Introduction

PQBaseCamp.jl is Julia package that encodes basic methods required by other Paliquant packages.

Installation and Requirements

PQBaseCamp.jl can be installed, updated, or removed using the Julia package management system. To access the package management interface, open the Julia REPL, and start the package mode by pressing ]. While in package mode, to install PQBaseCamp.jl, issue the command:

(@v1.7.x) pkg> add PQBaseCamp

To use PQBaseCamp.jl in your projects, issue the command:

julia> using PQBaseCampp

Quick start guide

PQBaseCamp.jl exports six functions for doing basic computation on the financial data. It is assumed the data is downloaded from Polygon.io using the PQPolygonSDK.jl package.

Compute log or linear price returns

The Δ function (and its associated methods) is used to compute either the log or simple (linear) return from price data encoded in a DataFrame:

Δ(model::LogReturnComputationModel; multiplier::Float64 = 1.0) --> DataFrame

or

Δ(model::LinearReturnComputationModel; multiplier::Float64 = 1.0) --> DataFrame

where LogReturnComputationModel or LogReturnComputationModel model instances (both of which can the same fields) can be constructed using the default constructor:

mutable struct LogReturnComputationModel <: AbstractBaseCampComputation

    # data -
    ticker::String
    data::DataFrame
    map::Pair{Symbol,Symbol}
    from::Union{Date,Nothing}
    to::Union{Date,Nothing}

    # constructor -
    LogReturnComputationModel() = new()
end

Fitting probability density functions to price return data

Sometimes we may want to fit a distribution to historical price returns e.g., when constructing random walk models for a particular asset or basket of assets. To facilitate this, PQBaseCamp.jl encodes the 𝒟 function(s):

𝒟(distribution::Type{T}, data::DataFrame; 
    colkey::Symbol = :Δ) --> UnivariateDistribution where {T<:ContinuousUnivariateDistribution}

where ContinuousUnivariateDistribution is any type of continuous univariate probability density function encoded in the Distributions.jl package. The optional colkey parameter holds the symbol of the column in the data DataFrame corresponding to the log or simple return values.

In cases where we have many assets that we are interested in, we export a broadcast version of the 𝒟 function:

𝒟(distribution::Type{T}, data::Dict{String, DataFrame}; 
    colkey::Symbol = :Δ) --> Dict{String, T} where {T<:ContinuousUnivariateDistribution}

The 𝒟(...) method returns a Dict holding the distribution models (ticker symbols as keys) where the input argument data is a Dict with ticker symbols as keys pointing to return DataFrames.

Computing beta

Beta is a measure of the volatility of an asset or portfolio relative to the overall market. Beta is defined as the covariance between an asset's return and the market return, dived by the variance of the market return:

β(tickers::Array{String,1}, data::Dict{String,DataFrame};
    key::Symbol = :Δ, base::String = "SPY") --> Array{Float64,1}

The β(...) function returns an array of beta values (in the same order as the tickers array). The tickers array holds a list of ticker symbols, and data is a Dict holding ticker symbols as keys pointing to return DataFrames. The optional argument key of type Symbol holds the column name for the return column in the data DataFrame, and base denotes the ticker symbol for the market, taken to be SPY by default.

Covariance

The covariance function is a wrapper around the cov function of the Statistics.jl package in the standard library:

covariance(tickers::Array{String,1}, data::Dict{String,DataFrame}; 
    key::Symbol = :Δ) --> Array{Float64,2}

The covariance(...) function returns the covariance matrix in the same order as the tickers array. The tickers array holds a list of ticker symbols, and data is a Dict holding ticker symbols as keys pointing to return DataFrames. The optional argument key of type Symbol holds the column name for the return data in the data DataFrame.

Sampling

Paliquant relies heavily on Monte-Carlo methods. A key component of Monte-Carlo approaches is sampling:

sample(model::T, number_of_steps::Int64;
    number_of_sample_paths = 100, number_of_strata = 1) --> Array{Float64,2} where {T<:ContinuousUnivariateDistribution}

The sample(...) function generates a number_of_steps by 2 * number_of_sample_paths array of random draws from the model, where model is any type of continuous univariate probability density function encoded in the Distributions.jl package. The optional argument number_of_strata (default: 1) is used for stratified sampling; the number_of_strata denotes the number of subpopulations to construct. The sample(...) uses the antithetic variates method for variance reduction when generating samples.

Sampling a collection of return models can be done using:

sample(models::Dict{String,T}, number_of_steps::Int64; 
    number_of_sample_paths = 100, number_of_strata = 1) --> Dict{String,Array{Float64,2}} where {T<:ContinuousUnivariateDistribution}

where models is a Dict holding ticker symbols as keys that point to individual return probability models. The probability models can be of any type of continuous univariate probability density function encoded in the Distributions.jl package.

To sample a multivariate distribution, use:

function sample(model::T, number_of_steps::Int64; 
    number_of_sample_paths = 100) --> Array{Array{Float64,2},1} where {T<:ContinuousMultivariateDistribution}

where model denotes any type of ContinuousMultivariateDistribution encoded in the Distributions.jl package. This version of the sample method returns a number_of_steps array of arrays where the inner array dimension is the number of dimensions of the model by number_of_sample_paths.

Disclaimer and Risks

Paliquant software and PQBaseCamp.jl is offered solely for training and informational purposes. No offer or solicitation to buy or sell securities or securities derivative products of any kind, or any type of investment or trading advice or strategy, is made, given or in any manner endorsed by Paliquant.

Trading involves risk. Carefully review your financial situation before investing in securities, futures contracts, options or commodity interests. Past performance, whether actual or indicated by historical tests of strategies, is no guarantee of future performance or success. Trading is generally not appropriate for someone with limited resources, investment or trading experience, or a low-risk tolerance. Only risk capital that will not be needed for living expenses.

You are fully responsible for any investment or trading decisions you make, and such decisions should be based solely on your evaluation of your financial circumstances, investment or trading objectives, risk tolerance and liquidity needs.