# HG changeset patch # User Christian Urban # Date 1510106814 0 # Node ID b1a51285de7eca3bca4bc55cc456338972284ace # Parent 166bb9b6b20a4def4ebd7adacdf35490d1241610 updated diff -r 166bb9b6b20a -r b1a51285de7e cws/cw01.pdf Binary file cws/cw01.pdf has changed diff -r 166bb9b6b20a -r b1a51285de7e cws/cw01.tex --- a/cws/cw01.tex Tue Nov 07 14:17:21 2017 +0000 +++ b/cws/cw01.tex Wed Nov 08 02:06:54 2017 +0000 @@ -138,7 +138,7 @@ This part is about web-scraping and list-processing in Scala. It uses online data about the per-capita alcohol consumption for each country -(per year?), and a file with the data about the population size of +(per year?), and a file containing the data about the population size of each country. From this data you are supposed to estimate how many litres of pure alcohol are consumed worldwide.\bigskip @@ -156,7 +156,8 @@ \noindent Your function should take a string (the URL) as input, and produce a list of strings as output, where each string is one line in -the corresponding CSV-list. This list should contain 194 lines.\medskip +the corresponding CSV-list. This list from the URL above should +contain 194 lines.\medskip \noindent Write another function that can read the file \texttt{population.csv} @@ -193,7 +194,7 @@ Write another function that processes the population size list. This is already of the form country name and population size.\footnote{Your friendly lecturer already did the messy processing for you from the - Worldbank database, see \url{https://github.com/datasets/population/tree/master/data}.} Again, split the + Worldbank database, see \url{https://github.com/datasets/population/tree/master/data} for the original.} Again, split the strings according to the commas. However, this time generate a \texttt{Map} from country names to population sizes.\hfill[1 Mark] @@ -202,8 +203,8 @@ country. From this generate next a sorted(!) list of the overall alcohol consumption for each country. The list should be sorted from highest alcohol consumption to lowest. The difficulty is that the - data is scrapped off from ``random'' sources on the Internet and - annoyingly the spelling of some country names does not always agree in the + data is scraped off from ``random'' sources on the Internet and + annoyingly the spelling of some country names does not always agree in both lists. For example the alcohol list contains \texttt{Bosnia-Herzegovina}, while the population writes this country as \texttt{Bosnia and Herzegovina}. In your sorted @@ -211,20 +212,21 @@ exact country name is also in the population size list. This means you can ignore countries like Bosnia-Herzegovina from the overall alcohol consumption. There are 177 countries where the names - agree. The UK is ranked 10th on this list with + agree. The UK is ranked 10th on this list by consuming 671,976,864 Litres of pure alcohol each year.\medskip \noindent Finally, write another function that takes an integer, say \texttt{n}, as argument. You can assume this integer is between 0 - and 177. The function should use the sorted list from above. It returns - a triple, where the first component is the sum of the alcohol - consumption in all countries (on the list); the second component is - the sum of the \texttt{n}-highest alcohol consumers on the list; and - the third component is the percentage the \texttt{n}-highest alcohol - consumers feast on with respect to the the world consumption. You will - see that according to our data, 164 countries (out of 177) gobble up 100\% - of the world alcohol consumption.\hfill\mbox{[1 Mark]} + and 177 (the number of countries in the sorted list above). The + function should return a triple, where the first component is the + sum of the alcohol consumption in all countries (on the list); the + second component is the sum of the \texttt{n}-highest alcohol + consumers on the list; and the third component is the percentage the + \texttt{n}-highest alcohol consumers drink with respect to the + the world consumption. You will see that according to our data, 164 + countries (out of 177) gobble up 100\% of the World alcohol + consumption.\hfill\mbox{[1 Mark]} \end{itemize} \noindent @@ -240,7 +242,7 @@ \newpage -\subsection*{Advanced Part 3 (3 Marks)} +\subsection*{Advanced Part 3 (4 Marks)} A purely fictional character named Mr T.~Drumb inherited in 1978 approximately 200 Million Dollar from his father. Mr Drumb prides @@ -265,53 +267,57 @@ 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 de-listed). -\item We do this for 38 years until January 2017 and check what would + some companies went bust or were de-listed). +\item We do this for 39 years until January 2017 and check what would have become out of our \$100. \end{itemize} - -\medskip +\noindent +Until Yahoo was bought by Altaba this summer, historical stock market +data was available online for free, but nowadays this kind of data is +difficult to obtain unless you are prepared to pay extortionate prices +or be severely rate-limited. Therefore this coursework comes with a +number of files containing CSV-lists about stock prices of +various companies. Use these files for the following tasks.\bigskip \noindent \textbf{Tasks (file drumb.scala):} \begin{itemize} -\item[(1.a)] Write a function that queries the Yahoo financial data - service and obtains the first trade (adjusted close price) of a - stock symbol and a year. 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 as - CSV-list and then select the earliest entry in this list. For this - you can specify a date range with the Yahoo service. For example if - you want to obtain all January data for Google in 2000, you can form - the query:\mbox{}\\[-8mm] +\item[(1.a)] Write a function \texttt{get\_january\_data} that takes a + stock symbol and a year as argument. 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{year-01-someday,someprice}. - \begin{center}\small - \mbox{\url{http://ichart.yahoo.com/table.csv?s=GOOG&a=0&b=1&c=2000&d=1&e=1&f=2000}} - \end{center} - - For other companies and years, you need to change the stock symbol - (\texttt{GOOG}) and the year \texttt{2000} (in the \texttt{c} and - \texttt{f} argument of the query). Such a request might fail, if the - company does not exist during this period. For example, if you query - for Google in January of 1980, then clearly Google did not exists yet. - Therefore you are asked to return a trade price as +\item[(1.b)] Write a function \texttt{get\_first\_price} that takes + again stock symbol and a year as arguments. It should return the + first January price for the stock symbol in the year. For this it + obtains 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 entry in this list. This entry should + be converted into a double. Such a price might not exist, if 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 exists + yet. Therefore you are asked to return a trade price as \texttt{Option[Double]}. -\item[(1.b)] Write a function that takes a portfolio (a list of stock symbols), - a years range and gets all the first trading prices for each year. 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: +\item[(1.c)] 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. 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(313.062468), Some(27.847252)), - List(Some(301.873641), Some(42.884065)), - List(Some(332.373186), Some(53.509768))) -\end{verbatim}\hfill[1 Mark] + List(List(Some(311.349976), Some(27.505054)), + List(Some(300.222351), Some(42.357094)), + List(Some(330.555054), Some(52.852215))) +\end{verbatim}\hfill[2 Marks] \item[(2.a)] 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 @@ -329,8 +335,8 @@ obtain 4 change factors: \begin{verbatim} - List(List(Some(-0.03573991820699504), Some(0.5399747522663995)) - List(Some(0.10103414428290529), Some(0.24777742035415723))) + List(List(Some(-0.03573992567129673), Some(0.5399749442411563)) + List(Some(0.10103412653643493), Some(0.2477771728154912))) \end{verbatim} That means Google did a bit badly in 2010, while Apple did very well. @@ -346,8 +352,8 @@ received in our running example \begin{verbatim} - $50 * -0.03573991820699504 + $50 * 0.5399747522663995 - = $25.211741702970222 + $50 * -0.03573992567129673 + $50 * 0.5399749442411563 + = $25.21175092849298 \end{verbatim} as profit for that year, and our new balance for 2011 is \$125 when @@ -361,10 +367,13 @@ \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 2016 would have turned a starting balance of \$100 -into \$23,794 for real estate and a whopping \$524,609 for blue chips.\medskip +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 2017 would have turned a starting +balance of \$100 into roughly \$30,895 for real estate and a whopping +\$188,172 for blue chips. Note when comparing these results with your +own results: there might be some small rounding errors, which when +compounded, lead to moderately different values.\medskip \noindent \textbf{Moral:} Reflecting on our assumptions, we are over-estimating @@ -374,7 +383,10 @@ 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. +equally well, if not much better.\medskip + +\noindent +\textbf{Hints:} \end{document} %%% Local Variables: diff -r 166bb9b6b20a -r b1a51285de7e progs/drumb_sol.scala --- a/progs/drumb_sol.scala Tue Nov 07 14:17:21 2017 +0000 +++ b/progs/drumb_sol.scala Wed Nov 08 02:06:54 2017 +0000 @@ -1,10 +1,13 @@ -// Advanvced Part 3 about really dumb investing strategy -//======================================================= +// Advanvced Part 3 about a really dumb investment strategy +//========================================================== + +object CW6c { + //two test portfolios -val blchip_portfolio = List("GOOG", "AAPL", "MSFT", "IBM", "FB", "YHOO", "AMZN", "BIDU") -val rstate_portfolio = List("PLD", "PSA", "AMT", "AIV", "AVB", "BXP", "CBG", "CCI", +val blchip_portfolio = List("GOOG", "AAPL", "MSFT", "IBM", "FB", "AMZN", "BIDU") +val rstate_portfolio = List("PLD", "PSA", "AMT", "AIV", "AVB", "BXP", "CCI", "DLR", "EQIX", "EQR", "ESS", "EXR", "FRT", "GGP", "HCP") // (1) The function below should obtain the first trading price @@ -14,22 +17,25 @@ // // and extracting the first January Adjusted Close price in a year. + import io.Source import scala.util._ -def get_yahoo_page(url: String): Option[List[String]] = { - Try(Some(Source.fromURL(url)("ISO-8859-1").getLines.toList)). - getOrElse { None } +def get_january_data(symbol: String, year: Int) : List[String] = + Source.fromFile(symbol ++ ".csv")("ISO-8859-1").getLines.toList.filter(_.startsWith(year.toString)) + + +get_trading_data("FB", 2015) +get_trading_data("GOOG", 2010).head + +def get_first_price(symbol: String, year: Int) : Option[Double] = { + val data = Try(Some(get_january_data(symbol, year).head)) getOrElse None + data.map(_.split(",").toList(1).toDouble) } -def get_first_price(symbol: String, year: Int): Option[Double] = { - //println(s"download..${symbol} at ${year}") - val year_string = year.toString - val date_string = s"&a=0&b=1&c=${year_string}&d=1&e=1&f=${year_string}" - val url = """http://ichart.yahoo.com/table.csv?s=""" + symbol + date_string - val data = get_yahoo_page(url) - data.map(_.last.split(",").toList(6).toDouble) -} +get_first_price("GOOG", 1980) +get_first_price("GOOG", 2010) +get_first_price("FB", 2014) // Complete the function below that obtains all first prices @@ -43,7 +49,7 @@ // test case val p_fb = get_prices(List("FB"), 2012 to 2014) -val p = get_prices(List("GOOG", "AAPL"), 2005 to 2012) +val p = get_prices(List("GOOG", "AAPL"), 2010 to 2012) val tt = get_prices(List("IBM", "BIDU"), 2004 to 2008) @@ -51,7 +57,7 @@ // a price in year n and a price in year n+1. The second function calculates // all change factors for all prices (from a portfolio). -def get_delta(price_old: Option[Double], price_new: Option[Double]): Option[Double] = { +def get_delta(price_old: Option[Double], price_new: Option[Double]) : Option[Double] = { (price_old, price_new) match { case (Some(x), Some(y)) => Some((y - x) / x) case _ => None @@ -85,13 +91,15 @@ } } -yearly_yield(ttd, 100, 0) +yearly_yield(d, 100, 0) yearly_yield(ttd, 100, 1) yearly_yield(ttd, 100, 2) -yearly_yield(ttd, 100, 3) assert((yearly_yield(ttd, 100, 0) - 107).abs <= 2) - assert((yearly_yield(ttd, 100, 1) - 85).abs <= 2) - assert((yearly_yield(ttd, 100, 2) - 156).abs <= 2) - assert((yearly_yield(ttd, 100, 3) - 210).abs <= 2) +yearly_yield(ttd, 100, 3) + +assert((yearly_yield(ttd, 100, 0) - 107).abs <= 2) +assert((yearly_yield(ttd, 100, 1) - 85).abs <= 2) +assert((yearly_yield(ttd, 100, 2) - 156).abs <= 2) +assert((yearly_yield(ttd, 100, 3) - 210).abs <= 2) @@ -123,8 +131,8 @@ //test cases for the two portfolios given above -println("Real data: " + investment(rstate_portfolio, 1978 to 2016, 100)) -println("Blue data: " + investment(blchip_portfolio, 1978 to 2016, 100)) +println("Real data: " + investment(rstate_portfolio, 1978 to 2017, 100)) +println("Blue data: " + investment(blchip_portfolio, 1978 to 2017, 100)) investment(List("IBM", "BIDU"), 2004 to 2008, 100) @@ -181,3 +189,4 @@ yearly_yield(rs_d, 126, 4) yearly_yield(rs_d, 169, 5) +} diff -r 166bb9b6b20a -r b1a51285de7e templates/AAPL.csv --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/templates/AAPL.csv Wed Nov 08 02:06:54 2017 +0000 @@ -0,0 +1,765 @@ +Date,Adj Close +1981-01-02,0.505916 +1981-01-05,0.494918 +1981-01-06,0.472922 +1981-01-07,0.452758 +1981-01-08,0.443594 +1981-01-09,0.467423 +1981-01-12,0.463757 +1981-01-13,0.447260 +1981-01-14,0.449092 +1981-01-15,0.458258 +1981-01-16,0.454591 +1981-01-19,0.482087 +1981-01-20,0.467423 +1981-01-21,0.476588 +1981-01-22,0.482087 +1981-01-23,0.480254 +1981-01-26,0.472922 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+2017-01-30,209.006058 +2017-01-31,209.015762 diff -r 166bb9b6b20a -r b1a51285de7e templates/alcohol.scala --- a/templates/alcohol.scala Tue Nov 07 14:17:21 2017 +0000 +++ b/templates/alcohol.scala Wed Nov 08 02:06:54 2017 +0000 @@ -6,64 +6,60 @@ import io.Source import scala.util._ -def get_csv_page(url: String) : List[String] = - Source.fromURL(url)("ISO-8859-1").getLines.toList - -def get_csv_file(file: String) : List[String] = - Source.fromFile(file)("ISO-8859-1").getLines.toList - - val url_alcohol = "https://raw.githubusercontent.com/fivethirtyeight/data/master/alcohol-consumption/drinks.csv" val file_population = "population.csv" -get_csv_page(url_alcohol) -get_csv_file(file_population) -get_csv_page(url_alcohol).size -get_csv_file(file_population).size +//(1) Complete the get_csv_page function below. It takes the URL-string +// as argument and generates a list of strings corresponing to each +// line in the csv list. The URL url_alcohol is one possible argument. -val alcs = get_csv_page(url_alcohol) -val pops = get_csv_file(file_population) +//def get_csv_page(url: String) : List[String] = ... -def process_alcs(lines: List[String]) : List[(String, Double)] = - for (l <- lines) yield { - val entries = l.split(",").toList - (entries(0), entries(4).toDouble) - } +// Complete the get_csv_file function below. It takes a file-string +// as argument and reads the content of the given file. Like above +// it should generates a list of strings corresponing to each +// line in the csv-list. The filename file_population is one possible +// argument. -def process_pops(lines: List[String]) : Map[String, Long] = - (for (l <- lines) yield { - val entries = l.split(",").toList - (entries(0), entries(1).toLong) - }).toMap +//def get_csv_file(file: String) : List[String] = ... + -def sorted_country_consumption() : List[(String, Long)] = { - val alcs2 = process_alcs(alcs.drop(1)) - val pops2 = process_pops(pops.drop(1)) - val cons_list = - for ((cname, cons) <- alcs2; - if pops2.isDefinedAt(cname)) yield (cname, (cons * pops2(cname)).toLong) - cons_list.sortBy(_._2).reverse -} +//(2) Complete the functions that process the csv-lists. For +// process_alcs extract the country name (as String) and the +// pure alcohol consumption (as Double). For process_pops +// generate a Map of Strings (country names) to Long numbers +// (population size). -sorted_country_consumption().take(10) -sorted_country_consumption().size +//def process_alcs(lines: List[String]) : List[(String, Double)] = ... -def percentage(n: Int) : (Long, Long, Double) = { - val cons_list = sorted_country_consumption() - val sum_n = cons_list.take(n).map(_._2).sum - val sum_all = cons_list.map(_._2).sum - val perc = (sum_n.toDouble / sum_all.toDouble) * 100.0 - (sum_all, sum_n, perc) -} +//def process_pops(lines: List[String]) : Map[String, Long] = ... + -percentage(10) -percentage(164) +//(3) Calculate for each country the overall alcohol_consumption using +// the data from the alcohol list and the population sizes list. You +// should only include countries on the alcohol list that are also +// (with the exact name) on the population sizes list. Note that +// the spelling of some names in the alcohol list differs from the +// population sizes list. Sort the resulting list according to the +// country with the highest alcohol consumption to the country +// with the lowest alcohol consumption. + +//def sorted_country_consumption() : List[(String, Long)] = ... + + +// Calculate the world consumption of pure alcohol of all countries, which +// should be the first element in the tuple below. The second element is +// the overall consumption of the first n countries in the sorted list +// from above; and finally the double should be the percentage of the +// first n countries of the the world consumption of alcohol. + +//def percentage(n: Int) : (Long, Long, Double) = ... } diff -r 166bb9b6b20a -r b1a51285de7e templates/collatz.scala --- a/templates/collatz.scala Tue Nov 07 14:17:21 2017 +0000 +++ b/templates/collatz.scala Wed Nov 08 02:06:54 2017 +0000 @@ -10,7 +10,7 @@ // performs the recursion. The function should expect // arguments in the range of 1 to 1 Million. -//def collatz(n: Long): ... = ... +//def collatz(n: Long) : Long = ... //(2) Complete the collatz bound function below. It should @@ -22,7 +22,7 @@ // the maximum number of steps and the second is the // corresponding number. -//def collatz_max(bnd: Long): (Long, Long) = ... +//def collatz_max(bnd: Long) : (Long, Long) = ... } diff -r 166bb9b6b20a -r b1a51285de7e templates/drumb.scala --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/templates/drumb.scala Wed Nov 08 02:06:54 2017 +0000 @@ -0,0 +1,69 @@ +// Advanvced Part 3 about a really dumb investment strategy +//========================================================== + +object CW6c { + + +//two test portfolios + +val blchip_portfolio = List("GOOG", "AAPL", "MSFT", "IBM", "FB", "YHOO", "AMZN", "BIDU") +val rstate_portfolio = List("PLD", "PSA", "AMT", "AIV", "AVB", "BXP", "CBG", "CCI", + "DLR", "EQIX", "EQR", "ESS", "EXR", "FRT", "GGP", "HCP") + + +// (1) The function below should obtain the first trading price +// for a stock symbol by using the query +// +// http://ichart.yahoo.com/table.csv?s=<>&a=0&b=1&c=<>&d=1&e=1&f=<> +// +// and extracting the first January Adjusted Close price in a year. + +//def get_january_data(symbol: String, year: Int) : List[String] = ... + +//def get_first_price(symbol: String, year: Int) : Option[Double] = ... + + +// Complete the function below that obtains all first prices +// for the stock symbols from a portfolio for the given +// range of years + +//def get_prices(portfolio: List[String], years: Range): List[List[Option[Double]]] = ... + +// test case +//val p = get_prices(List("GOOG", "AAPL"), 2010 to 2012) + + +// (2) The first function below calculates the change factor (delta) between +// a price in year n and a price in year n+1. The second function calculates +// all change factors for all prices (from a portfolio). + +//def get_delta(price_old: Option[Double], price_new: Option[Double]): Option[Double] = ... + +//def get_deltas(data: List[List[Option[Double]]]): List[List[Option[Double]]] = ... + +// test case using the prices calculated above +//val d = get_deltas(p) + + +// (3) Write a function that given change factors, a starting balance and a year +// calculates the yearly yield, i.e. new balanace, according to our dump investment +// strategy. Another function calculates given the same data calculates the +// compound yield up to a given year. Finally a function combines all +// calculations by taking a portfolio, a range of years and a start balance +// as arguments. + +//def yearly_yield(data: List[List[Option[Double]]], balance: Long, year: Int): Long = ... + +//test case +//yearly_yield(d, 100, 0) + +//def compound_yield(data: List[List[Option[Double]]], balance: Long, year: Int): Long = ... + +//def investment(portfolio: List[String], years: Range, start_balance: Long): Long = ... + +//test cases for the two portfolios given above + +//investment(rstate_portfolio, 1978 to 2016, 100) +//investment(blchip_portfolio, 1978 to 2016, 100) + +} diff -r 166bb9b6b20a -r b1a51285de7e templates/drumb.scala~ --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/templates/drumb.scala~ Wed Nov 08 02:06:54 2017 +0000 @@ -0,0 +1,62 @@ +// Advanvced Part 3 about really dumb investing strategy +//======================================================= + +//two test portfolios + +val blchip_portfolio = List("GOOG", "AAPL", "MSFT", "IBM", "FB", "YHOO", "AMZN", "BIDU") +val rstate_portfolio = List("PLD", "PSA", "AMT", "AIV", "AVB", "BXP", "CBG", "CCI", + "DLR", "EQIX", "EQR", "ESS", "EXR", "FRT", "GGP", "HCP") + + +// (1) The function below should obtain the first trading price +// for a stock symbol by using the query +// +// http://ichart.yahoo.com/table.csv?s=<>&a=0&b=1&c=<>&d=1&e=1&f=<> +// +// and extracting the first January Adjusted Close price in a year. + +def get_first_price(symbol: String, year: Int): Option[Double] = ... + +// Complete the function below that obtains all first prices +// for the stock symbols from a portfolio for the given +// range of years + +def get_prices(portfolio: List[String], years: Range): List[List[Option[Double]]] = ... + +// test case +//val p = get_prices(List("GOOG", "AAPL"), 2010 to 2012) + + +// (2) The first function below calculates the change factor (delta) between +// a price in year n and a price in year n+1. The second function calculates +// all change factors for all prices (from a portfolio). + +def get_delta(price_old: Option[Double], price_new: Option[Double]): Option[Double] = ... + +def get_deltas(data: List[List[Option[Double]]]): List[List[Option[Double]]] = ... + +// test case using the prices calculated above +//val d = get_deltas(p) + + +// (3) Write a function that given change factors, a starting balance and a year +// calculates the yearly yield, i.e. new balanace, according to our dump investment +// strategy. Another function calculates given the same data calculates the +// compound yield up to a given year. Finally a function combines all +// calculations by taking a portfolio, a range of years and a start balance +// as arguments. + +def yearly_yield(data: List[List[Option[Double]]], balance: Long, year: Int): Long = ... + +//test case +//yearly_yield(d, 100, 0) + +def compound_yield(data: List[List[Option[Double]]], balance: Long, year: Int): Long = ... + +def investment(portfolio: List[String], years: Range, start_balance: Long): Long = ... + + +//test cases for the two portfolios given above +//investment(rstate_portfolio, 1978 to 2016, 100) +//investment(blchip_portfolio, 1978 to 2016, 100) +