Stocks for the long run, this time with both stocks and bonds

#r "nuget: ExcelProvider, 2.0.0"
#r "nuget: FSharp.Stats, 0.5.0"
#r "nuget: Plotly.NET, 3.*"
#r "nuget: Plotly.NET.Interactive, 3.*"
#r "nuget: NovaSBE.Finance, 0.5.0"


open FSharp.Interop.Excel
open System
open FSharp.Stats
open Plotly.NET
open NovaSBE.Finance.Utils

Environment.CurrentDirectory <- __SOURCE_DIRECTORY__

Download the excel file from Robert Shiller's website to your current directory.

download "http://www.econ.yale.edu/~shiller/data/ie_data.xls" "shiller_data.xls"

Now loading the excel data.

let [<Literal>] shillerFile = __SOURCE_DIRECTORY__ + "/shiller_data.xls"
type ShillerXls = ExcelFile<shillerFile,SheetName="Data",Range="A8:V2000",ForceString = true>

let shiller = 
    ShillerXls().Data |> Seq.toList

Let's look at the dates.

shiller[..11] |> List.map (fun x -> x.Date)

Remember that is the same as

[ for x in shiller[..11] do x.Date ]

Function to parse the dates.

let parseDate (x: ShillerXls.Row) =
    let year = int x.Date[..3]
    let month = 
        let m = x.Date[5..]
        if m = "1" then 10 else int m
    DateTime(year, month, 1)

Parse the first few dates.

shiller[..11] 
|> List.map (fun x -> x.Date, parseDate x)

Check that we're getting the right data.

shiller[1823..1825]

Some specific columns.

shiller[1823..1825]
|> List.map (fun x -> 
    x.Date, x.D, x.E)

Take the data until I get to those bad rows.

let shillerClean =
    shiller
    |> List.takeWhile (fun x -> 
        not (isNull x.Date) &&
        not (isNull x.D) &&
        not (isNull x.E))

The S&P500 total (price + dividend) return index is the Price2 column. To calculate returns from it we want consecutive observations.

let x0 = shillerClean[0]
let x1 = shillerClean[1]

x0.Price2, x1.Price2

We can do this for the whole list using List.pairwise

shillerClean
|> List.pairwise
|> List.map (fun (x0, x1) -> x0.Price2, x1.Price2)
|> List.take 3

We'll calculate a log return.

let logReturn (p0, p1) = log (p1 / p0)

logReturn (float x0.Price2, float x1.Price2)

Now for the whole list.

shillerClean[0..5] 
|> List.map (fun x -> float x.Price2)
|> List.pairwise
|> List.map logReturn

A type to hold return data.

type ShillerObs =
    {
        Date: DateTime
        /// S&P 500 log return
        SP500RealReturn: float
        /// 10-year US Treasury log return
        GS10RealReturn: float
        CAPE: float
    }

Function to make the return data.

let makeShillerObs (x0: ShillerXls.Row, x1: ShillerXls.Row) =
    {
        Date = parseDate x0
        SP500RealReturn = logReturn (float x0.Price2, float x1.Price2)
        GS10RealReturn = logReturn (float x0.Returns2, float x1.Returns2)
        CAPE = if x0.CAPE = "NA" then nan else float x0.CAPE
    }

Making our list of records containing stock and bond returns.

let shillerObs =
    shillerClean
    |> List.pairwise
    |> List.map makeShillerObs

Average annualized stock and bond returns

let avgStock = shillerObs |> List.averageBy (fun x -> x.SP500RealReturn * 12.0)
let avgBond = shillerObs |> List.averageBy (fun x -> x.GS10RealReturn * 12.0)
let port6040 = shillerObs |> List.map (fun x -> x.SP500RealReturn * 0.6 + x.GS10RealReturn * 0.4)
let avg6040 = port6040 |> List.averageBy (fun x -> x * 12.0)

let sdStock = shillerObs |> Seq.stDevBy _.SP500RealReturn |> fun x ->  x * sqrt 12.0 
let sdBond = shillerObs |> Seq.stDevBy _.GS10RealReturn |> fun x ->  x * sqrt 12.0
let sd6040 = port6040 |> Seq.stDev |> fun x ->  x * sqrt 12.0 

let lev6040 = sdStock / sd6040
/// this is a cost above the risk-free rate
let costOfLeverage = 0.01
let lev6040Return = lev6040 * avg6040 - max 0.0 ((lev6040 - 1.0) * costOfLeverage)

Standard deviation of stock and bond returns

Let's look at returns by decade.

let dateToDecade (date: DateTime) = floor (float date.Year / 10.0) * 10.0

[ for i in [1..10] do 
    let y = DateTime(2005,1,1).AddYears(i) 
    y, dateToDecade y ]

Starting with stocks, remember how group by works

[ ("a", 1); ("a", 2); ("b", 3)]
|> List.groupBy (fun (x, y) -> x)

Now with the stock data.

shillerObs
|> List.groupBy (fun x -> dateToDecade x.Date)

Return by decade

let stockByDecade =
    shillerObs
    |> List.groupBy (fun x -> dateToDecade x.Date)
    |> List.map (fun (decade, obs) ->
        let decadeReturn = obs |> List.map (fun x -> x.SP500RealReturn) |> List.sum
        decade, decadeReturn)

Plot of stock return by decade

stockByDecade
|> Chart.Column

Now the same thing for bonds.

let bondByDecade =
    shillerObs
    |> List.groupBy (fun x -> dateToDecade x.Date)
    |> List.map (fun (decade, obs) ->
        let decadeReturn = obs |> List.map (fun x -> x.GS10RealReturn) |> List.sum
        decade, decadeReturn)

bondByDecade
|> Chart.Column

Combine them.

[ Chart.Column(stockByDecade, Name = "Stocks")
  Chart.Column(bondByDecade, Name = "Bonds")]
|> Chart.combine

Let's make a cumulative chart of stock returns.

let accStockRet =
    let mutable accRet = 0.0
    [ for x in shillerObs do 
        accRet <- accRet + x.SP500RealReturn 
        x.Date, accRet ]

accStockRet[..5]

A line chart of it

accStockRet
|> Chart.Line

If we wanted to see how 1 EUR would grow, remember that we have to plot \(e^r\).

[ for (date, ret) in accStockRet do date, exp ret]
|> Chart.Line

Practice: Plot a line chart of cumulative log returns for bonds.

Let's revisit our simulations, this time with stock and bond returns.

Grabbing stock and bond returns.

let stockReturns = shillerObs |> List.map (fun x -> x.SP500RealReturn)
let bondReturns = shillerObs |> List.map (fun x -> x.GS10RealReturn)

We need a covariance matrix of stock/bond returns to sample both from a multivariate normal distribution.

let covMatrix = 
    [[ var stockReturns            ; cov stockReturns bondReturns ]
     [ cov stockReturns bondReturns; var bondReturns              ]]
    |> matrix

Create a vector of average returns.

let avgStockReturn = stockReturns |> List.average
let avgBondReturn = bondReturns |> List.average
let avgReturns = [ avgStockReturn; avgBondReturn] |> vector

Annualize returns and covariances so that we sample annual values.

let annualizedCov = covMatrix * 12.0
let annualizedRet = avgReturns * 12.0

Our sampler.

let rmultinorm = 
    Distributions.Continuous.MultivariateNormal.Init annualizedRet annualizedCov

Try a sample.

let s = rmultinorm.Sample()

Stock return

s[0]

Bond return

s[1]

1k draws of 30 year investment returns.

type MarketDraw = { StockReturn: float; BondReturn: float}

let stockBondDraws =
    [ for i in [1..1000] do
        [ for  y in [1..30] do
            let s = rmultinorm.Sample()
            { StockReturn = s[0]; BondReturn = s[1]} ]]

let firstDraw = stockBondDraws[0]

Our wealth evolution setup.

let expenses = 50_000.0
let initialWealth = 1_000_000.0

We accumulate wealth from log returns this time.

let stockWealthEvolution =
    [ for life in stockBondDraws do
        let mutable wealth = initialWealth
        [ for r in life do
            // We'll take expenses out at the start of the year.
            if wealth > expenses then
                wealth <- (wealth - expenses) * exp r.StockReturn
            else
                wealth <- 0.0
            wealth ] ]

let stockTerminalWealth = [ for x in stockWealthEvolution do x[x.Length-1] ]

Chance of going broke with stocks?

let nBrokeStock =
    stockTerminalWealth
    |> List.filter (fun x -> x <= 0.0)
    |> List.length
    |> float

let chanceBrokeStock = nBrokeStock / (float stockTerminalWealth.Length)    

printfn $"chance broke=%.3f{chanceBrokeStock}"

Same thing for bonds.

let bondWealthEvolution =
    [ for life in stockBondDraws do
        let mutable wealth = initialWealth
        [ for r in life do
            // We'll take expenses out at the start of the year.
            if wealth > expenses then
                wealth <- (wealth - expenses) * exp r.BondReturn
            else
                wealth <- 0.0
            wealth ] ]

let bondTerminalWealth = [ for x in bondWealthEvolution do x[x.Length-1] ]

Chance of going broke with stocks?

let nBrokeBond =
    bondTerminalWealth
    |> List.filter (fun x -> x <= 0.0)
    |> List.length
    |> float

let chanceBrokeBond = nBrokeBond / (float bondTerminalWealth.Length)    

printfn $"chance broke=%.3f{chanceBrokeBond}"

Rather than repeating code, a function to do all that.

let calcChanceBroke expenses initialWealth lives =
    let wealthEvolution =
        [ for life in lives do
            let mutable wealth = initialWealth
            [ for r in life do
                // We'll take expenses out at the start of the year.
                if wealth > expenses then
                    wealth <- (wealth - expenses) * exp r
                else
                    wealth <- 0.0
                wealth ] ]

    let terminalWealth = [ for x in wealthEvolution do x[x.Length-1] ]

    (** Chance of going broke with stocks? *)
    let nBroke =
        terminalWealth
        |> List.filter (fun x -> x <= 0.0)
        |> List.length
        |> float

    let chanceBroke = nBroke / (float terminalWealth.Length)    
    chanceBroke

Try it for stocks.

let stockOnlyLives = 
    [ for life in stockBondDraws do
        [ for r in life do r.StockReturn ]]

calcChanceBroke 50_000 1_000_000 stockOnlyLives

Some different bond/stock ratios.

let bondStockRatios = [0.0 .. 0.2 .. 1.0]
let bondStockRatioLives =
    [ for ratio in bondStockRatios do 
        [ for life in stockBondDraws do
            [ for r in life do ratio * r.BondReturn + (1.0 - ratio) * r.StockReturn ]]]

[ for ratioLives in bondStockRatioLives do 
    calcChanceBroke 50_000 1_000_000 ratioLives ]

What are some things to consider?

Multiple items
namespace FSharp

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

namespace FSharp.Interop

namespace FSharp.Interop.Excel

namespace System

namespace FSharp.Stats

namespace Plotly

namespace Plotly.NET

namespace NovaSBE

namespace NovaSBE.Finance

module Utils from NovaSBE.Finance

type Environment = static member Exit: exitCode: int -> unit static member ExpandEnvironmentVariables: name: string -> string static member FailFast: message: string -> unit + 1 overload static member GetCommandLineArgs: unit -> string array static member GetEnvironmentVariable: variable: string -> string + 1 overload static member GetEnvironmentVariables: unit -> IDictionary + 1 overload static member GetFolderPath: folder: SpecialFolder -> string + 1 overload static member GetLogicalDrives: unit -> string array static member SetEnvironmentVariable: variable: string * value: string -> unit + 1 overload static member CommandLine: string ...
<summary>Provides information about, and means to manipulate, the current environment and platform. This class cannot be inherited.</summary>

property Environment.CurrentDirectory: string with get, set
<summary>Gets or sets the fully qualified path of the current working directory.</summary>
<exception cref="T:System.ArgumentException">Attempted to set to an empty string ("").</exception>
<exception cref="T:System.ArgumentNullException">Attempted to set to <see langword="null" />.</exception>
<exception cref="T:System.IO.IOException">An I/O error occurred.</exception>
<exception cref="T:System.IO.DirectoryNotFoundException">Attempted to set a local path that cannot be found.</exception>
<exception cref="T:System.Security.SecurityException">The caller does not have the appropriate permission.</exception>
<returns>The directory path.</returns>

val download: inputUrl: string -> outputFile: string -> unit

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

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

[<Literal>] val shillerFile: string = "D:\a\Teaching\Teaching\docs/shiller_data.xls"

type ShillerXls = ExcelFile<...>

type ExcelFile = inherit ExcelFileInternal
<summary>Typed representation of data in an Excel file.</summary> <param name='FileName'>Location of the Excel file.</param> <param name='SheetName'>Name of sheet containing data. Defaults to first sheet.</param> <param name='Range'>Specification using `A1:D3` type addresses of one or more ranges. Defaults to use whole sheet.</param> <param name='HasHeaders'>Whether the range contains the names of the columns as its first line.</param> <param name='ForceString'>Specifies forcing data to be processed as strings. Defaults to `false`.</param>

Multiple items
[<Struct>] type Range = new: start: Index * ``end`` : Index -> unit member Equals: value: obj -> bool + 1 overload member GetHashCode: unit -> int member GetOffsetAndLength: length: int -> struct (int * int) member ToString: unit -> string static member EndAt: ``end`` : Index -> Range static member StartAt: start: Index -> Range member End: Index member Start: Index static member All: Range
<summary>Represents a range that has start and end indexes.</summary>

--------------------
Range ()
Range(start: Index, ``end`` : Index) : Range

val shiller: ExcelFile<...>.Row list

Multiple items
namespace System.Data

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

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

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 x: ExcelFile<...>.Row

property ExcelFile<...>.Row.Date: string with get

val parseDate: x: ExcelFile<...>.Row -> DateTime

type Row = inherit Row member CAPE: string member CPI: string member D: string member Date: string member Dividend: string member E: string member Earnings: string member Earnings2: string member Fraction: string ...

val year: int

Multiple items
val int: value: 'T -> int (requires member op_Explicit)

--------------------
type int = int32

--------------------
type int<'Measure> = int

val month: int

val m: string

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)

property ExcelFile<...>.Row.D: string with get

property ExcelFile<...>.Row.E: string with get

val shillerClean: ExcelFile<...>.Row list

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

val isNull: value: 'T -> bool (requires 'T: null)

val x0: ExcelFile<...>.Row

val x1: ExcelFile<...>.Row

property ExcelFile<...>.Row.Price2: string with get

val pairwise: list: 'T list -> ('T * 'T) list

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

val logReturn: p0: float * p1: float -> float

val p0: float

val p1: float

val log: value: 'T -> 'T (requires member Log)

Multiple items
val float: value: 'T -> float (requires member op_Explicit)

--------------------
type float = Double

--------------------
type float<'Measure> = float

type ShillerObs = { Date: DateTime SP500RealReturn: float GS10RealReturn: float CAPE: float }

val makeShillerObs: x0: ExcelFile<...>.Row * x1: ExcelFile<...>.Row -> ShillerObs

property ExcelFile<...>.Row.Returns2: string with get

property ExcelFile<...>.Row.CAPE: string with get

val nan: float

val shillerObs: ShillerObs list

val avgStock: float

val averageBy: projection: ('T -> 'U) -> list: 'T list -> 'U (requires member (+) and member DivideByInt and member Zero)

val x: ShillerObs

ShillerObs.SP500RealReturn: float
S&P 500 log return

val avgBond: float

ShillerObs.GS10RealReturn: float
10-year US Treasury log return

val port6040: float list

val avg6040: float

val x: float

val sdStock: float

val stDevBy: f: ('T -> 'a) -> items: 'T seq -> 'U (requires member (-) and member Zero and member DivideByInt and member (+) and member ( * ) and member (+) and member (/) and member Sqrt)
<summary> Computes the sample standard deviation </summary>
<param name="f">A function applied to transform each element of the sequence.</param>
<param name="items">The input sequence.</param>
<remarks>Returns NaN if data is empty or if any entry is NaN.</remarks>
<returns>standard deviation of a sample (Bessel's correction by N-1)</returns>

val sqrt: value: 'T -> 'U (requires member Sqrt)

val sdBond: float

val sd6040: float

val stDev: items: 'T seq -> 'U (requires member (-) and member Zero and member DivideByInt and member (+) and member ( * ) and member (+) and member (/) and member Sqrt)
<summary> Computes the sample standard deviation </summary>
<param name="items">The input sequence.</param>
<remarks>Returns NaN if data is empty or if any entry is NaN.</remarks>
<returns>standard deviation of a sample (Bessel's correction by N-1)</returns>

val lev6040: float

val costOfLeverage: float
this is a cost above the risk-free rate

val lev6040Return: float

val max: e1: 'T -> e2: 'T -> 'T (requires comparison)

val dateToDecade: date: DateTime -> float

val date: DateTime

val floor: value: 'T -> 'T (requires member Floor)

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>

val i: int

val y: DateTime

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

val x: string

val y: int

ShillerObs.Date: DateTime

val stockByDecade: (float * float) list

val decade: float

val obs: ShillerObs list

val decadeReturn: float

val sum: list: 'T list -> 'T (requires member (+) and member Zero)

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.Column: keysValues: (#IConvertible * #IConvertible) seq * [<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))>] ?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))>] ?MarkerPatternShape: StyleParam.PatternShape * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: StyleParam.PatternShape seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerPattern: TraceObjects.Pattern * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 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 ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> IConvertible and 'a4 :> IConvertible)
static member Chart.Column: values: #IConvertible seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Keys: #IConvertible seq * [<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))>] ?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))>] ?MarkerPatternShape: StyleParam.PatternShape * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiMarkerPatternShape: StyleParam.PatternShape seq * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MarkerPattern: TraceObjects.Pattern * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Marker: TraceObjects.Marker * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Base: #IConvertible * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?Width: 'a4 * [<Runtime.InteropServices.Optional; Runtime.InteropServices.DefaultParameterValue ((null :> obj))>] ?MultiWidth: 'a4 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 ((true :> obj))>] ?UseDefaults: bool -> GenericChart.GenericChart (requires 'a2 :> IConvertible and 'a4 :> IConvertible)

val bondByDecade: (float * float) list

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

module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>

val toChartHTML: gChart: GenericChart.GenericChart -> string
<summary> Converts a GenericChart to it HTML representation. The div layer has a default size of 600 if not specified otherwise. </summary>

val accStockRet: (DateTime * float) list

val mutable accRet: float

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)

val ret: float

val exp: value: 'T -> 'T (requires member Exp)

val stockReturns: float list

val bondReturns: float list

val covMatrix: Matrix<float>

val var: items: 'T seq -> 'U (requires member (-) and member Zero and member DivideByInt and member (+) and member ( * ) and member (+) and member (/))
<summary> Computes the sample variance (Bessel's correction by N-1) </summary>
<param name="items">The input sequence.</param>
<remarks>Returns NaN if data is empty or if any entry is NaN.</remarks>
<returns>variance of a sample (Bessel's correction by N-1)</returns>

val cov: seq1: 'T seq -> seq2: 'T seq -> 'U (requires member ( * ) and member (+) and member (+) and member Zero and member DivideByInt and member (-) and member ( * ))
<summary> Computes the sample covariance of two random variables </summary>
<param name="seq1">The first input sequence.</param>
<param name="seq2">The second input sequence.</param>
<remarks>Returns NaN if data is empty or if any entry is NaN.</remarks>
<returns>sample covariance estimator (Bessel's correction by N-1)</returns>

Multiple items
val matrix: ll: #(float seq) seq -> Matrix<float>

--------------------
type matrix = Matrix<float>

val avgStockReturn: float

val average: list: 'T list -> 'T (requires member (+) and member DivideByInt and member Zero)

val avgBondReturn: float

val avgReturns: Vector<float>

Multiple items
val vector: l: float seq -> Vector<float>

--------------------
type vector = Vector<float>

val annualizedCov: Matrix<float>

val annualizedRet: Vector<float>

val rmultinorm: Distributions.ContinuousDistribution<vector,vector>

namespace FSharp.Stats.Distributions

namespace FSharp.Stats.Distributions.Continuous

type MultivariateNormal = static member CDF: mu: vector -> sigma: matrix -> x: vector -> 'a0 static member CheckParam: mu: vector -> sigma: matrix -> unit static member Init: mu: vector -> sigma: matrix -> ContinuousDistribution<vector,vector> static member InvCDF: mu: vector -> sigma: matrix -> x: vector -> 'a0 static member Mean: mu: vector -> sigma: matrix -> vector static member PDF: mu: vector -> sigma: matrix -> x: vector -> float static member Sample: mu: vector -> sigma: matrix -> Vector<float> static member StandardDeviation: mu: vector -> sigma: matrix -> 'a0 static member Variance: mu: vector -> sigma: matrix -> 'a0
<summary> multivariate normal distribution. </summary>

static member Distributions.Continuous.MultivariateNormal.Init: mu: vector -> sigma: matrix -> Distributions.ContinuousDistribution<vector,vector>

val s: vector

abstract Distributions.ContinuousDistribution.Sample: unit -> 'b

type MarketDraw = { StockReturn: float BondReturn: float }

val stockBondDraws: MarketDraw list list

val firstDraw: MarketDraw list

val expenses: float

val initialWealth: float

val stockWealthEvolution: float list list

val life: MarketDraw list

val mutable wealth: float

val r: MarketDraw

MarketDraw.StockReturn: float

val stockTerminalWealth: float list

val x: float list

property List.Length: int with get

val nBrokeStock: float

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

val length: list: 'T list -> int

val chanceBrokeStock: float

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

val bondWealthEvolution: float list list

MarketDraw.BondReturn: float

val bondTerminalWealth: float list

val nBrokeBond: float

val chanceBrokeBond: float

val calcChanceBroke: expenses: float -> initialWealth: float -> lives: #(float seq) seq -> float

val lives: #(float seq) seq

val wealthEvolution: float list list

val life: #(float seq)

val r: float

val terminalWealth: float list

val nBroke: float

val chanceBroke: float

val stockOnlyLives: float list list

val bondStockRatios: float list

val bondStockRatioLives: float list list list

val ratio: float

val ratioLives: float list list