Fundamentals

A good place to start is to define a one-period return calculation.

Objectives:

Interactive programming
How to calculate returns.
Working with data.
How to calculate return volatility

Interactive programming

We are going to focus on interactive programming. This is the most productive (and most common) type of analytic programming. In constrast to compiled programs (e.g, C, C++, Fortran, Java), interactive programs:

Allow rapid iterative development.
You can quickly quickly write and rewrite sections of code, evaluating the output, without having to rerun the entire program.
This is especially useful for financial analysis, because we often evaluate large datasets that take a long time to process.

Interactive programming typically involves a REPL (Read, Evaluate, Print, Loop). It is common for scripting langauges such as R, Python, Julia, Ruby, and Perl.

The terminal

The most basic way that you can run interactive code is at the command line using an interpreter. We can start the F# interactive interpreter by opening a terminal (e.g., terminal.app, cmd, powershell) and running dotnet fsi.

Once fsi is open, we can type a code snippet in the prompt followed by ";;" to terminate it and it will run.

fsi

It is fine to run code this way, but we can do better using an IDE (Integrated development environment) that incorportes syntax highlighting, intellisense tooltips, and execution. We will use two common IDE's: Visual Studio Code with the Ionide extension and Jupyter Notebooks.

Calculating returns

Basic calculations in fsi

Let's assume that you have $120.00 today and that you had $100.00 a year ago. Your annual return is then:

(120.0 / 100.0) - 1.0

val it: float = 0.2

Basic numerical types: float, int, and decimal

Notice that I included a decimal point "." in the numbers. The decimal point makes it a floating point number. Floating point numbers (floats) are the most commonly used numerical type for mathematical calculations.

If we left the decimal point off and wrote "120" without the ".0" at the end it would be an integer and we would get the wrong answer because integers cannot represent fractions.

(120/100) - 1

val it: int = 0

The other main numerical data type is decimal.

(120m/100m) - 1m

val it: decimal = 0.2M {Scale = 1uy;}

Decimals are used when you need an exact fractional amount. Floats are insufficient in these circumstances because "... such representations typically restrict the denominator to a power of two ... 0.3 (3/10) might be represented as 5404319552844595/18014398509481984 (0.299999999999999988897769...)" (see wiki).

Static type checking

Finally, since F# is staticly typed, we must do arithmetic using numbers that are all the same type. If we mix floats and integers we will get an error:

(120.0 / 100) - 1.0

fundamentals.fsx(18,10): error FS0001: The type 'int' does not match the type 'float'

Static tying can slow you down a bit writing simple small programs, but as programs get larger and more complex the benefits become apparent. Specifically, static typing as implemented by F#:

helps you ensure that the code is correct (i.e., the type of the input data matches what the function expects). In the words of Yaron Minksy at Janestreet, you can "make illegal states unrepresentable" (see here for F# examples).
it also facilitates editor tooling that can check your code without running it and give tooltip errors (you should have seen a tooltip error in your editor if you type (120.0 / 100) - 1.0 in your program file). It's like clippy on steriods (you are too young, but your parents might get this reference).

clippy

Image source

Assigning values

We could also do the same calculations by assigning $120.00 and $100.0 to named values.

let yearAgo = 100.0
let today = 120.0
(today / yearAgo) - 1.0

val yearAgo: float = 100.0
val today: float = 120.0
val it: float = 0.2

This works for one-off calculations, but if we want to do this more than once, then it makes more sense to define a function to do this calculation.

Defining functions

Functions map (or transform) inputs into outputs.

Here is a simple function named addOne. It takes an input x and then it adds 1 to whatever x is.

let addOne x = x + 1

addOne 0 // here x is 0
addOne 1 // here x is 1
addOne 2 // here x is 2

We can also chain them

addOne (addOne (addOne 0)) // = (1 + (1 + (1 + 0)))

We can define a function to calcuate a return.

let calcReturn pv fv = (fv / pv) - 1.0

The type signature tells us that calcReturn is a function with two float inputs (pv and fv) and it maps those two inputs into a float output. The program was able to infer that pv and fv are floats because of the 1.0 float in the calculation.

We can execute it on simple floats:

// here pv = 100., fv = 110.0
calcReturn 100.0 110.0

val it: float = 0.1

// here pv = 80.0, fv = 60.0
calcReturn 80.0 60.0

val it: float = -0.25

Or we can execute it on our previously defined yearAgo and today values:

calcReturn yearAgo today

val it: float = 0.2

Handling dividends

Our prior return calculation did not handle cash distributions such as dividends. We can incorporate dividends with a small modificaton:

let simpleReturn beginningPrice endingPrice dividend =
    // This is solving for `r` in FV = PV*(1+r)^t where t=1.
    (endingPrice + dividend) / beginningPrice - 1.0

The examples thus far have used simple (per period) compounding. We can also calculate continuously compounded returns, also known as log returns.

let logReturn beginningPrice endingPrice dividend =
    // This is solving for `r` in FV = PV*e^(rt) where t=1.
    log(endingPrice + dividend) - log(beginningPrice)

These two calculations give slightly different returns.

simpleReturn 100.0 110.0 0.0

val it: float = 0.1

logReturn 100.0 110.0 0.0

val it: float = 0.0953101798

It is typically not important which version of return you use so long as you are consistent and keep track of what type of return it is when you're compounding things.

Practice: Can you write a function to compound an initial investment of $100.00 at 6% for 5 years? You can calculate power and exponents using:

2.0**3.0

val it: float = 8.0

log 2.0

val it: float = 0.6931471806

exp 0.6931

val it: float = 1.999905641

exp(log(2.0))

val it: float = 2.0

Tuples

Looking at our return functions, we're starting to get several values that we're passing into the functions individaully. It can be useful to group these values together to make it easy to pass them around. Tuples are a simple way to group values.

Further information about tuples can be found in the F# Language reference and the F# for Fun and Profit websites.

(1,2)

val it: int * int = (1, 2)

(1,2,3)

val it: int * int * int = (1, 2, 3)

Tubles can contain mixed types.

(1,"2")

val it: int * string = (1, "2")

We can also deconstruct tuples. We can use built-in convenience functions for pairs.

fst (1,2)

val it: int = 1

snd (1,2)

val it: int = 2

We can also deconstruct tuples using pattern matching.

let (a, b) = (1, 2)

val b: int = 2
val a: int = 1

let (c, d, e) = (1, "2", 3.0)

val e: float = 3.0
val d: string = "2"
val c: int = 1

Now redefining our simple return function to take a single tuple as the input parameter.

let simpleReturnTuple (beginningPrice, endingPrice, dividend) =
    // This is solving for `r` in FV = PV*(1+r)^t where t=1.
    (endingPrice + dividend) / beginningPrice - 1.0

simpleReturnTuple (100.0, 110.0, 0.0)

val simpleReturnTuple:
  beginningPrice: float * endingPrice: float * dividend: float -> float
val it: float = 0.1

let xx = (100.0, 110.0, 0.0)
simpleReturnTuple xx

val xx: float * float * float = (100.0, 110.0, 0.0)
val it: float = 0.1

Records

If we want more structure than a tuple, then we can define a record.

For more information on records see the relevant sections of the F# language reference or F# for Fun and Profit websites.

You must first define the record type before you use it:

type RecordExample = 
    { BeginningPrice : float 
      EndingPrice : float 
      Dividend : float }

And construct a value with that record type.

let x = { BeginningPrice = 100.0; EndingPrice = 110.0; Dividend = 0.0}

val x: RecordExample = { BeginningPrice = 100.0
                         EndingPrice = 110.0
                         Dividend = 0.0 }

Similar to tuples, we can deconstruct our record value x using pattern matching.

let { BeginningPrice = aa; EndingPrice = bb; Dividend = cc} = x

val cc: float = 0.0
val bb: float = 110.0
val aa: float = 100.0

We can also access individual fields by name.

x.EndingPrice / x.BeginningPrice

val it: float = 1.1

We can define a return function that operates on the RecordExample type explicitly:

let simpleReturnRecord1 { BeginningPrice = beginningPrice; EndingPrice = endingPrice; Dividend = dividend} =
    // This is solving for `r` in FV = PV*(1+r)^t where t=1.
    (endingPrice + dividend) / beginningPrice - 1.0

Or we can let the compiler's type inference figure out the input type.

let simpleReturnRecord2 x =
    // This is solving for `r` in FV = PV*(1+r)^t where t=1.
    (x.EndingPrice + x.Dividend) / x.BeginningPrice - 1.0

Or we can provide a type hint to tell the compiler the type of the input.

let simpleReturnRecord3 (x : RecordExample) =
    // This is solving for `r` in FV = PV*(1+r)^t where t=1.
    (x.EndingPrice + x.Dividend) / x.BeginningPrice - 1.0

All 3 can be used interchangably, but when you have many similar types a type hint may be necessary to make the particular type that you want explicit.

simpleReturnRecord1 x

val it: float = 0.1

simpleReturnRecord2 x

val it: float = 0.1

simpleReturnRecord3 x

val it: float = 0.1

Pipelines and lambda expressions

Pipelines and lambda functions are two important tools. Pipelines are created using the pipe operator (|>) and allow you to pipe the output of one function to the input of another. Lambda expressions allow you to create functions on the fly.

Take this example from before

addOne (addOne (addOne 0)) // = (1 + (1 + (1 + 0)))

We can write the same thing using pipes.

0 |> addOne |> addOne |> addOne // = (1 + (1 + (1 + 0)))

lambda expressions fun x -> ... are used to create functions on the fly.

1.0 |> fun x -> x + 1.0 |> fun x -> x ** 2.0

val it: float = 4.0

Collections: Arrays, Lists, Sequences

Collections provide a way to store multiple values together. Maybe you want to store a list of stock prices, or an array of portfolios.

A simple int array.

let ar = [| 0 .. 10 |]

ar

val it: int array = [|0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10|]

When we look at the type signature of the elements in the array val ar : int [], it tells us that we have a integer array, meaning an array in which each element of the array is an integer. Arrays are "zero indexed", meaning the 0th item is the first in the array.

We can access the elements individually

ar[0]

val it: int = 0

ar[3]

val it: int = 3

Or we can access a range of elements.

ar[0 .. 2]

val it: int array = [|0; 1; 2|]

Lists and sequences are similar.

// List
[ 1.0 .. 10.0 ]

val it: float list = [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 9.0; 10.0]

// Sequence
seq { 1.0 .. 10.0 }

val it: float seq = seq [1.0; 2.0; 3.0; 4.0; ...]

Arrays, lists, and sequences have different properties that can make one data structure preferable to the others in a given setting. We'll discuss these different properties in due time, but for an overview you can see the F# collection language reference here. Sequences are the most different as they are "lazy", meaning "Sequences are particularly useful when you have a large, ordered collection of data but don't necessarily expect to use all the elements. Individual sequence elements are computed only as required, so a sequence can perform better than a list if not all the elements are used" (see F# language reference).

These collections have several built-in functions for operating on them such as map, filter, groupBy, etc.

Array.map applies a function to each element of an array.

ar
|> Array.map(fun x -> x + 1)

val it: int array = [|1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11|]

The Array.map function is equivalent to

[| for x in ar do x + 1 |]

Array.filter filters elements of a list to those for which a function evaluates to true.

ar
|> Array.filter(fun x -> x < 5)

val it: int array = [|0; 1; 2; 3; 4|]

Array.filter is equivalent to

[| for x in ar do if x < 5 then x |]

While the comprehension syntax [| for x in ar do ... |] is common to use, the Array module functions tend to be more useful when you're chaining multiple operations together using pipes.

For example, this is what a groupBy function does.

ar
|> Array.groupBy(fun x -> x < 5)

val it: (bool * int array) array =
  [|(true, [|0; 1; 2; 3; 4|]); (false, [|5; 6; 7; 8; 9; 10|])|]

Now a pipeline of two operations.

ar
|> Array.groupBy(fun x -> x < 5)
|> Array.map(fun (group, xs) -> Array.min xs, Array.max xs)

val it: (int * int) array = [|(0, 4); (5, 10)|]

Working with data

With this foundation, let's now try loading some data. We are going to load some helper code that allows us to download and plot this data. This will introduce using the nuget package manager for loading external libraries, and how to open namespaces.

We're going to use the Quotes.YahooFinance library for this. We download the code from the nuget.org package manager.

This is equivalent to loading libraries with pip or conda in python or install.packages in R.

#r "nuget: Quotes.YahooFinance, 0.0.5"

We now have access to the code in the Quotes.YahooFinance library. The library has a function called YahooFinance.History that we can use to download quote histories from yahoo finance.

We can access code using fully qualified names.

Quotes.YahooFinance.YahooFinance.History("AAPL")

However, it's common to open a library's namespace in order to access the library's functionality directly.

open Quotes.YahooFinance

YahooFinance.History("AAPL")

Namespaces such as Quotes.YahooFinance are a hierarchical way of organizing code.

We are ready to request some data. Let's define our start and end dates. DateTime is a type in the System namespace.

open System

let myStart = DateTime(2020,1,1)
let myEnd = DateTime.UtcNow
myEnd

2/20/2024 12:48:53 PM

let aapl = YahooFinance.History("AAPL",startDate=myStart,endDate=myEnd,interval = Interval.Daily)

Plotting

Now let's plot the stock price using Plotly.NET.

#r "nuget: Plotly.NET, 3.*"
#r "nuget: Plotly.NET.Interactive, 3.*"
open Plotly.NET


let dateAdjClose = [ for x in aapl do x.Date, x.AdjustedClose ]

dateAdjClose[..3]

input.fsx (6,31)-(6,35) typecheck error The value or constructor 'aapl' is not defined.
input.fsx (6,39)-(6,45) typecheck error Lookup on object of indeterminate type based on information prior to this program point. A type annotation may be needed prior to this program point to constrain the type of the object. This may allow the lookup to be resolved.
input.fsx (6,47)-(6,62) typecheck error Lookup on object of indeterminate type based on information prior to this program point. A type annotation may be needed prior to this program point to constrain the type of the object. This may allow the lookup to be resolved.
[Loading C:\Users\runneradmin\.packagemanagement\nuget\Projects\4004--03f285cf-3b4a-49d5-ac0c-0ca5f8fdd20f\Project.fsproj.fsx]
module FSI_0231.Project.fsproj

dateAdjClose
|> Chart.Line

No value returned by any evaluator

Let's calculate returns for this data. Typically we calculate close-close returns. Looking at the data, we could use the close, divCash, and splitFacor columns to calculate returns accounting for stock splits and dividends (a good at home exercise). But there is also an adjClose column that accounts for both those things. So we we can use this

// Returns
let returns = 
    aapl
    |> List.sortBy(fun x -> x.Date)
    |> List.pairwise
    |> List.map(fun (a,b) -> b.Date, calcReturn a.AdjustedClose b.AdjustedClose)

let avgReturnEachMonth = 
    returns
    |> List.groupBy(fun (date, ret) -> DateTime(date.Year, date.Month,1))
    |> List.map(fun (month, xs) -> 
        let avgPrice = [ for (date, price) in xs do price ] |> List.average
        month, xs.Length, avgPrice)

We can look at a few of these

avgReturnEachMonth |> List.take 3

input.fsx (1,1)-(1,19) typecheck error The value or constructor 'avgReturnEachMonth' is not defined.

let monthlyReturnChart =
    avgReturnEachMonth
    |> List.map(fun (month, cnt, ret) -> month, ret)
    |> Chart.Bar

monthlyReturnChart

No value returned by any evaluator

Volatility

We represent volatility by the standard deviation of returns. We can define a standard deviation function ourself.

let stddev xs =
    let mu = xs |> Seq.average
    let sse = xs |> Seq.sumBy(fun x -> (x - mu)**2.0)
    let n = xs |> Seq.length |> float
    sqrt (sse / (n - 1.0))

[1.0 .. 10.0 ] |> stddev

val stddev: xs: float seq -> float
val it: float = 3.027650354

But it is also convenient to use the FSharp.Stats

#r "nuget: FSharp.Stats, 0.5.0"

open FSharp.Stats

[1.0 .. 10.0 ] |> stDev

[Loading C:\Users\runneradmin\.packagemanagement\nuget\Projects\4004--03f285cf-3b4a-49d5-ac0c-0ca5f8fdd20f\Project.fsproj.fsx]
module FSI_0254.Project.fsproj

val it: float = 3.027650354

Now let's look at 5-day rolling volatilities.

let rollingVols =
    returns
    // Sort by date again because you never can be too careful
    // about making sure that you have the right sort order.
    |> List.sortBy fst 
    |> List.windowed 5
    |> List.map(fun xs ->
        let maxWindowDate = xs |> Seq.map fst |> Seq.max
        let dailyVol = 
            xs 
            |> List.map (fun (date, ret) -> ret) 
            |> stDev
        let annualizedVolInPct = dailyVol * sqrt(252.0) * 100.0
        maxWindowDate, annualizedVolInPct)

let volChart = 
    rollingVols
    |> Chart.Line

volChart

No value returned by any evaluator

val yearAgo: float

val today: float

val addOne: x: int -> int

val x: int

val calcReturn: pv: float -> fv: float -> float

val pv: float

val fv: float

val simpleReturn: beginningPrice: float -> endingPrice: float -> dividend: float -> float

val beginningPrice: float

val endingPrice: float

val dividend: float

val logReturn: beginningPrice: float -> endingPrice: float -> dividend: float -> float

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

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

val fst: tuple: ('T1 * 'T2) -> 'T1

val snd: tuple: ('T1 * 'T2) -> 'T2

val a: int

val b: int

val c: int

val d: string

val e: float

val simpleReturnTuple: beginningPrice: float * endingPrice: float * dividend: float -> float

val xx: float * float * float

type RecordExample = { BeginningPrice: float EndingPrice: float Dividend: float }

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

--------------------
type float = System.Double

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

val x: RecordExample

val aa: float

val bb: float

val cc: float

RecordExample.EndingPrice: float

RecordExample.BeginningPrice: float

val simpleReturnRecord1: RecordExample -> float

val simpleReturnRecord2: x: RecordExample -> float

RecordExample.Dividend: float

val simpleReturnRecord3: x: RecordExample -> float

val x: float

val ar: int array

Multiple items
val seq: sequence: 'T seq -> 'T seq

--------------------
type 'T seq = System.Collections.Generic.IEnumerable<'T>

module Array from Microsoft.FSharp.Collections

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

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

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

val group: bool

val xs: int array

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

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

namespace Quotes

namespace Quotes.YahooFinance

type YahooFinance = static member Dividends: symbols: string list * ?startDate: DateTime * ?endDate: DateTime * ?interval: Interval * ?displayLogs: bool -> Dividend list static member History: symbol: string * ?startDate: DateTime * ?endDate: DateTime * ?interval: Interval * ?displayLogs: bool -> Quote list + 1 overload static member Meta: symbols: string list * ?startDate: DateTime * ?endDate: DateTime * ?interval: Interval * ?displayLogs: bool -> Meta list

static member Quotes.YahooFinance.YahooFinance.History: symbols: string seq * ?startDate: System.DateTime * ?endDate: System.DateTime * ?interval: Quotes.YahooFinance.Interval * ?displayLogs: bool -> Quotes.YahooFinance.Quote list
static member Quotes.YahooFinance.YahooFinance.History: symbol: string * ?startDate: System.DateTime * ?endDate: System.DateTime * ?interval: Quotes.YahooFinance.Interval * ?displayLogs: bool -> Quotes.YahooFinance.Quote list

static member YahooFinance.History: symbols: string seq * ?startDate: System.DateTime * ?endDate: System.DateTime * ?interval: Interval * ?displayLogs: bool -> Quote list
static member YahooFinance.History: symbol: string * ?startDate: System.DateTime * ?endDate: System.DateTime * ?interval: Interval * ?displayLogs: bool -> Quote list

namespace System

val myStart: 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 myEnd: DateTime

property DateTime.UtcNow: DateTime with get
<summary>Gets a <see cref="T:System.DateTime" /> object that is set to the current date and time on this computer, expressed as the Coordinated Universal Time (UTC).</summary>
<returns>An object whose value is the current UTC date and time.</returns>

val aapl: Quote list

static member YahooFinance.History: symbols: string seq * ?startDate: DateTime * ?endDate: DateTime * ?interval: Interval * ?displayLogs: bool -> Quote list
static member YahooFinance.History: symbol: string * ?startDate: DateTime * ?endDate: DateTime * ?interval: Interval * ?displayLogs: bool -> Quote list

union case Interval.Daily: Interval

namespace Plotly

namespace Plotly.NET

val dateAdjClose: (DateTime * float) list

val x: Quote

Quote.Date: DateTime

Quote.AdjustedClose: float
<summary> Split and dividend adjusted Close price </summary>

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)

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 returns: (DateTime * float) 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 sortBy: projection: ('T -> 'Key) -> list: 'T list -> 'T list (requires comparison)

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

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

val a: Quote

val b: Quote

val avgReturnEachMonth: (DateTime * int * float) list

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

val date: DateTime

val ret: float

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>

val month: DateTime

val xs: (DateTime * float) list

val avgPrice: float

val price: float

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

property List.Length: int with get

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

val monthlyReturnChart: GenericChart.GenericChart

val cnt: int

static member Chart.Bar: 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.Bar: 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 stddev: xs: float seq -> float

val xs: float seq

val mu: float

module Seq from Microsoft.FSharp.Collections

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

val sse: float

val sumBy: projection: ('T -> 'U) -> source: 'T seq -> 'U (requires member (+) and member Zero)

val n: float

val length: source: 'T seq -> int

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

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type float = Double

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type float<'Measure> = float

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

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namespace FSharp

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namespace Microsoft.FSharp

namespace FSharp.Stats

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 rollingVols: (DateTime * float) list

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

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module List from Microsoft.FSharp.Collections

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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

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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 ...

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new: unit -> List

val windowed: windowSize: int -> list: 'T list -> 'T list list

val maxWindowDate: DateTime

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

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module Seq from Microsoft.FSharp.Collections

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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

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new: unit -> Seq

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

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

val dailyVol: float

val annualizedVolInPct: float

val volChart: GenericChart.GenericChart