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\section*{Core Part 6 (Scala)}

\IMPORTANT{This part is about Scala. It is due on \cwSIXa{} at 4pm and worth 7\%.}

\noindent

Also note that the running time of each part will be restricted to a

maximum of 30 seconds on my laptop.

\DISCLAIMER{}

\subsection*{Reference Implementation}

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

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

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

apply an automated marking script to them.\medskip

\noindent

In addition, the Scala coursework comes with a reference implementation

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

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

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

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

the functions ???

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

\texttt{CW6b}.

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

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

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

$ scala -cp collatz.jar

scala> CW6a.collatz(6)

...

scala> CW6a.collatz_max(6)

...

\end{lstlisting}%$

\subsection*{Hints}

\noindent

\textbf{For Core Part:} useful string functions:

\texttt{.startsWith(...)} for checking whether a string has a given

prefix, \texttt{\_ ++ \_} for concatenating two strings; useful option

functions: \texttt{.flatten} flattens a list of options such that it

filters way all \texttt{None}'s, \texttt{Try(...).getOrElse ...} runs

some code that might raise an exception---if yes, then a default value

can be given; useful list functions: \texttt{.head} for obtaining the

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

a list; \texttt{.filter(...)} for filtering out elements in a list;

\texttt{.getLines.toList} for obtaining a list of lines from a file;

\texttt{.split(",").toList} for splitting strings according to a

comma.\bigskip

\noindent

\textbf{Note!} Fortunately Scala supports operator overloading. But

make sure you understand the difference between \texttt{100 / 3} and

\texttt{100.0 / 3}!

\newpage

\subsection*{Core Part (7 Marks, file drumb.scala)}

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

approximately 200 Million Dollar from his father. Mr Drumb prides

himself to be a brilliant business man because nowadays it is

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

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

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

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

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

follow a really dumb investment strategy, namely:

\begin{itemize}

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

  or some Real Estate stocks.

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

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

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

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

  from each. (Be careful to also test cases where you trade with 3 stocks.) 

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

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

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

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

  some companies went bust or were de-listed).

\item We do this for 41 years until January 2019 and check what would

  have become out of our \$100.

\end{itemize}

\noindent

Until Yahoo was bought by Altaba a few years ago, historical stock market

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

online. Unfortunately nowadays this kind of data is more difficult to

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

severely rate-limited.  Therefore this part comes with a number

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

companies in our portfolios. Use these files for the following

tasks.\bigskip

\newpage

\noindent

\textbf{Tasks}

\begin{itemize}

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

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

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

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

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

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

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

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

  it uses the list of strings generated by

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

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

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

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

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

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

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

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

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

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

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

  price.\hfill[1 Mark]

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

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

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

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

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

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

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

\begin{verbatim}

  List(List(Some(312.204773), Some(26.782711)), 

       List(Some(301.0466),   Some(41.244694)), 

       List(Some(331.462585), Some(51.464207))))

\end{verbatim}\hfill[1 Mark]

%\end{itemize}

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

%

%\noindent

%\textbf{Tasks}

%\begin{itemize}  

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

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

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

  years. In this case you can calculate

  \[

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

  \]

  If the change factor is defined, you should return it

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

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

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

  (deltas) for the prices we obtained in Task (2). For the running

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

  obtain 4 change factors:

\begin{verbatim}

  List(List(Some(-0.03573991804411003), Some(0.539974575389325)), 

       List(Some(0.10103414222249969), Some(0.24777764141006836)))

\end{verbatim}

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

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

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

  (recall Task~(4)).

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

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

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

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

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

  unchanged. Otherwise we invest in each existing company an equal

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

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

  received in our running example involving Google and Apple:

  \begin{verbatim}

  $50 * -0.03573991804411003 + $50 * 0.539974575389325

                                       = $25.21173286726075

  \end{verbatim}

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

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

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

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

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

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

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

\end{itemize}\medskip  

\noindent

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

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

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

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

investment strategy from 1978 until 2019 would have turned a starting

balance of \$100 into roughly \$39,162 for real estate and a whopping

\$462,199 for blue chips.  Note when comparing these results with your

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

when compounded lead to moderately different values.\bigskip

\noindent

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

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

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

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

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

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

his inheritance, a really dumb investment strategy would have done

equally well, if not much better.\medskip

\end{document}