Signal Portfolio

#r "nuget: FSharp.Data, 5.0.2"
#r "nuget: FSharp.Stats, 0.5.0"
#r "nuget: Plotly.NET, 3.*"
#r "nuget: Plotly.NET.Interactive, 3.*"

open System
open FSharp.Data
open Plotly.NET
open FSharp.Stats

Load Data

First, make sure that you're referencing the correct files.

Here I'm assuming that you have a class folder with this signal-exploration.ipynb notebook and a data folder inside of it. The folder hierarchy would look like below where you have the below files and folders accessible:

/class
    signal-portfolio.ipynb
    id_and_return_data.csv
    zero_trades_252d.csv

First, make sure that our working directory is the source file directory.

We will use the portfolio module

We will use the Portfolio module. Make sure that you load this code

#r "nuget: NovaSBE.Finance, 0.5.0"
open NovaSBE.Finance
open NovaSBE.Finance.Portfolio

Data files

We assume the id_and_return_data.csv file and the signal csv file are in the same folder as the notebook. In this example the signal file is be_me.csv. You should replace that file name with your signal file name.

let [<Literal>] IdAndReturnsFilePath = "id_and_return_data.csv"
let [<Literal>] MySignalFilePath = "be_me.csv"
let strategyName = "book to market"

If my paths are correct, then this code should read the first few lines of the files. If it doesn't show the first few lines, fix the above file paths.

IO.File.ReadLines(IdAndReturnsFilePath) |> Seq.truncate 5

IO.File.ReadLines(MySignalFilePath) |> Seq.truncate 5

Assuming the paths are defined correctly and you saw the first 5 rows above, we can now read the data using the CSV provider that parses the fields in the file.

First define the Csv types from the sample files:

type IdAndReturnsType = 
    CsvProvider<Sample=IdAndReturnsFilePath,
                ResolutionFolder=ResolutionFolder>

type MySignalType = 
    CsvProvider<MySignalFilePath,
                ResolutionFolder=ResolutionFolder>

Now read in the data.

let idAndReturnsCsv = IdAndReturnsType.GetSample()

let mySignalCsv = MySignalType.GetSample()

Columns in the idAndReturnsCsv are:

idAndReturnsCsv.Headers

Columns in the mySignalCsv are:

mySignalCsv.Headers

There are a lot of columns in the id and returns csv. You can look at the data documentation to figure out what they are.

Put the rows into a list (we're more familiar with lists).

let idAndReturnsRows = idAndReturnsCsv.Rows |> Seq.toList
let mySignalRows = mySignalCsv.Rows |> Seq.toList

We want to be able to look up idAndReturn data and signal data using a security's ID and month. To do that, we create a Map collection where the key is a tuple of the security id and month.

In this dataset, we'll use row.Id as the identifier. We'll assign it to the Other SecurityId case, because it's a dataset specific one.
In this dataset, the Eom variable defines the "end of month".
The returns are for the month ending in EOM.
The signals are "known" as of EOM. So you can use them on/after EOM. We'll form portfolios in the month ending EOM; that's the FormationMonth.

let msfBySecurityIdAndMonth =
    idAndReturnsRows
    |> List.map(fun row -> 
        let id = Other row.Id
        let month = DateTime(row.Eom.Year,row.Eom.Month,1)
        let key = id, month
        key, row)
    |> Map    

let signalBySecurityIdAndMonth =
    mySignalRows
    |> List.choose(fun row -> 
        // we'll use choose to drop the security if the signal is None.
        // The signal is None when it is missing.
        match row.Signal with
        | None -> None // choose will drop these None observations
        | Some signal ->
            let id = Other row.Id
            let month = DateTime(row.Eom.Year,row.Eom.Month,1)
            let key = id, month
            // choose will convert Some(key,signal) into
            // (key,signal) and keep that.
            Some (key, signal))
    |> Map

The securitiesByFormationMonth that we'll use to define our investment universe.

let securitiesByFormationMonth =
    idAndReturnsRows
    |> List.groupBy(fun x -> DateTime(x.Eom.Year, x.Eom.Month,1))
    |> List.map(fun (ym, obsThisMonth) -> 
        let idsThisMonth = [ for x in obsThisMonth do Other x.Id ]
        ym, idsThisMonth)
    |> Map

let getInvestmentUniverse formationMonth =
    match Map.tryFind formationMonth securitiesByFormationMonth with
    | Some securities -> 
        { FormationMonth = formationMonth 
          Securities = securities }
    | None -> failwith $"{formationMonth} is not in the date range"

Checking universe

let testUniverseObs = getInvestmentUniverse (DateTime(2015,4,1))

Formation month.

testUniverseObs.FormationMonth

First few securities

testUniverseObs.Securities[0..4]

Now I want to be able to get my signal. We're going to assume here that a "high" signal predicts high returns. If you have a signal where a "high" signal predicts low returns, you can multiply the signal by -1.0 below.

let getMySignal (securityId, formationMonth) =
    match Map.tryFind (securityId, formationMonth) signalBySecurityIdAndMonth with
    | None -> None
    | Some signal ->
        Some { SecurityId = securityId 
               // if a high signal means low returns,
               // use `-signal` here instead of `signal`
               Signal = signal }

Test it

[ for securityId in testUniverseObs.Securities[0..4] do
    let testObs = (securityId, testUniverseObs.FormationMonth)
    getMySignal testObs ]

A function to do it for the whole investment universe.

let getMySignals (investmentUniverse: InvestmentUniverse) =
    let listOfSecuritySignals =
        investmentUniverse.Securities
        |> List.choose(fun security -> 
            getMySignal (security, investmentUniverse.FormationMonth))    
    
    { FormationMonth = investmentUniverse.FormationMonth 
      Signals = listOfSecuritySignals }

And I should be able to get my market capitalization

msfBySecurityIdAndMonth
|> Map.toList
|> List.take 3
|> List.map (fun ((id, month), row) -> id, row.MarketEquity)

Now a function to do this.

let getMarketCap (security, formationMonth) =
    match Map.tryFind (security, formationMonth) msfBySecurityIdAndMonth with
    | None -> None
    | Some row -> 
        match row.MarketEquity with
        | None -> None
        | Some me -> Some (security, me)

And I should be able to get my returns.

let getSecurityReturn (security, formationMonth) =
    // If the security has a missing return, assume that we got 0.0.
    // Note: If we were doing excess returns, we would need 0.0 - rf.
    let missingReturn = 0.0
    match Map.tryFind (security, formationMonth) msfBySecurityIdAndMonth with
    | None -> security, missingReturn
    | Some x ->  
        match x.Ret with 
        | None -> security, missingReturn
        | Some r -> security, r

The data is already filtered to valid securities based on the data documentation section 1.2, "How to use the data", from the paper the data came from.

Define sample months

let startSample = 
    idAndReturnsRows
    |> List.map(fun row -> DateTime(row.Eom.Year,row.Eom.Month,1))
    |> List.min

let endSample = 
    let lastMonthWithData = 
        idAndReturnsRows
        |> Seq.map(fun row -> DateTime(row.Eom.Year,row.Eom.Month,1))
        |> Seq.max
    // The end of sample is the last month when we have returns.
    // So the last month when we can form portfolios is one month
    // before that.
    lastMonthWithData.AddMonths(-1) 

let sampleMonths = getSampleMonths (startSample, endSample)

Strategy function

let formStrategy ym =
    ym
    |> getInvestmentUniverse
    |> getMySignals
    |> assignSignalSort strategyName 3
    |> Seq.toList
    |> List.map (giveValueWeights getMarketCap)
    |> List.map (getPortfolioReturn getSecurityReturn)

Your strategy portfolios

let doParallel = true
let portfolios =
    if doParallel then
        sampleMonths
        |> List.toArray
        |> Array.Parallel.map formStrategy
        |> Array.toList
        |> List.collect id
    else
        sampleMonths
        |> List.collect formStrategy

A few of the portfolio return observations.

portfolios[..2]

These portfolios were value-weighted. Can you do a version that is equal-weighted?.

let giveEqualWeights (port: AssignedPortfolio): Portfolio =
    let makePosition securityId weight : Position =
        { SecurityId = securityId; Weight = weight }
    
    { FormationMonth = failwith "unimplemented"
      Name = failwith "unimplemented"
      Index = failwith "unimplemented"
      Positions = failwith "unimplemented" }

Now make the equal-weight strategy.

let formEqualWeightStrategy ym =
    ym
    |> getInvestmentUniverse
    |> getMySignals
    |> assignSignalSort strategyName 3
    |> Seq.toList
    |> List.map giveEqualWeights
    |> List.map (getPortfolioReturn getSecurityReturn)

If you have defined giveEqualWeights above then you can calculate equal weight portfolios with

let portfoliosEW = sampleMonths |> List.collect formEqualWeightStrategy

Plotting returns

Common.fsx has some easy to use code to get Fama-French factors. We're going to use the French data to get monthly risk-free rates.

open NovaSBE.Finance.French

let ff3 = getFF3 Frequency.Monthly
let monthlyRiskFreeRate =
    [ for obs in ff3 do 
        let key = DateTime(obs.Date.Year,obs.Date.Month,1)
        key, obs.Rf ]
    |> Map

Now I'll convert my portfolios into excess returns.

let portfolioExcessReturns =
    portfolios
    |> List.map(fun x -> 
        match Map.tryFind x.Month monthlyRiskFreeRate with 
        | None -> failwith $"Can't find risk-free rate for {x.Month}"
        | Some rf -> { x with Return = x.Return - rf })

Single portfolio plot

Let's plot the top portfolio, calling it long.

let long = 
    portfolioExcessReturns 
    |> List.filter(fun x -> x.Index = 3)

let cumulateSimpleReturn (xs: PortfolioReturn list) =
    let xs = xs |> List.sortBy (fun x -> x.Month)
    let mutable cr = 1.0
    [ for x in xs do 
        cr <- cr * (1.0 + x.Return)
        { x with Return = cr - 1.0 } ]

let longCumulative = long |> cumulateSimpleReturn

let longCumulativeChart =
    longCumulative
    |> List.map(fun x -> x.Month, x.Return)
    |> Chart.Line 
    |> Chart.withTitle "Growth of 1 Euro"

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And function to do the plot

let portfolioReturnPlot (xs:PortfolioReturn list) =
    xs
    |> List.map(fun x -> x.Month, x.Return)
    |> Chart.Line 
    |> Chart.withTitle "Growth of 1 Euro"

Using the function:

let longWithFunctionsPlot =
    long
    |> cumulateSimpleReturn
    |> portfolioReturnPlot

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Multiple portfolio plot

Now let's use the functions to do a bunch of portfolios at once.

First, let's add a version of value-weighted market portfolio that has the same time range and same F# type as our portfolios.

let vwMktRf =
    let portfolioMonths = 
        portfolioExcessReturns 
        |> List.map(fun x -> x.Month)
    let minYm = portfolioMonths |> List.min
    let maxYm = portfolioMonths |> List.max
    
    [ for x in ff3 do
        if x.Date >= minYm && x.Date <= maxYm then
            { Name = "Mkt-Rf"
              Index = 1
              Month = x.Date
              Return = x.MktRf } ]

Let's also create a long-short portfolio.

let short = 
    portfolioExcessReturns 
    |> List.filter(fun x -> 
        x.Name = strategyName && x.Index = 1)

let longShort = 
    // We'll loop through the long portfolio observations,
    // looking for the short portfolio observation for that month.
    // For efficiently looking up the short portfolio by month,
    // put it in a Map collection indexed by month.
    let shortByYearMonthMap = 
        short 
        |> List.map(fun row -> row.Month, row) 
        |> Map
    
    [ for longObs in long do
        match Map.tryFind longObs.Month shortByYearMonthMap with
        | None -> failwith "probably your date variables are not aligned for a weird reason"
        | Some shortObs ->
            { Name = "Long-Short"
              Index = 1
              Month = longObs.Month
              Return = longObs.Return - shortObs.Return } ] 
  

let combinedChart =
    List.concat [long; longShort; vwMktRf]
    |> List.groupBy(fun x -> x.Name, x.Index)
    |> List.map(fun ((name, index), xs) ->
        xs
        |> cumulateSimpleReturn
        |> portfolioReturnPlot
        |> Chart.withTraceInfo (Name=($"{name}: {index}")))
    |> Chart.combine

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You might also want to save your results to a csv file.

let [<Literal>] OutputSchema =
    "Name(string),Index(int),Month(date),Ret(float)"

type PortfolioReturnCsv = CsvProvider<OutputSchema>

let makePortfolioReturnCsvRow (row:PortfolioReturn) =
    PortfolioReturnCsv
        .Row(name=row.Name,
             index = row.Index,
             month=row.Month,
             ret = row.Return)

let csvRows =
    portfolioExcessReturns
    |> List.map makePortfolioReturnCsvRow

let csv = new PortfolioReturnCsv(csvRows)
csv.Save("myExcessReturnPortfolios.csv")

namespace System

Multiple items
namespace FSharp

--------------------
namespace Microsoft.FSharp

Multiple items
namespace FSharp.Data

--------------------
namespace Microsoft.FSharp.Data

namespace Plotly

namespace Plotly.NET

namespace FSharp.Stats

namespace NovaSBE

namespace NovaSBE.Finance

module Portfolio from NovaSBE.Finance

Multiple items
type LiteralAttribute = inherit Attribute new: unit -> LiteralAttribute

--------------------
new: unit -> LiteralAttribute

[<Literal>] val IdAndReturnsFilePath: string = "id_and_return_data.csv"

[<Literal>] val MySignalFilePath: string = "be_me.csv"

val strategyName: string

namespace System.IO

type File = static member AppendAllLines: path: string * contents: IEnumerable<string> -> unit + 1 overload static member AppendAllLinesAsync: path: string * contents: IEnumerable<string> * encoding: Encoding * ?cancellationToken: CancellationToken -> Task + 1 overload static member AppendAllText: path: string * contents: string -> unit + 1 overload static member AppendAllTextAsync: path: string * contents: string * encoding: Encoding * ?cancellationToken: CancellationToken -> Task + 1 overload static member AppendText: path: string -> StreamWriter static member Copy: sourceFileName: string * destFileName: string -> unit + 1 overload static member Create: path: string -> FileStream + 2 overloads static member CreateSymbolicLink: path: string * pathToTarget: string -> FileSystemInfo static member CreateText: path: string -> StreamWriter static member Decrypt: path: string -> unit ...
<summary>Provides static methods for the creation, copying, deletion, moving, and opening of a single file, and aids in the creation of <see cref="T:System.IO.FileStream" /> objects.</summary>

IO.File.ReadLines(path: string) : Collections.Generic.IEnumerable<string>
IO.File.ReadLines(path: string, encoding: Text.Encoding) : Collections.Generic.IEnumerable<string>

Multiple items
module Seq from FSharp.Stats
<summary> Module to compute common statistical measure </summary>

--------------------
module Seq from Microsoft.FSharp.Collections

--------------------
type Seq = new: unit -> Seq static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float seq static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float seq

--------------------
new: unit -> Seq

val truncate: count: int -> source: 'T seq -> 'T seq

type IdAndReturnsType = obj

type CsvProvider
<summary>Typed representation of a CSV file.</summary> <param name='Sample'>Location of a CSV sample file or a string containing a sample CSV document.</param> <param name='Separators'>Column delimiter(s). Defaults to <c>,</c>.</param> <param name='InferRows'>Number of rows to use for inference. Defaults to <c>1000</c>. If this is zero, all rows are used.</param> <param name='Schema'>Optional column types, in a comma separated list. Valid types are <c>int</c>, <c>int64</c>, <c>bool</c>, <c>float</c>, <c>decimal</c>, <c>date</c>, <c>datetimeoffset</c>, <c>timespan</c>, <c>guid</c>, <c>string</c>, <c>int?</c>, <c>int64?</c>, <c>bool?</c>, <c>float?</c>, <c>decimal?</c>, <c>date?</c>, <c>datetimeoffset?</c>, <c>timespan?</c>, <c>guid?</c>, <c>int option</c>, <c>int64 option</c>, <c>bool option</c>, <c>float option</c>, <c>decimal option</c>, <c>date option</c>, <c>datetimeoffset option</c>, <c>timespan option</c>, <c>guid option</c> and <c>string option</c>. You can also specify a unit and the name of the column like this: <c>Name (type<unit>)</c>, or you can override only the name. If you don't want to specify all the columns, you can reference the columns by name like this: <c>ColumnName=type</c>.</param> <param name='HasHeaders'>Whether the sample contains the names of the columns as its first line.</param> <param name='IgnoreErrors'>Whether to ignore rows that have the wrong number of columns or which can't be parsed using the inferred or specified schema. Otherwise an exception is thrown when these rows are encountered.</param> <param name='SkipRows'>Skips the first n rows of the CSV file.</param> <param name='AssumeMissingValues'>When set to true, the type provider will assume all columns can have missing values, even if in the provided sample all values are present. Defaults to false.</param> <param name='PreferOptionals'>When set to true, inference will prefer to use the option type instead of nullable types, <c>double.NaN</c> or <c>""</c> for missing values. Defaults to false.</param> <param name='Quote'>The quotation mark (for surrounding values containing the delimiter). Defaults to <c>"</c>.</param> <param name='MissingValues'>The set of strings recognized as missing values specified as a comma-separated string (e.g., "NA,N/A"). Defaults to <c>NaN,NA,N/A,#N/A,:,-,TBA,TBD</c>.</param> <param name='CacheRows'>Whether the rows should be caches so they can be iterated multiple times. Defaults to true. Disable for large datasets.</param> <param name='Culture'>The culture used for parsing numbers and dates. Defaults to the invariant culture.</param> <param name='Encoding'>The encoding used to read the sample. You can specify either the character set name or the codepage number. Defaults to UTF8 for files, and to ISO-8859-1 the for HTTP requests, unless <c>charset</c> is specified in the <c>Content-Type</c> response header.</param> <param name='ResolutionFolder'>A directory that is used when resolving relative file references (at design time and in hosted execution).</param> <param name='EmbeddedResource'>When specified, the type provider first attempts to load the sample from the specified resource (e.g. 'MyCompany.MyAssembly, resource_name.csv'). This is useful when exposing types generated by the type provider.</param>

type MySignalType = obj

val idAndReturnsCsv: HttpResponseWithStream

val mySignalCsv: HttpResponseWithStream

HttpResponseWithStream.Headers: Map<string,string>
<summary> If the same header is present multiple times, the values will be concatenated with comma as the separator </summary>

val idAndReturnsRows: obj list

val toList: source: 'T seq -> 'T list

val mySignalRows: Signal list

val msfBySecurityIdAndMonth: Map<(SecurityId * DateTime),obj>

Multiple items
module List from FSharp.Stats
<summary> Module to compute common statistical measure on list </summary>

--------------------
module List from Microsoft.FSharp.Collections

--------------------
type List = new: unit -> List static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float list static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float list

--------------------
type List<'T> = | op_Nil | op_ColonColon of Head: 'T * Tail: 'T list interface IReadOnlyList<'T> interface IReadOnlyCollection<'T> interface IEnumerable interface IEnumerable<'T> member GetReverseIndex: rank: int * offset: int -> int member GetSlice: startIndex: int option * endIndex: int option -> 'T list static member Cons: head: 'T * tail: 'T list -> 'T list member Head: 'T member IsEmpty: bool member Item: index: int -> 'T with get ...

--------------------
new: unit -> List

val map: mapping: ('T -> 'U) -> list: 'T list -> 'U list

val row: obj

val id: SecurityId

union case SecurityId.Other: string -> SecurityId

val month: DateTime

Multiple items
[<Struct>] type DateTime = new: year: int * month: int * day: int -> unit + 16 overloads member Add: value: TimeSpan -> DateTime member AddDays: value: float -> DateTime member AddHours: value: float -> DateTime member AddMicroseconds: value: float -> DateTime member AddMilliseconds: value: float -> DateTime member AddMinutes: value: float -> DateTime member AddMonths: months: int -> DateTime member AddSeconds: value: float -> DateTime member AddTicks: value: int64 -> DateTime ...
<summary>Represents an instant in time, typically expressed as a date and time of day.</summary>

--------------------
DateTime ()
   (+0 other overloads)
DateTime(ticks: int64) : DateTime
   (+0 other overloads)
DateTime(ticks: int64, kind: DateTimeKind) : DateTime
   (+0 other overloads)
DateTime(date: DateOnly, time: TimeOnly) : DateTime
   (+0 other overloads)
DateTime(year: int, month: int, day: int) : DateTime
   (+0 other overloads)
DateTime(date: DateOnly, time: TimeOnly, kind: DateTimeKind) : DateTime
   (+0 other overloads)
DateTime(year: int, month: int, day: int, calendar: Globalization.Calendar) : DateTime
   (+0 other overloads)
DateTime(year: int, month: int, day: int, hour: int, minute: int, second: int) : DateTime
   (+0 other overloads)
DateTime(year: int, month: int, day: int, hour: int, minute: int, second: int, kind: DateTimeKind) : DateTime
   (+0 other overloads)
DateTime(year: int, month: int, day: int, hour: int, minute: int, second: int, calendar: Globalization.Calendar) : DateTime
   (+0 other overloads)

val key: SecurityId * DateTime

Multiple items
module Map from FSharp.Stats
<summary> Module to strore specialised computations on maps </summary>

--------------------
module Map from Microsoft.FSharp.Collections

--------------------
type Map<'Key,'Value (requires comparison)> = interface IReadOnlyDictionary<'Key,'Value> interface IReadOnlyCollection<KeyValuePair<'Key,'Value>> interface IEnumerable interface IStructuralEquatable interface IComparable interface IEnumerable<KeyValuePair<'Key,'Value>> interface ICollection<KeyValuePair<'Key,'Value>> interface IDictionary<'Key,'Value> new: elements: ('Key * 'Value) seq -> Map<'Key,'Value> member Add: key: 'Key * value: 'Value -> Map<'Key,'Value> ...

--------------------
new: elements: ('Key * 'Value) seq -> Map<'Key,'Value>

val signalBySecurityIdAndMonth: Map<(SecurityId * DateTime),float>

val choose: chooser: ('T -> 'U option) -> list: 'T list -> 'U list

val row: Signal

Signal.Signal: float

union case Option.None: Option<'T>

union case Option.Some: Value: 'T -> Option<'T>

val id: x: 'T -> 'T

val securitiesByFormationMonth: Map<DateTime,SecurityId list>

val groupBy: projection: ('T -> 'Key) -> list: 'T list -> ('Key * 'T list) list (requires equality)

val x: obj

val ym: DateTime

val obsThisMonth: obj list

val idsThisMonth: SecurityId list

val getInvestmentUniverse: formationMonth: DateTime -> InvestmentUniverse

val formationMonth: DateTime

val tryFind: key: 'Key -> table: Map<'Key,'T> -> 'T option (requires comparison)

val securities: SecurityId list

val failwith: message: string -> 'T

val testUniverseObs: InvestmentUniverse

InvestmentUniverse.FormationMonth: DateTime

InvestmentUniverse.Securities: SecurityId list

val getMySignal: securityId: SecurityId * formationMonth: DateTime -> SecuritySignal option

val securityId: SecurityId

val signal: float

Multiple items
namespace FSharp.Stats.Signal

--------------------
type Signal = { SecurityId: SecurityId FormationDate: DateTime Signal: float }

val testObs: SecurityId * DateTime

val getMySignals: investmentUniverse: InvestmentUniverse -> SecuritiesWithSignals

val investmentUniverse: InvestmentUniverse

type InvestmentUniverse = { FormationMonth: DateTime Securities: SecurityId list }

val listOfSecuritySignals: SecuritySignal list

val security: SecurityId

val toList: table: Map<'Key,'T> -> ('Key * 'T) list (requires comparison)

val take: count: int -> list: 'T list -> 'T list

val getMarketCap: security: SecurityId * formationMonth: DateTime -> (SecurityId * 'a) option

val me: 'a

val getSecurityReturn: security: SecurityId * formationMonth: DateTime -> SecurityId * float

val missingReturn: float

val r: float

val startSample: DateTime

val min: list: 'T list -> 'T (requires comparison)

val endSample: DateTime

val lastMonthWithData: DateTime

val map: mapping: ('T -> 'U) -> source: 'T seq -> 'U seq

val max: source: 'T seq -> 'T (requires comparison)

DateTime.AddMonths(months: int) : DateTime

val sampleMonths: DateTime list

val getSampleMonths: sampleStart: DateTime * sampleEnd: DateTime -> DateTime list
<summary> This function takes a sample start and sample end and returns a list with all months from start to end. Don't worry about understanding what this function does. The details are beyond the scope of the class, but if you're curious it's a recursive function: https://docs.microsoft.com/en-us/dotnet/fsharp/language-reference/functions/recursive-functions-the-rec-keyword </summary>

val formStrategy: ym: DateTime -> PortfolioReturn list

val assignSignalSort: name: string -> n: int -> xs: SecuritiesWithSignals -> AssignedPortfolio seq

val giveValueWeights: marketCapGetter: GetsMarketCaps -> x: AssignedPortfolio -> Portfolio
<summary> Defining this type alias makes it easier to read the type of the function that I want for marketCapGetter in the function that I have below. Otherwise it might look something like let giveValueWeights (marketCapGetter: (SecurityId * YearMonth -> (SecurityId * float) Option) ... which is the same thing but not as clear what we're trying to do. </summary>

val getPortfolioReturn: returnGetter: GetsReturn -> x: Portfolio -> PortfolioReturn

val doParallel: bool

val portfolios: PortfolioReturn list

val toArray: list: 'T list -> 'T array

Multiple items
type Array = new: unit -> Array static member geomspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array static member linspace: start: float * stop: float * num: int * ?IncludeEndpoint: bool -> float array

--------------------
new: unit -> Array

module Parallel from Microsoft.FSharp.Collections.ArrayModule

val map: mapping: ('T -> 'U) -> array: 'T array -> 'U array

val toList: array: 'T array -> 'T list

val collect: mapping: ('T -> 'U list) -> list: 'T list -> 'U list

val giveEqualWeights: port: AssignedPortfolio -> Portfolio

val port: AssignedPortfolio

type AssignedPortfolio = { Name: string Index: int FormationMonth: DateTime Signals: SecuritySignal list }

Multiple items
module Portfolio from NovaSBE.Finance

--------------------
type Portfolio = { Name: string Index: int FormationMonth: DateTime Positions: Position list }

val makePosition: securityId: SecurityId -> weight: float -> Position

val weight: float

type Position = { SecurityId: SecurityId Weight: float }

Multiple items
[<Struct>] type Index = new: value: int * ?fromEnd: bool -> unit member Equals: other: Index -> bool + 1 overload member GetHashCode: unit -> int member GetOffset: length: int -> int member ToString: unit -> string static member FromEnd: value: int -> Index static member FromStart: value: int -> Index static member op_Implicit: value: int -> Index member IsFromEnd: bool member Value: int ...
<summary>Represents a type that can be used to index a collection either from the beginning or the end.</summary>

--------------------
Index ()
Index(value: int, ?fromEnd: bool) : Index

type Positions = { FormationMonth: DateTime Positions: Position list }

val formEqualWeightStrategy: ym: DateTime -> PortfolioReturn list

Multiple items
module List from Microsoft.FSharp.Collections

--------------------
type List<'T> = | op_Nil | op_ColonColon of Head: 'T * Tail: 'T list interface IReadOnlyList<'T> interface IReadOnlyCollection<'T> interface IEnumerable interface IEnumerable<'T> member GetReverseIndex: rank: int * offset: int -> int member GetSlice: startIndex: int option * endIndex: int option -> 'T list static member Cons: head: 'T * tail: 'T list -> 'T list member Head: 'T member IsEmpty: bool member Item: index: int -> 'T with get ...

val portfoliosEW: PortfolioReturn list

val printfn: format: Printf.TextWriterFormat<'T> -> 'T

module French from NovaSBE.Finance

val ff3: FF3Obs array

val getFF3: frequency: Frequency -> FF3Obs array

type Frequency = | Daily | Monthly

union case Frequency.Monthly: Frequency

val monthlyRiskFreeRate: Map<DateTime,float>

val obs: FF3Obs

val key: DateTime

FF3Obs.Date: DateTime

property DateTime.Year: int with get
<summary>Gets the year component of the date represented by this instance.</summary>
<returns>The year, between 1 and 9999.</returns>

property DateTime.Month: int with get
<summary>Gets the month component of the date represented by this instance.</summary>
<returns>The month component, expressed as a value between 1 and 12.</returns>

FF3Obs.Rf: float

val portfolioExcessReturns: PortfolioReturn list

val x: PortfolioReturn

PortfolioReturn.Month: DateTime

val rf: float

PortfolioReturn.Return: float

val long: PortfolioReturn list

val filter: predicate: ('T -> bool) -> list: 'T list -> 'T list

PortfolioReturn.Index: int

val cumulateSimpleReturn: xs: PortfolioReturn list -> PortfolioReturn list

val xs: PortfolioReturn list

type PortfolioReturn = { Name: string Index: int Month: DateTime Return: float }

type 'T list = List<'T>

val sortBy: projection: ('T -> 'Key) -> list: 'T list -> 'T list (requires comparison)

val mutable cr: float

val longCumulative: PortfolioReturn list

val longCumulativeChart: GenericChart.GenericChart

type Chart = static member AnnotatedHeatmap: zData: #('a1 seq) seq * annotationText: #(string seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a5 :> IConvertible) + 1 overload static member Area: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Bar: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member BoxPlot: [<Optional; DefaultParameterValue ((null :> obj))>] ?X: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxPoints: BoxPoints * [<Optional; DefaultParameterValue ((null :> obj))>] ?BoxMean: BoxMean * [<Optional; DefaultParameterValue ((null :> obj))>] ?Jitter: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?PointPos: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutlineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Outline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Notched: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?NotchWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?QuartileMethod: QuartileMethod * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 2 overloads static member Bubble: x: #IConvertible seq * y: #IConvertible seq * sizes: int seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: MarkerSymbol * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: MarkerSymbol seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?LineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?GroupNorm: GroupNorm * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) + 1 overload static member Candlestick: ``open`` : #IConvertible seq * high: #IConvertible seq * low: #IConvertible seq * close: #IConvertible seq * x: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a5 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a5 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?IncreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Increasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?DecreasingColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?Decreasing: FinanceMarker * [<Optional; DefaultParameterValue ((null :> obj))>] ?WhiskerWidth: float * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a5 :> IConvertible) + 1 overload static member Column: values: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Keys: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPatternShape: PatternShape * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: PatternShape seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerPattern: Pattern * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible and 'a4 :> IConvertible) + 1 overload static member Contour: zData: #('a1 seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineDash: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLineSmoothing: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursColoring: ContourColoring * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursOperation: ConstraintOperation * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContoursType: ContourType * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowContourLabels: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ContourLabelFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?Contours: Contours * [<Optional; DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?NContours: int * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a4 :> IConvertible) static member Funnel: x: #IConvertible seq * y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Width: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Offset: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextPosition: TextPosition * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: TextPosition seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Orientation: Orientation * [<Optional; DefaultParameterValue ((null :> obj))>] ?AlignmentGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?OffsetGroup: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Marker: Marker * [<Optional; DefaultParameterValue ((null :> obj))>] ?TextInfo: TextInfo * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLineStyle: DrawingStyle * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorFillColor: Color * [<Optional; DefaultParameterValue ((null :> obj))>] ?ConnectorLine: Line * [<Optional; DefaultParameterValue ((null :> obj))>] ?Connector: FunnelConnector * [<Optional; DefaultParameterValue ((null :> obj))>] ?InsideTextFont: Font * [<Optional; DefaultParameterValue ((null :> obj))>] ?OutsideTextFont: Font * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a2 :> IConvertible) static member Heatmap: zData: #('a1 seq) seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?Name: string * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Optional; DefaultParameterValue ((null :> obj))>] ?X: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?XGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Y: #IConvertible seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?YGap: int * [<Optional; DefaultParameterValue ((null :> obj))>] ?Text: 'a4 * [<Optional; DefaultParameterValue ((null :> obj))>] ?MultiText: 'a4 seq * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorBar: ColorBar * [<Optional; DefaultParameterValue ((null :> obj))>] ?ColorScale: Colorscale * [<Optional; DefaultParameterValue ((null :> obj))>] ?ShowScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ReverseScale: bool * [<Optional; DefaultParameterValue ((null :> obj))>] ?ZSmooth: SmoothAlg * [<Optional; DefaultParameterValue ((null :> obj))>] ?Transpose: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Optional; DefaultParameterValue ((false :> obj))>] ?ReverseYAxis: bool * [<Optional; DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart (requires 'a1 :> IConvertible and 'a4 :> IConvertible) + 1 overload ...

static member Chart.Line: xy: (#IConvertible * #IConvertible) seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> IConvertible)
static member Chart.Line: x: #IConvertible seq * y: #IConvertible seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowMarkers: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Opacity: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiOpacity: float seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Text: 'a2 * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiText: 'a2 seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TextPosition: StyleParam.TextPosition * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiTextPosition: StyleParam.TextPosition seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerOutline: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerSymbol: StyleParam.MarkerSymbol * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerSymbol: StyleParam.MarkerSymbol seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineColorScale: StyleParam.Colorscale * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineWidth: float * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LineDash: StyleParam.DrawingStyle * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Line: Line * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?StackGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Orientation: StyleParam.Orientation * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?GroupNorm: StyleParam.GroupNorm * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Fill: StyleParam.Fill * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?FillColor: Color * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((false :> obj))>] ?UseWebGL: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> IConvertible)

static member Chart.withTitle: title: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)
static member Chart.withTitle: title: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?TitleFont: Font -> (GenericChart.GenericChart -> GenericChart.GenericChart)

module HTML from Plotly.NET
<summary> HTML template for Plotly.js </summary>

val portfolioReturnPlot: xs: PortfolioReturn list -> GenericChart.GenericChart

val longWithFunctionsPlot: GenericChart.GenericChart

val vwMktRf: PortfolioReturn list

val portfolioMonths: DateTime list

val minYm: DateTime

val maxYm: DateTime

val max: list: 'T list -> 'T (requires comparison)

val x: FF3Obs

FF3Obs.MktRf: float

val short: PortfolioReturn list

PortfolioReturn.Name: string

val longShort: PortfolioReturn list

val shortByYearMonthMap: Map<DateTime,PortfolioReturn>

val row: PortfolioReturn

val longObs: PortfolioReturn

val shortObs: PortfolioReturn

val combinedChart: GenericChart.GenericChart

val concat: lists: 'T list seq -> 'T list

val name: string

val index: int

static member Chart.withTraceInfo: [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Name: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Visible: StyleParam.Visible * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?ShowLegend: bool * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendRank: int * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroup: string * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?LegendGroupTitle: Title -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.combine: gCharts: GenericChart.GenericChart seq -> GenericChart.GenericChart

[<Literal>] val OutputSchema: string = "Name(string),Index(int),Month(date),Ret(float)"

type PortfolioReturnCsv = CsvProvider<...>

val makePortfolioReturnCsvRow: row: PortfolioReturn -> CsvProvider<...>.Row

val csvRows: CsvProvider<...>.Row list

val csv: PortfolioReturnCsv

member Runtime.CsvFile.Save: path: string * [<Runtime.InteropServices.Optional>] ?separator: char * [<Runtime.InteropServices.Optional>] ?quote: char -> unit
member Runtime.CsvFile.Save: stream: IO.Stream * [<Runtime.InteropServices.Optional>] ?separator: char * [<Runtime.InteropServices.Optional>] ?quote: char -> unit
member Runtime.CsvFile.Save: writer: IO.TextWriter * [<Runtime.InteropServices.Optional>] ?separator: char * [<Runtime.InteropServices.Optional>] ?quote: char -> unit