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COMP226 Assignment 2: Strategy

 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 Thursday 18 March 2020
Deadline 17:00 Friday 1st May 2020
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_v5.3
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.
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
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_v5.3.zip, which will create
a directory backtester_v5.3 on your hard drive. Here is a listing of the zip file contents:
backtester_v5.3
├── DATA
│   ├── A2
│   │   ├── 01.csv
│   │   └── 02.csv
│   └── EXAMPLE
│   ├── 01.csv
│   ├── 02.csv
│   ├── 03.csv
│   ├── 04.csv
│   └── 05.csv
├── example_strategies.R
├── framework
│   ├── backtester.R
│   ├── data.R
│   ├── processResults.R
│   └── utilities.R
├── in-sample_period.R
├── main.R
├── main_optimize.R
├── main_template.R
└── strategies
 ├── a2_template.R
 ├── bankrupt.R
 ├── bbands_contrarian.R
 ├── bbands_holding_period.R
 ├── bbands_trend_following.R
 ├── big_spender.R
 ├── copycat.R
 ├── extreme_limit.R
 ├── fixed.R
 ├── random.R
 ├── rsi_contrarian.R
 └── simple_limit.R
5 directories, 28 files
Next you should open R and make sure that the working directory is the backtester_v5.3
directory on your hard drive (you can use setwd if required). You can now try the example
code as follows:
source('main.R')
If this doesn't 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:
Active on 100 % of days; PD ratio = −153.44
Jan Apr Jul
999400
999600
999800
1000000
05 : PD ratio = 3.88 / 13.7 = 0.28
03 : PD ratio = −0.19 04 : PD ratio = 23.02 / 138 = 0.17
01 : PD ratio = 0.06 / 0.03 = 1.97 02 : PD ratio = −180.2
Jan Apr Jul
Jan Apr Jul Jan Apr Jul
Jan Apr Jul Jan Apr Jul
−600
−400
−200
0
−50
0
50
100
0.00
0.02
0.04
0.06
−0.5
−0.4
−0.3
−0.2
−0.1
0.0
−5
0
5
There is one equity curve for each series in the data (5 of them in this case), and one
aggregate equity curve.
Let's go through main.R and see what the individual parts do.
Sourcing the framework and example strategies
First we source the framework itself.
source('framework/data.R') 
source('framework/backtester.R')
source('framework/processResults.R') 
source('framework/utilities.R') 
Then we load example_strategies.R, which provides an easy way to run several examples,
and which we will return to shortly.
source('example_strategies.R')
Loading data
Next, we load in data that we will use via the function getData, which is defined in
framework/data.R. This function 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 you will need to do for assignment 2).
# load data
dataList <- getData(directory="EXAMPLE")
There are 5 series in the directory backtester_5.3/DATA/EXAMPLE/, and therefore the list
dataList 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 High Low Close 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
Loading a strategy
We will now load a strategy using the load_strategy function that is defined in
example_strategies.R. We can pick a strategy from a list of examples strategies that is
specified at the start of example_strategies.R:
example_strategies <- c("fixed",
 "big_spender",
"bankrupt",
"copycat",
"random",
"rsi_contrarian",
"bbands_trend_following",
"bbands_contrarian",
"bbands_holding_period",
"simple_limit")
Returning now to main.R we see that we have picked one of these (and then checked that it
was a valid choice with)
# choose strategy from example_strategies
strategy <- "fixed"
 
# check that the choice is valid
is_valid_example_strategy <- function(strategy) {
 strategy %in% example_strategies
}
stopifnot(is_valid_example_strategy(strategy))
Now we actually "load the strategy".
# load in strategy and params
load_strategy(strategy) # function from example_strategies.R
We used the function load_strategy from example_strategies.R. This function sources
the strategy file, in this case backtester_v5.3/strategies/fixed.R, and sets a variable
params using example_params from example_strategies.R:
load_strategy <- function(strategy) {
 # load strategy
 strategyFile <- file.path('strategies', paste0(strategy,'.R'))
 cat("Sourcing",strategyFile,"\n")
 source(strategyFile) # load in getOrders
 # set params via global assignment
 params <<- example_params[[strategy]]
 print("Parameters:")
 print(params)
}
The structure of a strategy
Here is the contents of the strategy file backtester_v5.3/strategies/fixed.R:
# This strategy only uses market orders 
# params$sizes specifies a fixed number of contracts per series
# We take the corresponding long/short position in each series 
# by placing a market order on the 1st iteration
# No further orders are placed by getOrders
# The backtester automatically exits all positions 
# as market orders at the end when the data runs out
getOrders <- function(store, newRowList, currentPos, info, params) {
 allzero <- rep(0,length(newRowList))
 marketOrders <- allzero
 if (is.null(store)) {
 # take position during first iteration and hold
 marketOrders <- params$sizes
 store <- 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 to
getOrders are fixed, i.e., they are the same for all strategies. In the example strategy
fixed.R, getOrders is the only function. The arguments to getOrders are as follows:
getOrders <- function(store, newRowList, currentPos, info, params) {
• store: contains all data you choose to save from one period to the next
• newRowList: new day's data (a list of single rows from the series)
• currentPos: the vector of current positions in each series
• params: a list of parameters that are sent to the function
Here's how the strategy fixed.R works. In the very first period the backtester always (for
every 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 parameter
params$sizes, which should be a vector of positions with length equal to the number of
series, which is 5 in this case. In example_strategies.R we see this parameter
params$sizes, which is the only parameter for fixed.R, set as follows:
list(sizes=rep(1,5))
With these sizes, we buy and hold one unit in every series.
Changing the parameters
We can change the parameters and take positions in only some series and go short in some
series, e.g., with:
params <- list(sizes=c(1,2,0,0,-1))
We can set this either in example_strategies.R, or in main.R, as long as it comes after we
have called load_strategy.
Active on 100 % of days; PD ratio = −364.37
Jan Apr Jul
998500
999000
999500
1000000
05 : PD ratio = −4.02
03 : PD ratio = 0 04 : PD ratio = 0
01 : PD ratio = 0.06 / 0.03 = 1.97 02 : PD ratio = −360.4
Jan Apr Jul
Jan Apr Jul Jan Apr Jul
Jan Apr Jul Jan Apr Jul
−1500
−1000
−500
0
−0.050
−0.025
0.000
0.025
0.050
0.00
0.02
0.04
0.06
−0.050
−0.025
0.000
0.025
0.050
−5
0
5
Compare the new equity curves with the ones above. Note that for series 1 they are the
same, for series 2 the new one is scaled by 2, for series 3 and 4 we no longer trade, and for
series 5 we now take a short position, so the new series 5 is a reflection (in the profit and
loss axis) of the old series 5 equity curve.
Market orders
The fixed example strategy enters position at the first opportunity using market orders. The
backester framework supports market and limit orders and some of the example strategies
use limit orders. However, we will not use limit orders for assignment 2, only market orders.
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 market order for each series, and two limit orders 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 executed at the open on day k+1. 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.
To repeat, 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.
Subsetting the data
The next thing in main.R is a subsetting of the time period for the backtest as follows:
inSampDays <- 200 # in-sample period 1:inSampDays
dataList <- lapply(dataList, function(x) x[1:inSampDays])
So we are only using the first 200 days.
Hint
You should adapt this use of lapply on dataList in order to define the in-sample
period in assignment 2.
Running the backtest
Finally we actually do the backtest and plot the results as follows:
# Do backtest
results <- 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 strategy
• params - the parameters for the strategy
• sMult - slippage multiplier (proportion of overnight gap)
Results for individual series are available in results$pnlList. The portfolio results are
available in pfolioPnL, which is produced by plotResults(dataList,results). This
function also automatically plots individual and aggregate equity curves, and computes
variant of the Calmar Ratio that we call the Profit Drawdown Ratio (PD ratio for short) - it is
the final profit divided by the maximum drawdown in terms of profit and loss, or if the
strategy makes a loss overall the PD ratio is just that loss (which is negative). You do not
need to write code to compute this, since it has already been done for you. In assignment 2
we will optimize the aggregate PD ratio - this value is stored in pfolioPnL$fitAgg, e.g., for
our first example we have:
> print(pfolioPnL$fitAgg)
[1] -153.44
This matches up with the PD ratio that appears at the top of the aggregate equity curve
produced by plotResults.
Parameter optimization
Before we move on to assignment 2, we will briefly look at an example of parameter
optimization that will be useful for assignment 2. To make it easier to carry out parameter
optimizations, getOrders takes an argument params. This can be used to pass a parameter
combination to a strategy. This in turn can be used to do a parameter optimization as
main_optimize.R demonstrates. Here is the source code for main_optmize.R, which uses
the example strategy bbands_contrarian, which is an implementation of the "BBands
Overbought/Oversold" strategy from the slides:
source('framework/data.R'); source('framework/backtester.R')
source('framework/processResults.R'); source('strategies/bbands_contrarian.R')
numOfDays <- 200
dataList <- getData(directory="EXAMPLE")
dataList <- lapply(dataList, function(x) x[1:numOfDays])
sMult <- 0.2 # slippage multiplier
lookbackSeq <- seq(from=20,to=40,by=10)
sdParamSeq <- seq(from=1.5,to=2,by=0.5)
paramsList <- list(lookbackSeq,sdParamSeq)
numberComb <- prod(sapply(paramsList,length))
resultsMatrix <- matrix(nrow=numberComb,ncol=3)
colnames(resultsMatrix) <- c("lookback","sdParam","PD Ratio")
pfolioPnLList <- vector(mode="list",length=numberComb)
count <- 1
for (lb in lookbackSeq) {
 for (sdp in sdParamSeq) {
 params <- list(lookback=lb,sdParam=sdp,series=1:5,posSizes=rep(1,5))
 results <- backtest(dataList, getOrders, params, sMult)
 pfolioPnL <- plotResults(dataList,results)
 resultsMatrix[count,] <- c(lb,sdp,pfolioPnL$fitAgg)
 pfolioPnLList[[count]]<- pfolioPnL
 cat("Just completed",count,"out of",numberComb,"\n")
 #print(resultsMatrix[count,])
 count <- count + 1
 }
}
print(resultsMatrix[order(resultsMatrix[,"PD Ratio"]),])
The code template and data for assignment 2
You are now ready to start working on assignment 2. To do so you should read and work
through the rest of this document very carefully.
As a first step, try to run main_template.R, which is setup to use the right data for the
assignment and to load in the template strategy code strategies/a2_template.R. If you
try to source main_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.
For all 6 functions, example outputs are provided so that you can test whether you
have implemented the functions 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 17.
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 long
The function getPosSignFromTMA should use a function getTMA. The position size, i.e., the
number 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 are
given to the backtester in the function getOrders. Here are the detailed specification and
marks available for these first 4 functions.
Function
name
Input parameters Expected behaviour Marks available for a
correct implementation
getTMA close_prices;
lookbacks. The
specific form that
these arguments
should take is
specified in the
template code via
the 6 checks that
you need to
implement.
You should first implement
the checks as described in
the template. Hints of how
to implement them are
given below.
The function should return
a list with three named
elements (named short,
medium, and long). Each
element should be equal to
the value of a simple
moving average with the
respective window size as
defined by lookbacks. The
windows should all end in
the same period, which
should be the final row of
close_prices.
18% (3% per check) for
the checks; 12% for a
correct return
getPosSign
FromTMA
tma_list is a list
with three named
elements, short,
medium, and long.
These correspond
to the simple
moving averages
as returned by
getTMA.
Note: You do not
need to check the
validity of the
function argument
in this case, or for
the remaining
functions either.
This function should return
either 0, 1, or -1.
If the short value of
tma_list is less than the
medium value, and the
medium value is less than
the long value, it should
return 1 (indicating a long
position).
If the short value of
tma_list is greater than
the medium value, and the
medium value is greater
than the long value, it
should return -1 (indicating
a short position).
Otherwise, the return value
should be 0 (indicating a
flat position).
15%
getPosSize current_close:
this is the current
close for one of
the series.
constant: this
argument should
have a default
value of 1000.
The function should return
(constant divided by
current_close) rounded
down to the nearest
integer.
5%
getOrders The arguments to
this function are
always the same
for all strategies
used in the
backtester
framework.
This function should
implement the strategy
outlined above and again
below in "Strategy
specification".
20%
Strategy specification
The strategy should apply the following logic independently for both series.
The strategy does nothing until there have been params$lookbacks$long-many
periods.
In the (params$lookbacks$long+1)-th period, and in every period after, the strategy
computes three simple moving averages with window lengths equal to:
• params$lookbacks$short
• params$lookbacks$medium
• params$lookbacks$long
The corresponding windows always end in the current period. The strategy should in
this period send market orders to assume a position (make sure you take into
account positions from earlier) according to getPosSignFromTMA and getPosSize.
(Limit orders are not required at all, and can be left as all zero.)
Hints
For 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 SMA from the TTR package.
Note: The list returned by getTMA should work as input to the function
getPosSignFromTMA.
For getPosSize, you can use the function floor.
As in the template, use the negative of currentPos summed with the new positions
you 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 next
give some examples of how correct implementations of the functions will behave. These
examples assume that you have correctly implemented the first 4 functions in
a2_template.R and sourced the resulting code to make the functions available in the R
environment.
Example output for getTMA
First you should make sure that you have correctly implemented all 6 checks on the
function 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] 169
$medium
[1] 170.4
$long
[1] 171.05
Example output for getPosSignFromTMA
> 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
> 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
Warning
The last two functions require a working implementation of getOrders. If your
implementation of getOrders does not work, then you will receive 0 marks for these
last two functions, even if they return the correct numbers. This is a simple protection
again plagiarism and collusion.
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 MWS 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 MWS 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 par
ameters
Expected behaviour Marks available for a
correct implementation
getInSampleR
esult
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.
The function should not contain
ANY code except the return
value; it should run and
complete instantanously.
10% (0 marks will be
given if the function
contains any code other
than the return statement)
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_v5.3/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).
Function
name
Input pa
rameters
Expected behaviour Marks available for a
correct implementation
getInSampleO
ptResult
None This function should return the
best PD ratio than can be
achieved with the stated
allowable parameter
combinations on your
username-specific in-sample
period.
The function should not contain
ANY code except the return
value; it should run and
complete instantanously.
20% (0 marks will be
given if the function
contains any code other
than the return statement)
Next we give some example output for these two functions.
Example output for getInSampleResult
Username Correct return value
x1xxx -747.6
x1yyy -231.6
x1zzx -639.8
Example output for getInSampleOptResult
Username Correct return value
x1xxx 4.23
x1yyy 3.42
x1zzx 4.43
Marks summary
Function Marks
getTMA 30
getPosSignFromTMA 15
getPosSize 5
getOrders 20
getInSampleResult 10 (0 if getOrders does not work)
getInSampleOptResult 20 (0 if getOrders does not work)
Submission
You need to submit a single R file that contains your implementation of 6 functions. The file
shoud be called MWS-username.R where you should replace MWS-username by your MWS
username. For example if your username is "abcd" then you should submit a file named
"abcd.R".
Submission is via the department electronic submission system:
http://www.csc.liv.ac.uk/cgi-bin/submit.pl
Warning
Your code will be put through the department's automatic plagiarism and collusion
detection system. Student's found to have plagiarized or colluded will likely receive a
mark of zero. Do not show your work to other students.
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