Basic Portfolio Statistics

This page covers important fundamentals for building portfolios.

Portfolio Weights
Mean and Variance of Portfolio Returns
Leverage

Portfolio Weights

An investment portfolio consists of positions in assets. It is common to refer to a position's size as its share of the portfolio's total value. This is known as the asset's portfolio weight.

The portfolio weight of asset $i$ in portfolio $p$ is

\[w_i=(\text{positionValue}_i)/(\text{portfolioValue}_p)\]

Long positions

When an investor buys a long position, they pay for the position now and hope to sell it later at a higher price.

Let's look at cash flows for long positions.

At time 0: investor has $100 cash and no shares.
At time 1: investor takes their $100 of cash and buys 4 shares of stock at a price of $25 per share. They have no cash and are long 4 shares.
At time 2: the stock has risen to $27, the investor sells their 4 shares. They have $108 of cash and no shares.

We can define some functions to update an account given these trades.

// A record type that defines an account
type AccountBalances =
    { Time: int
      Cash: float 
      Shares: float }

// A record type that defines a trade
type Trade = 
    { Shares: float 
      Price : float }

let accountAt0 = { Time = 0; Cash = 100.0; Shares = 0.0 }
let tradeAt1 = { Shares = 4.0; Price = 25.0 }

updateAccount is a function that updates an account after a trade is made.

(trade: Trade) restricts the trade parameter to data of type Trade.

(inAccount: AccountBalances) restricts the inAccount parameter to data of type AccountBalances

/// Function that updates an account after a trade is made.
let updateAccount (trade: Trade) (inAccount: AccountBalances) =
    let tradeValue = trade.Price * trade.Shares
    let newCash = inAccount.Cash - tradeValue
    let newShares = inAccount.Shares + trade.Shares
    let newTime = inAccount.Time + 1
    { Time = newTime 
      Cash = newCash 
      Shares = newShares }

You can make names with spaces using "``" before and after.

let ``expected account at t1`` = { Time = 1; Cash = 0.0; Shares = 4.0}
let ``actual account at t1`` = updateAccount tradeAt1 accountAt0 

``actual account at t1``

{ Time = 1
  Cash = 0.0
  Shares = 4.0 }

if ``actual account at t1`` <> ``expected account at t1`` then
    failwith "You are not updating account correctly after a trade"

Now we can calculate how the account value changes over time.

let accountAt1 = updateAccount tradeAt1 accountAt0

accountAt1

{ Time = 1
  Cash = 0.0
  Shares = 4.0 }

let tradeAt2 = { Shares = -4.0; Price = 27.0 }
let accountAt2 = updateAccount tradeAt2 accountAt1

accountAt2

{ Time = 2
  Cash = 108.0
  Shares = 0.0 }

We could have also written this code using the pipe operator.

let accountAt1' = accountAt0 |> updateAccount tradeAt1 // same as "updateAccount tradeAt1 accountAt0"
let accountAt2' = accountAt1 |> updateAccount tradeAt2 // same as "updateAccount tradeAt2 accountAt1"

accountAt1'

{ Time = 1
  Cash = 0.0
  Shares = 4.0 }

accountAt2'

{ Time = 2
  Cash = 108.0
  Shares = 0.0 }

The pipe operator does not look very useful above because we are only doing one operation. It is more useful when you're doing a series of multiple operations. This example recomputes the account value at time 2 by chaining together updates for the trades at times 1 and 2.

let accountAt2'' =
    accountAt0
    |> updateAccount tradeAt1
    |> updateAccount tradeAt2

accountAt2''

{ Time = 2
  Cash = 108.0
  Shares = 0.0 }

This code is closer to how you would describe it in English: "Start with the account at time 0, update it for the trade at time 1, then update it for the trade at time 2."

Practice: complete the code for the accountValue function below. It should calculate total account value of the stock and cash positiions. If it is correct then the account value test below should evaluate to true

let accountValue (stockPrice: float) (account: AccountBalances) =
    failwith "unimplemented"

// simple account value test
(accountValue 27.0 accountAt2) = 108.0

Portfolio weights of long positions

Now that we understand long positions we can calculate portfolio weights for them. Let's calculate weights for an example Portfolio A consisting of

$100 invested in AAPL
$300 invested in GOOG
$500 invested in TSLA

These are all long positions, meaning that they have positive costs.

let aaplPositionValue = 100.0
let googPositionValue = 300.0
let tslaPositionValue = 500.0

// This implies:

let portfolioValueA = aaplPositionValue + googPositionValue + tslaPositionValue

portfolioValueA

900.0

The portfolio weights are then

let aaplWeight = aaplPositionValue / portfolioValueA

aaplWeight

0.1111111111

let googWeight = googPositionValue / portfolioValueA

googWeight

0.3333333333

let tslaWeight = tslaPositionValue / portfolioValueA

tslaWeight

0.5555555556

These weights for AAPL, GOOG, and TSLA are all positive. Long positions always have positive weights.

Another thing to notice is that the portfolio weights add up to one (or 100%):

aaplWeight + googWeight + tslaWeight

val it: float = 1.0

This portfolio is a net long portfolio, meaning that it costs you money to purchase it. Net long portfolios such as this one must have portfolio weights that add up to one. Due to margin requirements, real-world portfolios are generally net long--you must put up capital to acquire the portfolio.

The other type of portfolio is a zero-cost portfolio. As the name implies, zero-cost portfolios do not require any investment to purchase. There is no cost because long positions are funded by offsetting short positions. To see how this works we need to examine how short positions work.

Short positions

When an investor buys a long position, they pay for the position now and hope to sell it later at a higher price. A short sale reverses this. The investor sells the position now and hopes to buy it back later at a lower price.

We now go through an example to see how the cash flows work.

At time 0: investor has $100 cash and no shares.
At time 1: investor borrows 4 shares of stock and sells them for a price of $25 per share. They have $200 cash and are short 4 shares.
At time 2: the stock has risen to $27, the investor buys back the 4 shares that they sold short and returns them to the person that they borrowed them from. They have $92 of cash and 0 shares.

The investor's cash and stock balances at the end of each period will look something like

let shortAt1 = { Shares = -4.0; Price = 25.0 }
let shortCoverAt2 = { Shares = 4.0; Price = 27.0 }

// positions at t1
accountAt0 
|> updateAccount shortAt1

{ Time = 1
  Cash = 200.0
  Shares = -4.0 }

// positions at t2
accountAt0 
|> updateAccount shortAt1 
|> updateAccount shortCoverAt2

{ Time = 2
  Cash = 92.0
  Shares = 0.0 }

Portfolio weights for short positions

Let's create a new portfolio, Portfolio B, that includes short sales and calculate weights. Assume that you start with Portfolio A and short $150 of AMZN stock. This generates $150 of cash that you have to put somewhere. For individual investors, often your broker puts it in bonds and gives you none of the interest. Institutional investors can get some of the interest or even reinvest the proceeds in something else. We will assume that we are an institution and can reinvest all of the short proceeds. We will take the $150 and add $50 to each of our AAPL, GOOG, and TLSA positions.

Short positions have negative portfolio weights.

let amznPositionValueB = -150.0
let aaplPositionValueB = aaplPositionValue + 50.0
let googPositionValueB = googPositionValue + 50.0
let tslaPositionValueB = tslaPositionValue + 50.0

let portfolioValueB = 
    amznPositionValueB +
    aaplPositionValueB +
    googPositionValueB +
    tslaPositionValueB

portfolioValueB

900.0

Compare to Portfolio A

portfolioValueA = portfolioValueB

val it: bool = true

The weights in Portfolio B:

let amznWeightB = amznPositionValueB / portfolioValueB

amznWeightB

-0.1666666667

let aaplWeightB = aaplPositionValueB / portfolioValueB

aaplWeightB

0.1666666667

let googWeightB = googPositionValueB / portfolioValueB

googWeightB

0.3888888889

let tslaWeightB = tslaPositionValueB / portfolioValueB

tslaWeightB

0.6111111111

The weights of Portfolio B also add up to one.

amznWeightB + aaplWeightB + googWeightB + tslaWeightB

val it: float = 1.0

Zero-cost portfolios

Another type of portfolio that you will see is zero-cost portfolios. They are called self funding because the short sale proceeds fund the long investments. The portfolio weights add up to 0. You can scale weights relative to what they would be per $ long or short.

An example:

// Portfolio C
let koPositionValue = -50.0
let hogPositionValue = 40.0
let yumPositionValue = 10.0

let dollarsLong = 50.0
let koWeight = koPositionValue / dollarsLong
let hogWeight = hogPositionValue / dollarsLong
let yumWeight = yumPositionValue / dollarsLong

printfn $"koWeight = {koWeight}"
printfn $"hogWeight= {hogWeight}"
printfn $"yumWeight= {yumWeight}"

koWeight = -1
hogWeight= 0.8
yumWeight= 0.2

koWeight + hogWeight + yumWeight

5.551115123e-17

Calculating weights using a list of positions

The calculations that we did thus far required code for each position. We did the same thing to each position, so there was some repetition. We can reduce the repetition by putting the positions into a list and then operating on the elements of the list via iteration.

// defining a position record type
type Position = { Id: string; PositionValue: float }

// assigning a list of positions to a value named portfolio
let portfolio =
    [ { Id = "AMZN"; PositionValue = amznPositionValueB }
      { Id = "AAPL"; PositionValue = aaplPositionValueB }
      { Id = "GOOG"; PositionValue = googPositionValueB }
      { Id = "TSLA"; PositionValue = tslaPositionValueB } ]

// This is called a list comprehension
let positionValues = [ for p in portfolio do p.PositionValue ]

[-150.0; 150.0; 350.0; 550.0]

The list module has many different functions for operating on lists. If you type List. you should see many different functions pop up. These functions are very useful. We will explore them in more detail later.

For now, let's see what List.map does.

portfolio |> List.map (fun p -> p.PositionValue)

val it: float list = [-150.0; 150.0; 350.0; 550.0]

This is the same result as the positionValues value that we calculated using the list comprehension. List.map "maps" each element of the list to an output using a function. In this case, our function (fun p -> p.PositionValue) was an anonymous function.

Another useful function from the list module is List.sum. We can use it to calculate the total value of the portfolio by summing position values.

let portfolioValue = positionValues |> List.sum

900.0

And with this we can calculate portfolio weights.

let portfolioWeights =
    [ for p in portfolio do 
        let weight = p.PositionValue / portfolioValue 
        p.Id, weight ]
portfolioWeights

[("AMZN", -0.1666666667); ("AAPL", 0.1666666667); ("GOOG", 0.3888888889);
 ("TSLA", 0.6111111111)]

Mean and Variance of Portfolio Returns

A portfolio's return.

A portfolio's return is the weighted average return of the portfolio's positions.

\[ r_p = \Sigma^N_{i=1} w_i r_i,\]

where $r$ is return, $i$ indexes stocks, and $w$ is portfolio weights.

type PositionsWithReturn =
    { Id: string 
      Weight: float 
      Return: float }

let exPortfolio =
    [ { Id = "A"; Weight = 0.25; Return = 0.1 }
      { Id = "B"; Weight = 0.75; Return = 0.2 } ]

let weightsXreturn = [ for pos in exPortfolio do pos.Weight * pos.Return ]
weightsXreturn

[0.025; 0.15]

let exPortfolioReturn = weightsXreturn |> List.sum 
exPortfolioReturn

0.175

We are now going to look at returns of actual stock and bond portfolios. The two portfolios are VTI and BND. These are value-weighted exchange traded funds (ETFs). VTI tracks a stock market index and BND tracks a bond market index. They are good proxies for the return of the overall US stock and bond markets.

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(2010,1,1)
let myEnd = DateTime.UtcNow
myEnd

2/20/2024 12:51:30 PM

let bnd = YahooFinance.History("BND",startDate=myStart,endDate=myEnd,interval = Interval.Daily)
let vti = YahooFinance.History("VTI",startDate=myStart,endDate=myEnd,interval = Interval.Daily)

This returns several data items for each point in time.

vti[0..3]

No value returned by any evaluator

The adjusted close is adjusted for stock splits and dividends. This adjustment is done so that you can calculate returns from the price changes.

Let's see what it looks like to plot it. We're going to use the plotly.NET library for this.

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

open Plotly.NET

Above we are loading an exact version by using a "," and version number.

Plot prices as a line chart.

let vtiAdjPrices = [ for period in vti do period.Date, period.AdjustedClose ]

Chart.Line(vtiAdjPrices)

No value returned by any evaluator

Ok, back to the main objective. We need to calculate returns. We calculate returns from sequential days, so we need to make sure that our data is sorted correctly from the oldest to the newest data. We can do this with List.Sort.

[1; 7; 10; 2; -1] |> List.sort

[-1; 1; 2; 7; 10]

Sort it by the date field.

let sortedBnd = bnd |> List.sortBy (fun x -> x.Date)

The first three observations.

sortedBnd[0..2]

No value returned by any evaluator

The last 3 observations.

sortedBnd[(sortedBnd.Length-3)..]

No value returned by any evaluator

Great, they are properly sorted. Now I want sequential pairs of data. List.pairwise is good for this.

[1 .. 5] |> List.pairwise

[(1, 2); (2, 3); (3, 4); (4, 5)]

let sequentialBnd = bnd |> List.pairwise

sequentialBnd[0]

No value returned by any evaluator

sequentialBnd[1]

No value returned by any evaluator

Take the first pair to see how to calculate returns.

Extract the first and second elements of the tuple using pattern matching.

let (bndA, bndB) = sequentialBnd[0]
bndA

No value returned by any evaluator

bndB

No value returned by any evaluator

Remember that with continuous compounding, $FV_T = PV_t \times e^{r}$ where $FV$ is the future value, $PV$ is the present value, $r$ is return between period $t$ and $T$.

If we take the log of both sides of the equation, we get

\[ log(FV) = log(PV) + r \rightarrow log(FV) - log (PV) = r\]

This $r$ is known as the log return. So to find the log return between two periods we can take the difference of the log prices (where the prices are adjusted for dividends).

(log bndB.AdjustedClose) - (log bndA.AdjustedClose)

No value returned by any evaluator

Putting it all together.

let bndReturn = 
    bnd
    |> List.sortBy (fun x -> x.Date)
    |> List.pairwise
    |> List.map (fun (a, b) -> (log b.AdjustedClose) - (log a.AdjustedClose))

let vtiReturn =
    vti
    |> List.sortBy (fun x -> x.Date)
    |> List.pairwise
    |> List.map (fun (a, b) -> (log b.AdjustedClose) - (log a.AdjustedClose))


let bndAvgReturn = bndReturn |> List.average
bndAvgReturn

No value returned by any evaluator

let vtiAvgReturn = vtiReturn |> List.average
vtiAvgReturn

No value returned by any evaluator

Portfolio returns for different weights.

let differentReturns =
  [ for w in [0.0 .. 0.2 .. 1.0] do w, w*bndAvgReturn + (1.0-w)*vtiAvgReturn ]

differentReturns

No value returned by any evaluator

Chart.Line(differentReturns)

Portfolio Variance

For a portfolio of $N$ assets, the portfolio variance $\sigma_p^2$ is

\[ \sigma_p^2 = \sum^N_{i=1} \sum^N_{j=1} w_i w_j cov(r_i,r_j) = \sum^N_{i=1} w^2_i\sigma^2_i + 2\sum_{j<i} w_i w_j cov(r_i,r_j)\]

where $i$ and $j$ index assets, $r_i$ is the return of asset $i$, $\sigma^2_i$ is the variance of $r_i$, and $cov(r_i,r_j)$ is the covariance between $r_i$ and $r_j$.

For a portfolio of two assets $x$ and $y$ this simplifies to:

\[ \sigma^2_p = w_x^2 \sigma^2_x + w_y^2 \sigma^2_y + 2 w_x w_y cov(r_x,r_y).\]

this. For next time: Portfolio Variance and Leverage

Leverage

#r "nuget: FSharp.Stats, 0.5.0"

open FSharp.Stats
open FSharp.Stats.Correlation




Seq.pearson bndReturn vtiReturn

type AccountBalances = { Time: int Cash: float Shares: float }

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

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

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

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

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

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

type Trade = { Shares: float Price: float }

val accountAt0: AccountBalances

val tradeAt1: Trade

val updateAccount: trade: Trade -> inAccount: AccountBalances -> AccountBalances
Function that updates an account after a trade is made.

val trade: Trade

val inAccount: AccountBalances

val tradeValue: float

Trade.Price: float

Trade.Shares: float

val newCash: float

AccountBalances.Cash: float

val newShares: float

AccountBalances.Shares: float

val newTime: int

AccountBalances.Time: int

val failwith: message: string -> 'T

val accountAt1: AccountBalances

val tradeAt2: Trade

val accountAt2: AccountBalances

val accountAt1': AccountBalances

val accountAt2': AccountBalances

val accountAt2'': AccountBalances

val accountValue: stockPrice: float -> account: AccountBalances -> 'a

val stockPrice: float

val account: AccountBalances

val aaplPositionValue: float

val googPositionValue: float

val tslaPositionValue: float

val portfolioValueA: float

val aaplWeight: float

val googWeight: float

val tslaWeight: float

val shortAt1: Trade

val shortCoverAt2: Trade

val amznPositionValueB: float

val aaplPositionValueB: float

val googPositionValueB: float

val tslaPositionValueB: float

val portfolioValueB: float

val amznWeightB: float

val aaplWeightB: float

val googWeightB: float

val tslaWeightB: float

val koPositionValue: float

val hogPositionValue: float

val yumPositionValue: float

val dollarsLong: float

val koWeight: float

val hogWeight: float

val yumWeight: float

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

type Position = { Id: string PositionValue: float }

Multiple items
val string: value: 'T -> string

--------------------
type string = System.String

val portfolio: Position list

val positionValues: float list

val p: Position

Position.PositionValue: float

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

val portfolioValue: float

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

val portfolioWeights: (string * float) list

val weight: float

Position.Id: string

type PositionsWithReturn = { Id: string Weight: float Return: float }

val exPortfolio: PositionsWithReturn list

val weightsXreturn: float list

val pos: PositionsWithReturn

PositionsWithReturn.Weight: float

PositionsWithReturn.Return: float

val exPortfolioReturn: float

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 bnd: 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

val vti: Quote list

namespace Plotly

namespace Plotly.NET

val vtiAdjPrices: (DateTime * float) list

val period: 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 sort: list: 'T list -> 'T list (requires comparison)

val sortedBnd: Quote list

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

val x: Quote

property List.Length: int with get

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

val sequentialBnd: (Quote * Quote) list

val bndA: Quote

val bndB: Quote

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

val bndReturn: float list

val a: Quote

val b: Quote

val vtiReturn: float list

val bndAvgReturn: float

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

val vtiAvgReturn: float

val differentReturns: (float * float) list

val w: float

Multiple items
namespace FSharp

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

namespace FSharp.Stats

module Correlation from FSharp.Stats
<summary> Contains correlation functions for different data types </summary>

Multiple items
module Seq from FSharp.Stats.Correlation
<summary> Contains correlation functions optimized for sequences </summary>

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

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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

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new: unit -> Seq

val pearson: seq1: 'T seq -> seq2: 'T seq -> float (requires member op_Explicit and member Zero and member One)
<summary> Calculates the pearson correlation of two samples. Homoscedasticity must be assumed. </summary>