4 %%\usepackage{../langs}

     4 \usepackage{../langs}

     8 \section*{Coursework 6 (Scala)}

     8 \section*{Assignment 6 (Scala)}

     9  

     9 

    10 This coursework is about Scala and is worth 10\%. The first and second

    10 \mbox{}\hfill\textit{``The most effective debugging tool is still careful thought,}\\

    11 \mbox{}\hfill\textit{coupled with judiciously placed print statements.''}\smallskip\\

    12 \mbox{}\hfill\textit{ --- Brian W. Kernighan, in Unix for Beginners (1979)}\bigskip

    13 

    14 

    15 \noindent

    16 This assignemnt is about Scala and worth 10\%. The first and second

    12 at 11pm. You are asked to implement three programs about list

    18 at 11pm. You are asked to implement two programs about list

    16 

    22  

    21 maximum of 360 seconds on my laptop.

    27 maximum of 30 seconds on my laptop.

    25 

    31 \subsubsection*{Reference Implementation}

    26 \subsection*{Part 1 (3 Marks)}

    32 

    33 Like the C++ assignments, the Scala assignments will work like this: you

    34 push your files to GitHub and receive (after sometimes a long delay) some

    35 automated feedback. In the end we take a snapshot of the submitted files and

    36 apply an automated marking script to them.

    37 

    38 In addition, the Scala assignments come with a reference implementation

    39 in form of a \texttt{jar}-file. This allows you to run any test cases

    40 on your own computer. For example you can call Scala on the command

    41 line with the option \texttt{-cp collatz.jar} and then query any

    42 function from the template file. Say you want to find out what

    43 the functions \texttt{collatz} and \texttt{collatz\_max}

    44 produce: for this you just need to prefix them with the object name

    45 \texttt{CW6a} (and \texttt{CW6b} respectively for \texttt{drumb.jar}).

    46 If you want to find out what these functions produce for the argument

    47 \texttt{6}, you would type something like:

    48 

    49 \begin{lstlisting}[language={},numbers=none,basicstyle=\ttfamily\small]

    50 $ scala -cp collatz.jar

    51   

    52 scala> CW6a.collatz(6)

    53 ...

    54 scala> CW6a.collatz_max(6)

    55 ...

    56 \end{lstlisting}%$

    57 

    58 \subsection*{Part 1 (3 Marks, file collatz.scala)}

    41 For example if you start with $6$, respectively $9$, you obtain the

    73 For example if you start with $6$, or $9$, you obtain the

    46 6, 3, 10, 5, 16, 8, 4, 2, 1 & \text{(= 9 steps)}\\

    78 6, 3, 10, 5, 16, 8, 4, 2, 1 & \text{(= 8 steps)}\\

    47 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1  & \text{(= 20 steps)}\\

    79 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1  & \text{(= 19 steps)}\\

    70 \textbf{Tasks (file collatz.scala):}

   102 \textbf{Tasks}

    75   with $1$. In case of starting with $6$, it takes $9$ steps and in

   107   with $1$. In case of starting with $6$, it takes $8$ steps and in

    76   case of starting with $9$, it takes $20$ (see above). In order to

   108   case of starting with $9$, it takes $19$ (see above). In order to

    95 \item 1 to 10 where $9$ takes 20 steps 

   127 \item 1 to 10 where $9$ takes 19 steps 

    96 \item 1 to 100 where $97$ takes 119 steps,

   128 \item 1 to 100 where $97$ takes 118 steps,

    97 \item 1 to 1,000 where $871$ takes 179 steps,

   129 \item 1 to 1,000 where $871$ takes 178 steps,

    98 \item 1 to 10,000 where $6,171$ takes 262 steps,

   130 \item 1 to 10,000 where $6,171$ takes 261 steps,

    99 \item 1 to 100,000 where $77,031$ takes 351 steps, 

   131 \item 1 to 100,000 where $77,031$ takes 350 steps, 

   100 \item 1 to 1 Million where $837,799$ takes 525 steps

   132 \item 1 to 1 Million where $837,799$ takes 524 steps

   101   %%\item[$\bullet$] $1 - 10$ million where $8,400,511$ takes 686 steps

   133   %% runs out of stack space

   134   %% \item[$\bullet$] $1 - 10$ million where $8,400,511$ takes 685 steps

   113 \subsection*{Part 2 (3 Marks)}

   146 \subsection*{Part 2 (3 Marks, file drumb.scala)}

   147 

   148 A purely fictional character named Mr T.~Drumb inherited in 1978

   149 approximately 200 Million Dollar from his father. Mr Drumb prides

   150 himself to be a brilliant business man because nowadays it is

   151 estimated he is 3 Billion Dollar worth (one is not sure, of course,

   152 because Mr Drumb refuses to make his tax records public).

   153 

   154 Since the question about Mr Drumb's business acumen remains open,

   155 let's do a quick back-of-the-envelope calculation in Scala whether his

   156 claim has any merit. Let's suppose we are given \$100 in 1978 and we

   157 follow a really dumb investment strategy, namely:

   158 

   159 \begin{itemize}

   160 \item We blindly choose a portfolio of stocks, say some Blue-Chip stocks

   161   or some Real Estate stocks.

   162 \item If some of the stocks in our portfolio are traded in January of

   163   a year, we invest our money in equal amounts in each of these

   164   stocks.  For example if we have \$100 and there are four stocks that

   165   are traded in our portfolio, we buy \$25 worth of stocks

   166   from each. Be careful to also test cases where you trade with 3 stocks, for example. 

   167 \item Next year in January, we look at how our stocks did, liquidate

   168   everything, and re-invest our (hopefully) increased money in again

   169   the stocks from our portfolio (there might be more stocks available,

   170   if companies from our portfolio got listed in that year, or less if

   171   some companies went bust or were de-listed).

   172 \item We do this for 40 years until January 2018 and check what would

   173   have become out of our \$100.

   174 \end{itemize}

   175 

   176 \noindent

   177 Until Yahoo was bought by Altaba this summer, historical stock market

   178 data for such back-of-the-envelope calculations was freely available

   179 online. Unfortuantely nowadays this kind of data is difficult to

   180 obtain, unless you are prepared to pay extortionate prices or be

   181 severely rate-limited.  Therefore this coursework comes with a number

   182 of files containing CSV-lists with the historical stock prices for the

   183 companies in our portfolios. Use these files for the following

   184 tasks.\bigskip

   185 

   186 \noindent

   187 \textbf{Tasks}

   188 

   189 \begin{itemize}

   190 \item[(1)] Write a function \texttt{get\_january\_data} that takes a

   191   stock symbol and a year as arguments. The function reads the

   192   corresponding CSV-file and returns the list of strings that start

   193   with the given year (each line in the CSV-list is of the form

   194   \texttt{someyear-01-someday,someprice}).\hfill[1 Mark]

   195 

   196 \item[(2)] Write a function \texttt{get\_first\_price} that takes

   197   again a stock symbol and a year as arguments. It should return the

   198   first January price for the stock symbol in the given year. For this

   199   it uses the list of strings generated by

   200   \texttt{get\_january\_data}.  A problem is that normally a stock

   201   exchange is not open on 1st of January, but depending on the day of

   202   the week on a later day (maybe 3rd or 4th). The easiest way to solve

   203   this problem is to obtain the whole January data for a stock symbol

   204   and then select the earliest, or first, entry in this list. The

   205   stock price of this entry should be converted into a double.  Such a

   206   price might not exist, in case the company does not exist in the given

   207   year. For example, if you query for Google in January of 1980, then

   208   clearly Google did not exist yet.  Therefore you are asked to

   209   return a trade price with type \texttt{Option[Double]}\ldots\texttt{None}

   210   will be the value for when no price exists; \texttt{Some} if  there is a

   211   price.\hfill[1 Mark]

   212 

   213 \item[(3)] Write a function \texttt{get\_prices} that takes a

   214   portfolio (a list of stock symbols), a years range and gets all the

   215   first trading prices for each year in the range. You should organise

   216   this as a list of lists of \texttt{Option[Double]}'s. The inner

   217   lists are for all stock symbols from the portfolio and the outer

   218   list for the years.  For example for Google and Apple in years 2010

   219   (first line), 2011 (second line) and 2012 (third line) you obtain:

   220 

   221 \begin{verbatim}

   222   List(List(Some(311.349976), Some(20.544939)), 

   223        List(Some(300.222351), Some(31.638695)),

   224        List(Some(330.555054), Some(39.478039)))

   225 \end{verbatim}\hfill[1 Marks]

   226 \end{itemize}

   227 

   228 \subsection*{Advanced Part 3 (4 Marks, continue in file drumb.scala)}

   229 

   230 \noindent

   231 \textbf{Tasks}

   232 

   233 \begin{itemize}  

   234 \item[(4)] Write a function that calculates the \emph{change factor} (delta)

   235   for how a stock price has changed from one year to the next. This is

   236   only well-defined, if the corresponding company has been traded in both

   237   years. In this case you can calculate

   238 

   239   \[

   240   \frac{price_{new} - price_{old}}{price_{old}}

   241   \]

   242 

   243   If the change factor is defined, you should return it

   244   as \texttt{Some(change\_factor)}; if not, you should return

   245   \texttt{None}.\mbox{}\hfill\mbox{[1 Mark]}

   246   

   247 \item[(5)] Write a function that calculates all change factors

   248   (deltas) for the prices we obtained under Part 2. For the running

   249   example of Google and Apple for the years 2010 to 2012 you should

   250   obtain 4 change factors:

   251 

   252 \begin{verbatim}  

   253   List(List(Some(-0.03573992567129673), Some(0.539975124774038))

   254        List(Some(0.10103412653643493), Some(0.24777709700099845)))

   255 \end{verbatim}

   256 

   257   That means Google did a bit badly in 2010, while Apple did very well.

   258   Both did OK in 2011. Make sure you handle the cases where a company is

   259   not listed in a year. In such cases the change factor should be \texttt{None}

   260   (see~(4)).

   261   \mbox{}\hfill\mbox{[1 Mark]}

   262 

   263 \item[(6)] Write a function that calculates the ``yield'', or

   264   balance, for one year for our portfolio.  This function takes the

   265   change factors, the starting balance and the year as arguments. If

   266   no company from our portfolio existed in that year, the balance is

   267   unchanged. Otherwise we invest in each existing company an equal

   268   amount of our balance. Using the change factors computed under Task

   269   2, calculate the new balance. Say we had \$100 in 2010, we would have

   270   received in our running example involving Google and Apple:

   271 

   272   \begin{verbatim}

   273   $50 * -0.03573992567129673 + $50 * 0.539975124774038

   274                                        = $25.21175995513706

   275   \end{verbatim}

   276 

   277   as profit for that year, and our new balance for 2011 is \$125 when

   278   converted to a \texttt{Long}.\mbox{}\hfill\mbox{[1 Mark]}

   279   

   280 \item[(7)] Write a function that calculates the overall balance

   281   for a range of years where each year the yearly profit is compounded to

   282   the new balances and then re-invested into our portfolio.

   283   For this use the function and results generated under (6).\\

   284   \mbox{}\hfill\mbox{[1 Mark]}

   285 \end{itemize}\medskip  

   286 

   287 

   288 

   289 \noindent

   290 \textbf{Test Data:} File \texttt{drumb.scala} contains two portfolios

   291 collected from the S\&P 500, one for blue-chip companies, including

   292 Facebook, Amazon and Baidu; and another for listed real-estate

   293 companies, whose names I have never heard of. Following the dumb

   294 investment strategy from 1978 until 2018 would have turned a starting

   295 balance of \$100 into roughly \$101,589 for real estate and a whopping

   296 \$1,587,528 for blue chips.  Note when comparing these results with your

   297 own calculations: there might be some small rounding errors, which

   298 when compounded lead to moderately different values.\bigskip

   299 

   300 \noindent

   301 \textbf{Hints:} useful string functions: \texttt{.startsWith(...)} for

   302 checking whether a string has a given prefix, \texttt{\_ ++ \_} for

   303 concatenating two strings; useful option functions: \texttt{.flatten}

   304 flattens a list of options such that it filters way all

   305 \texttt{None}'s, \texttt{Try(...) getOrElse ...} runs some code that

   306 might raise an exception---if yes, then a default value can be given;

   307 useful list functions: \texttt{.head} for obtaining the first element

   308 in a non-empty list, \texttt{.length} for the length of a

   309 list.\bigskip

   310 

   311 

   312 \noindent

   313 \textbf{Moral:} Reflecting on our assumptions, we are over-estimating

   314 our yield in many ways: first, who can know in 1978 about what will

   315 turn out to be a blue chip company.  Also, since the portfolios are

   316 chosen from the current S\&P 500, they do not include the myriad

   317 of companies that went bust or were de-listed over the years.

   318 So where does this leave our fictional character Mr T.~Drumb? Well, given

   319 his inheritance, a really dumb investment strategy would have done

   320 equally well, if not much better.\medskip

   321 

   322 \end{document}

   323 

   324 \newpage

   222 \subsection*{Advanced Part 3 (4 Marks)}

   433 

   223 

   434 

   224 A purely fictional character named Mr T.~Drumb inherited in 1978

   435 

   225 approximately 200 Million Dollar from his father. Mr Drumb prides

   436 

   226 himself to be a brilliant business man because nowadays it is

   227 estimated he is 3 Billion Dollar worth (one is not sure, of course,

   228 because Mr Drumb refuses to make his tax records public).

   229 

   230 Since the question about Mr Drumb's business acumen remains open,

   231 let's do a quick back-of-the-envelope calculation in Scala whether his

   232 claim has any merit. Let's suppose we are given \$100 in 1978 and we

   233 follow a really dumb investment strategy, namely:

   234 

   235 \begin{itemize}

   236 \item We blindly choose a portfolio of stocks, say some Blue-Chip stocks

   237   or some Real Estate stocks.

   238 \item If some of the stocks in our portfolio are traded in January of

   239   a year, we invest our money in equal amounts in each of these

   240   stocks.  For example if we have \$100 and there are four stocks that

   241   are traded in our portfolio, we buy \$25 worth of stocks

   242   from each.

   243 \item Next year in January, we look how our stocks did, liquidate

   244   everything, and re-invest our (hopefully) increased money in again

   245   the stocks from our portfolio (there might be more stocks available,

   246   if companies from our portfolio got listed in that year, or less if

   247   some companies went bust or were de-listed).

   248 \item We do this for 39 years until January 2017 and check what would

   249   have become out of our \$100.

   250 \end{itemize}

   251 

   252 \noindent

   253 Until Yahoo was bought by Altaba this summer, historical stock market

   254 data for such back-of-the-envelope calculations was freely available

   255 online. Unfortuantely nowadays this kind of data is difficult to

   256 obtain, unless you are prepared to pay extortionate prices or be

   257 severely rate-limited.  Therefore this coursework comes with a number

   258 of files containing CSV-lists with the historical stock prices for the

   259 companies in our portfolios. Use these files for the following

   260 tasks.\bigskip

   261 

   262 \noindent

   263 \textbf{Tasks (file drumb.scala):}

   264 

   265 \begin{itemize}

   266 \item[(1.a)] Write a function \texttt{get\_january\_data} that takes a

   267   stock symbol and a year as arguments. The function reads the

   268   corresponding CSV-file and returns the list of strings that start

   269   with the given year (each line in the CSV-list is of the form

   270   \texttt{year-01-someday,someprice}).

   271 

   272 \item[(1.b)] Write a function \texttt{get\_first\_price} that takes

   273   again a stock symbol and a year as arguments. It should return the

   274   first January price for the stock symbol in the given year. For this

   275   it uses the list of strings generated by

   276   \texttt{get\_january\_data}.  A problem is that normally a stock

   277   exchange is not open on 1st of January, but depending on the day of

   278   the week on a later day (maybe 3rd or 4th). The easiest way to solve

   279   this problem is to obtain the whole January data for a stock symbol

   280   and then select the earliest, or first, entry in this list. The

   281   stock price of this entry should be converted into a double.  Such a

   282   price might not exist, in case the company does not exist in the given

   283   year. For example, if you query for Google in January of 1980, then

   284   clearly Google did not exist yet.  Therefore you are asked to

   285   return a trade price as \texttt{Option[Double]}\ldots\texttt{None}

   286   will be the value for when no price exists.

   287 

   288 \item[(1.c)] Write a function \texttt{get\_prices} that takes a

   289   portfolio (a list of stock symbols), a years range and gets all the

   290   first trading prices for each year in the range. You should organise

   291   this as a list of lists of \texttt{Option[Double]}'s. The inner

   292   lists are for all stock symbols from the portfolio and the outer

   293   list for the years.  For example for Google and Apple in years 2010

   294   (first line), 2011 (second line) and 2012 (third line) you obtain:

   295 

   296 \begin{verbatim}

   297   List(List(Some(311.349976), Some(27.505054)), 

   298        List(Some(300.222351), Some(42.357094)),

   299        List(Some(330.555054), Some(52.852215)))

   300 \end{verbatim}\hfill[2 Marks]

   301  

   302 \item[(2.a)] Write a function that calculates the \emph{change factor} (delta)

   303   for how a stock price has changed from one year to the next. This is

   304   only well-defined, if the corresponding company has been traded in both

   305   years. In this case you can calculate

   306 

   307   \[

   308   \frac{price_{new} - price_{old}}{price_{old}}

   309   \]

   310 

   311   If the change factor is defined, you should return it

   312   as \texttt{Some(change factor)}; if not, you should return

   313   \texttt{None}.

   314   

   315 \item[(2.b)] Write a function that calculates all change factors

   316   (deltas) for the prices we obtained under Task 1. For the running

   317   example of Google and Apple for the years 2010 to 2012 you should

   318   obtain 4 change factors:

   319 

   320 \begin{verbatim}  

   321   List(List(Some(-0.03573992567129673), Some(0.5399749442411563))

   322         List(Some(0.10103412653643493), Some(0.2477771728154912)))

   323 \end{verbatim}

   324 

   325   That means Google did a bit badly in 2010, while Apple did very well.

   326   Both did OK in 2011. Make sure you handle the cases where a company is

   327   not listed in a year. In such cases the change factor should be \texttt{None}

   328   (see 2.a).\\

   329   \mbox{}\hfill\mbox{[1 Mark]}

   330 

   331 \item[(3.a)] Write a function that calculates the ``yield'', or

   332   balance, for one year for our portfolio.  This function takes the

   333   change factors, the starting balance and the year as arguments. If

   334   no company from our portfolio existed in that year, the balance is

   335   unchanged. Otherwise we invest in each existing company an equal

   336   amount of our balance. Using the change factors computed under Task

   337   2, calculate the new balance. Say we had \$100 in 2010, we would have

   338   received in our running example involving Google and Apple:

   339 

   340   \begin{verbatim}

   341   $50 * -0.03573992567129673 + $50 * 0.5399749442411563

   342                                        = $25.21175092849298

   343   \end{verbatim}

   344 

   345   as profit for that year, and our new balance for 2011 is \$125 when

   346   converted to a \texttt{Long}.

   347   

   348 \item[(3.b)] Write a function that calculates the overall balance

   349   for a range of years where each year the yearly profit is compounded to

   350   the new balances and then re-invested into our portfolio.\\

   351   \mbox{}\hfill\mbox{[1 Mark]}

   352 \end{itemize}\medskip  

   353 

   354 \noindent

   355 \textbf{Test Data:} File \texttt{drumb.scala} contains two portfolios

   356 collected from the S\&P 500, one for blue-chip companies, including

   357 Facebook, Amazon and Baidu; and another for listed real-estate

   358 companies, whose names I have never heard of. Following the dumb

   359 investment strategy from 1978 until 2017 would have turned a starting

   360 balance of \$100 into roughly \$30,895 for real estate and a whopping

   361 \$349,597 for blue chips.  Note when comparing these results with your

   362 own calculations: there might be some small rounding errors, which

   363 when compounded lead to moderately different values.\bigskip

   364 

   365 \noindent

   366 \textbf{Hints:} useful string functions: \texttt{.startsWith(...)} for

   367 checking whether a string has a given prefix, \texttt{\_ ++ \_} for

   368 concatenating two strings; useful option functions: \texttt{.flatten}

   369 flattens a list of options such that it filters way all

   370 \texttt{None}'s, \texttt{Try(...) getOrElse ...} runs some code that

   371 might raise an exception---if yes, then a default value can be given;

   372 useful list functions: \texttt{.head} for obtaining the first element

   373 in a non-empty list, \texttt{.length} for the length of a

   374 list.\bigskip

   375 

   376 

   377 \noindent

   378 \textbf{Moral:} Reflecting on our assumptions, we are over-estimating

   379 our yield in many ways: first, who can know in 1978 about what will

   380 turn out to be a blue chip company.  Also, since the portfolios are

   381 chosen from the current S\&P 500, they do not include the myriad

   382 of companies that went bust or were de-listed over the years.

   383 So where does this leave our fictional character Mr T.~Drumb? Well, given

   384 his inheritance, a really dumb investment strategy would have done

   385 equally well, if not much better.\medskip

   386 

   387 

   388 \end{document}