.
Partial credit for a function may be awarded if some but not all
automated tests for that function are passed. The marks
available for each function are given below.

Submission necessary
in order to satisfy
module requirements

No

Late Submission
Penalty

Standard UoL policy; note that no resubmissions after the
deadline will be considered.

Expected time taken Roughly 8 hours

https://www2.csc.liv.ac.uk/~rahul/teaching/comp226/_downloads/a2.pdf

Introduction: the backtester framework

You will write a strategy that should run in the backtester framework, which is available
from

http://www2.csc.liv.ac.uk/~rahul/teaching/comp226/bt.html#backtester

The first thing you should do is download and unzip backtester_v4.2.zip, which will create
a directory backtester_v4.2 on your hard drive. Here is a listing of the zip file contents:

backtester_v4.2
DATA
A2
01.csv
02.csv
EXAMPLE
01.csv
02.csv
03.csv
04.csv
05.csv
framework
backtester.R
data.R
pdratio.R
processResults.R
utilities.R
in-sample_period.R
main.R
main_optimize.R
main_template.R
strategies
a2_template.R
bbands.R
copycat.R
fixed.R

5 directories, 20 files

Next you should open R and set the working directory to the backtester_v4.2 directory on
your hard drive. You can now try the example code as follows:

source(main.R)

If this doesnt work, first make sure you are have set the working directory correctly, and
then make sure you have installed all the required packages (see the error messages you
get to figure out what the problem is). When it works it will produce a plot like the following:

http://www2.csc.liv.ac.uk/~rahul/teaching/comp226/bt.html#backtester

Active on 100 % of days; PD ratio =153.44

600

400

200

0

Jan Feb Mar Apr May Jun Jul

01 : PD ratio =0.06 / 0.03 = 1.97 02 : PD ratio =180.2

03 : PD ratio =0.19 04 : PD ratio =23.02 / 138 = 0.17

05 : PD ratio =3.88 / 13.7 = 0.28

0.00

0.02

0.04

0.06

600

400

200

0

0.5
0.4
0.3
0.2
0.1

0.0

50

0

50

100

5

0

5

Jan Feb Mar Apr May Jun Jul Jan Feb Mar Apr May Jun Jul

Jan Feb Mar Apr May Jun Jul Jan Feb Mar Apr May Jun Jul

Jan Feb Mar Apr May Jun Jul

There is one equity curve for each series in the data (5 of them in this case), and one
aggregate equity curve. Lets go through main.R and see what the individual parts do.

First we source the framework itself.

source(framework/data.R)
source(framework/backtester.R)
source(framework/processResults.R)

Next, we load in the data using the function getData that is defined in framework/data.R.
It returns a list of xts objects. These will be passed to the function backtester, though we
may first change the start and end dates of the xts objects (which we will do in assignment
2).

# Read in data
dataList <- getData(directory=”EXAMPLE”)There are 5 series in the directory backtester_4.2/DATA/EXAMPLE/, and therefore the listdataList has 5 elements too.> length(dataList)
[1] 5

Each element is an xts:

> for (x in dataList) print(class(x))
[1] xts zoo
[1] xts zoo
[1] xts zoo
[1] xts zoo
[1] xts zoo

All the series have the same start and end dates:

> for (x in dataList) print(paste(start(x),end(x)))
[1] 1970-01-02 1973-01-05
[1] 1970-01-02 1973-01-05
[1] 1970-01-02 1973-01-05
[1] 1970-01-02 1973-01-05
[1] 1970-01-02 1973-01-05

The individual series contain Open, High, Low, Close, and Volume columns:

> head(dataList[[1]])
Open HighLowClose Volume
1970-01-02 0.7676 0.7698 0.7667 0.7691 3171
1970-01-03 0.7689 0.7737 0.7683 0.7729 6311
1970-01-04 0.7725 0.7748 0.7718 0.7732 4317
1970-01-05 0.7739 0.7756 0.7739 0.7751 3409
1970-01-06 0.7760 0.7770 0.7754 0.7757 2904
1970-01-07 0.7738 0.7744 0.7728 0.7743 3514

The next thing we do in main.R is source a strategy file.

# Choose strategy
strategyFile <-‘strategies/fixed.R’# strategyFile <-‘strategies/copycat.R’# strategyFile <-‘strategies/bbands.R’# strategyFile <-‘strategies/a2_template.R’cat(“Sourcing”,strategyFile,”
“)source(strategyFile) # load in getOrdersHere is the contents of the strategy file backtester_v4.2/strategies/fixed.R:# This strategy uses only market orders (and only in the first period).# It takes a position in the first period and holds it for the duration.# The backtester automatically exits all positions as market orders at the end.getOrders <- function(store, newRowList, currentPos, params) {allzero<- rep(0,length(newRowList)) marketOrders <- allzeroif (is.null(store)) { # take position during first iteration and holdmarketOrders <- params$sizesstore <- 1 # not null}return(list(store=store,marketOrders=marketOrders,limitOrders1=allzero, limitPrices1=allzero,limitOrders2=allzero,limitPrices2=allzero))}The backtester framework runs a strategy by calling getOrders. The arguments togetOrders are fixed, i.e., they are the same for all strategies. In the example strategyfixed.R, getOrders is the only function. The arguments to getOrders are as follows:getOrders <- function(store,newRowList,currentPos,params) {store: contains all data you choose to save from one period to the nextnewRowList: new day’s data (a list of single rows from the series)currentPos: the vector of current positions in each seriesparams: a list of parameters that are sent to the functionHere’s how the strategy fixed.R works. In the very first period the backtester always (forevery strategy) passes store to getOrders with NULL as its value. Thus in the first period,and the first period only, the vector marketOrders will be set to the parameterparams$sizes, which should be a vector of positions with length equal to the number ofseries, which is 5 in this case. In main.R we see this parameter params$series, which isthe only parameter for fixed.R, set as follows:params <- list(sizes=rep(1,5))With these sizes, we buy and hold one unit in every series. We can change the parametersand take positions in only some series and go short in some series, e.g., with:params <- list(sizes=c(1,2,0,0,-1))Compare with the equity curves above and note that for series 1 they are the same, forseries 2 the new one is scaled by 2, for series 3 and 4 we no longer trade, and for series 5we now take a short position, so the new series 5 is a reflection of the old series 5 equitycurve.Active on 100 % of days; PD ratio =364.37150010005000Jan Feb Mar Apr May Jun Jul01 : PD ratio =0.06 / 0.03 = 1.97 02 : PD ratio =360.403 : PD ratio =0 04 : PD ratio =005 : PD ratio =4.020.000.020.040.061500100050000.500.250.000.250.500.500.250.000.250.50505Jan Feb Mar Apr May Jun Jul Jan Feb Mar Apr May Jun JulJan Feb Mar Apr May Jun Jul Jan Feb Mar Apr May Jun JulJan Feb Mar Apr May Jun JulThe next thing in main.R is a subsetting of the time period for the backtest as follows:inSampDays <- 200# in-sample perioddataList <- lapply(dataList, function(x) x[1:inSampDays])So we are only using the first 200 days.HintYou should adpat this use of lapply on dataList in order to define the in-sampleperiod in assignment 2.Finally we actually do the backtest and plot the results as follows:# Do backtestresults <- backtest(dataList,getOrders,params,sMult=0.2)pfolioPnL <- plotResults(dataList,results)The arguments to the function backtest are the following:dataList – list of (daily) xts objects (with identical indexes)getOrders – the strategyparams – the parameters for the strategysMult – slippage multiplier (proportion of overnight gap)Results for individual series are available in results$pnlList. The portfolio results areavailable in pfolioPnL, which is produced by plotResults(dataList,results). Thisfunction also automatically plots individual and aggregate equity curves, and computesvariant of the Calmar Ratio that we call the Profit Drawdown Ratio (PD ratio for short) – it isthe final profit divided by the maximum drawdown in terms of profit and loss, or if thestrategy makes a loss overall the PD ratio is just that loss (which is negative). You do notneed to write code to compute this, since it has already been done for you. In assignment 2we will optimize the aggregate PD ratio – this value is stored in pfolioPnL$fitAgg, e.g., forour first example we have:> print(pfolioPnL$fitAgg)
[1] -153.44

This matches up with the PD ratio that appears at the top of the aggregate equity curve
produced by plotResults.

Recall that market orders specify volume and direction (but not price), and limit orders
specify price, volume, and direction. In the backtester framework, trading decisions are
made after the close of day k, and trades are executed on day k+1. For each day, the
framework supports one marketorder for each series, and twolimitorders for each
series. These orders are returned from getOrders as follows:

return(list(store=store,marketOrders=marketOrders,
limitOrders1=limitOrders1,
limitPrices1=limitPrices1,
limitOrders2=limitOrders2,
limitPrices2=limitPrices2))

Market orders will be executedattheopen on day k+1. They incur slippage (20% of the
overnight gap for assignment 2). Market orders are specified by

size (number of units to trade)

direction (buy/sell)

The sizes and directions of market orders are encoded in the vector marketOrders of
the return list of getOrders. For example, the vector

c(0,-5,0,1,0)

means place a market order for 5 units short in series 2, and 1 unit long in series 4.

We will not use limit orders for assignment 2, so you can leave limitOrders1,
limitPrices1, limitOrders2, limitPrices2 as zero vectors when you do assignment 2
(i.e., you do not need to edit that part of the template). We will introduce the limit order
functionality in detail in COMP396.

As well as fixed.R, two other example strategies are available now: copycat.R, bbands.R.
It is left to you to explore how these work. These strategies implement the copycat strategy
and mean-reversion Bollinger bands strategies from slides 06, respectively. Note that
bbands.R and a2_template.R make use of the store to remember past data. You will need
to adapt the store for COMP396, but for now, for COMP226 assignment 2 you just need to
understand how close prices can be retrieved from the store as described below.

Before we move on to assignment 2, we will briefly look at an example of parameter
optimization that will be useful for assignment 2. To make it easier to carry out parameter
optimizations, getOrders takes an argument params. This can be used to pass a parameter
combination to a strategy. This is turn can be used to do a parameter optimization as
main_optimize.R demonstrates. Here is the source code for main_optmize.R:

source(framework/data.R);
source(framework/backtester.R)
source(framework/processResults.R);
source(strategies/bbands.R)

numOfDays <- 200dataList <- getData(directory=”EXAMPLE”)dataList <- lapply(dataList, function(x) x[1:numOfDays])sMult <- 0.2 # slippage multiplierlookbackSeq <- seq(from=20,to=40,by=10)sdParamSeq<- seq(from=1.5,to=2,by=0.5) paramsList<- list(lookbackSeq,sdParamSeq)numberComb <- prod(sapply(paramsList,length))resultsMatrix <- matrix(nrow=numberComb,ncol=3)colnames(resultsMatrix) <- c(“lookback”,”sdParam”,”PDratio”)pfolioPnLList <- vector(mode=”list”,length=numberComb)count <- 1for (lb in lookbackSeq) {for (sdp in sdParamSeq) {params <- list(lookback=lb,sdParam=sdp,series=1:4,posSizes=rep(1,10)) results <- backtest(dataList, getOrders, params, sMult)pfolioPnL <- plotResults(dataList,results)resultsMatrix[count,] <- c(lb,sdp,pfolioPnL$fitAgg)pfolioPnLList[[count]]<- pfolioPnLcat(“Just completed”,count,”out of”,numberComb,”
“)print(resultsMatrix[count,])count <- count + 1}}print(resultsMatrix[order(resultsMatrix[,”PDratio”]),])The code template and data for assignment 2You are now ready to start working on assignment 2. To do so you should read and workthrough the rest of this document very carefully.As a first step, try to run main_template.R. It uses strategies/a2_template.R which is acode template that should serve as your starting point. If you try to sourcemain_template.R you will get an error as follows:Error in if (store$iter > params$lookbacks$long) { :
argument is of length zero

If you read on you will see that the final strategy requires a parameter called lookbacks.
Read on to see what form this parameter should take.

The code template contains templates for the 6 functions that you need to complete. These
functions are:

1. getTMA

2. getPosSignFromTMA

3. getPosSize

4. getOrders

5. getInSampleResult

6. getInSampleOptResult

The rest of the document is split into two parts. The first part describes the function
requirements and marking criteria for the first 4 functions, which relate to the strategy
implementation. The second part describes the function requirements and marking criteria
for the last 2 functions. Hints are given on how best to implement things, so read carefully.
The examples below should give you an idea how you can test these functions to check
whether you have implemented them correctly.

Note

You can develop the first three functions without running the backtester, which may
be easier.

Part 1: strategy implementation

The overall goal of the assignment is the implementation and optimization of a triple moving
average crossover (TMA) trading strategy. The specification of the strategy and the
functions that it should comprise are given in full detail, so the correctness of your code
can and will be checked automatically.

The TMA strategy you will implement is related to Example 1 in COMP226 slides 06.
However, long and short positions are swapped as compared to that example (so you will
here implement a mean-reversion as opposed to a trend following type strategy).

The strategy uses three moving averages with three different lookbacks (window lengths).
The short lookback should be smaller than the medium window, which in turn should be
smaller than the long lookback. In every trading period, the strategy will compute the value
of these three moving averages. You will achieve this be completing the implementation of
the function getTMA.

The following table indicates the position that the strategy will take depending on the
relative values of the three moving averages (MAs). You will compute this position (sign, but
not size) by completing the function getPosSignFromTMA. The system is out of the market
(i.e., flat) when the relationship between the short moving average and the medium moving
average does not match the relationship between the medium moving avergage and long
moving average.

MA MA MA Position

short > medium > long short

short < medium < long longThe function getPosSignFromTMA should use a function getTMA. The position size, i.e., thenumber of units to be long or short, will be determined by the function getPosSize. Finally,as usual in the backtester framework for COMP226 and COMP396, the position sizes aregiven to the backtester in the function getOrders. Here are the detailed specification andmarks available for these first 4 functions.FunctionnameInput parameters Expected behaviour Marks available for acorrect implementationgetTMA close_prices;lookbacks. Thespecific form thatthese argumentsshould take isspecified in thetemplate code viathe 6 checks thatyou need toimplement.You should first implementthe checks as described inthe template. Hints of howto implement them aregiven below.18% (3% per check)The function should returna list with three namedelements (named short,medium, and long). Eachelement should be equal tothe value of a simplemoving average with therespective window size asdefined by lookbacks. Thewindows should all end inthe same period, whichshould be the final row ofclose_prices.12%getPosSignFromTMAtma_list is a listwith three namedelements, short,medium, and long.These correspondto the simplemoving averagesas returned bygetTMA.Note: You do notneed to check thevalidity of thefunction argumentin this case, or forthe remainingfunctions either.This function should returna single number thatshould be 0, 1, or -1.If the short value oftma_list is less than themedium value, and themedium value is less thanthe long value, then thereturn value should be 1(indicating a long position).If the short value oftma_list is greater thanthe medium value, and themedium value is greaterthan the long value, thenthe return value should be-1 (indicating a shortposition).Otherwise, the return valueshould be 0 (indicating aflat position).15%getPosSize current_close:this is the currentclose for one ofthe series; it doesnot have a defaultvalue.constant: thisargument shouldhave a defaultvalue of 1000.The function should return(constant divided bycurrent_close) roundeddown to the nearestinteger.5%getOrders The arguments tothis function arealways the samefor all strategiesused in thebacktesterframework.This function shouldimplement the strategyoutlined above and againbelow in “Strategyspecification”.20%Strategy specificationThe strategy should apply the following logic independently for both series.The strategy does nothing until there have been params$lookbacks$long-manyperiods.In the params$lookbacks$long-th period, and in every period after, the strategycomputes three simple moving averages with window lengths equal to:params$lookbacks$shortparams$lookbacks$mediumparams$lookbacks$longThe corresponding windows always end in the current period. The strategy should inthis period send market orders to assume a position (make sure you take intoaccount positions from earlier) according to getPosSignFromTMA and getPosSize.(Limit orders are not required at all, and can be left as all zero.)HintsFor the checks for getTMA you may find the following functions useful:The operator ! means not, and can be used to negate a boolean.sapply allows one to apply a function element-wise to a vector or list (e.g.,to a vector list c(“short”,”medium”,”long”)).all is a function that checks if all elements of a vector are true (for example,it can be used on the result of sapply).%in% can be used to check if a element exists inside a vector.To compute the moving average in getTMA you can use the function SMA from theTTR package.Note: The list returned by getTMA should work as input to the functiongetPosSignFromTMA.For getPosSize, to round down to the nearest integer you can use the functionfloor.As in the template, use the negative of currentPos summed with the new positionsyou want to take to make sure that you assume the correct position.In order to help you check whether you have implemented the functions correctly, we nextgive some examples of how correct implementations of the functions will behave. Theseexamples assume that you have correctly implemented the first 4 functions ina2_template.R and sourced the resulting code to make the functions available in the Renvironment.Example output for getTMAFirst you should make sure that you have correctly implemented all 6 checks on thefunction arguments. Here are 3 examples of expected behaviour:> close_prices <- c(1,2,3)> lookbacks <- list(short=as.integer(5),medium=as.integer(10),long=as.integer(20))> getTMA(close_prices,lookbacks) # bad close_prices
Error in getTMA(close_prices, lookbacks) :
E04: close_prices is not an xts according to is.xts()

> dataList <- getData(directory=”A2″)Read 2 series from DATA/A2> close_prices <- dataList[[1]]$Close[1:19]> getTMA(close_prices,lookbacks) # bad close_prices; too short
Error in getTMA(close_prices, lookbacks) :
E05: close_prices does not enough rows

> lookbacks <- list(5,10,25)> getTMA(close_prices,lookbacks) # bad lookbacks; list elements not named
Error in getTMA(close_prices, lookbacks) :
E01: At least one of short, medium, long is missing from names(lookbacks)

Here is an example where we give the function valid arguments.

> lookbacks <- list(short=as.integer(5),medium=as.integer(10),long=as.integer(20))> close_prices <- dataList[[1]]$Close[1:20]> getTMA(close_prices,lookbacks)
$short
[1] 16.948

$medium
[1] 17.086

$long
[1] 17.1525

Example output for getPosSignFromTMA
Here are three examples of correct output:

> getPosSignFromTMA(list(short=10,medium=20,long=30))
[1] 1
> getPosSignFromTMA(list(short=10,medium=30,long=20))
[1] 0
> getPosSignFromTMA(list(short=30,medium=20,long=10))
[1] -1

Example output for getPosSize
Here are two examples of correct output:

> current_close <- 100.5> getPosSize(current_close)
[1] 9
> getPosSize(current_close,constant=100.4)
[1] 0

Example output for getOrders
To check your implementation of getOrders, see part 2 for examples of correct output for
the function getInSampleResult below.

Part 2: in-sample tests

There are two more functions that you need to implement: getInSampleResult and
getInSampleOptResult. For both functions you will need to compute your own in-sample
period, which is based on your computer science (CS) username. This ensures that for part
2 there are different answers for different students. To get your in-sample period you should
use in-sample_period.R as follows. Source it and run the function getInSamplePeriod
with your CS username as per the following example. Then use the first number in the
returned vector as the start of the in-sample period and the second number as the end.

> source(in-sample_period.R)
> getInSamplePeriod(x4xz1)
[1]230 644

So for this example username the start of the in-sample period is day 230 and the end is
644. Note: you may need to install the package digest to use this code.

Once you have your own in-sample period (and a correct implementation of getOrders),
you are ready to complete the implementation of getInSampleResult.

Function
name

Input parameters Expected behaviour Marks available for a
correct implementation

getInSampl
eResult

None This function should return
the PD ratio that is
achieved when the strategy
is run with short lookback
10, medium lookback 20,
and long lookback 30, on
your username-specific
in-sample period.

10%

To complete the final function getInSampleOptResult you need to do an in-sample
parameter optimization using the following parameter combinations for the:

short lookback

medium lookback

long lookback

You should not optimize the constant used with getPosSize, and leave it as 1000 as defined
in the template code.

The parameter combinations are defined by two things: parameter ranges and a further
restriction. Make sure you correctly use both to produce the correct set of parameter
combinations. The ranges are:

Parameter Minimum value Increment Maximum Value

short lookback 100 5 110

medium lookback 105 5 120

long lookback 110 5 130

The further restriction is the following:

Further restriction on parameter values

You should further restrict the parameter combinations as follows:

The medium lookback should always be strictly greater than the short lookback.

The long lookback should always be strictly greater than the medium lookback.

You need to find the best PD ratio that can be achieved one this set of parameter
combinations for the in-sample period that corresponds to your username, and set it as the
return value of getInSampleOptResult.

Hint

The correct resulting number of parameter combinations is 28.

You can adapt backtester_v4.2/main_optimize.R. It is probably easiest to use
three nested for loops in order to ensure that you only check valid parameter
combinations (where the short < medium < long for the respective window lengths).FunctionnameInput parameters Expected behaviour Marks available for acorrect implementationgetInSampleOptResultNone This function should returnthe best PD ratio than canbe achieved with thestated allowable parametercombinations on yourusername-specificin-sample period.20%Next we give some example output for these two functions.Example output for getInSampleResultTo help you check the correctness of your code, here are three example return values formade up usernames:Username Correct return valuex1xxx -1664.35x1yyy -541.94x1zzx -1776.39Example output for getInSampleOptResultTo help you check the correctness of your code, here are three example return values formade up usernames:Username Correct return valuex1xxx 3.28x1yyy 1.42x1zzx 3.01Marks summaryFunction MarksgetTMA 30getPosSignFromTMA 15getPosSize 5getOrders 20getInSampleResult 10getInSampleOptResult 20SubmissionYou need to submit a single R file that contains your implementation of 6 functions.Submission is via the department electronic submission system:http://www.csc.liv.ac.uk/cgi-bin/submit.plIn what follows replace x1xx by your CS username (which you use to log on to thesubmission system).Submit one ascii R filex1xx.R – an R file containing your code (implementations of all the functions)WarningYour code will be put through the department’s automatic plagiarism and collusiondetection system. Student’s found to have plagiarized or colluded will likely receive amark of zero. Do not discuss or show your work to other students.http://www.csc.liv.ac.uk/cgi-bin/submit.plIntroduction: the backtester frameworkThe code template and data for assignment 2Part 1: strategy implementationExample output for getTMAExample output for getPosSignFromTMAExample output for getPosSizeExample output for getOrdersPart 2: in-sample testsExample output for getInSampleResultExample output for getInSampleOptResultMarks summarySubmission