Package 'rolloptim'

Rolling Optimizations

Description

Analytical computation of rolling optimizations for time-series data.

Details

rolloptim is a package that provides analytical computation of rolling optimization for time-series data.

Author(s)

Jason Foster

References

Markowitz, H.M. (1952). "Portfolio Selection." The Journal of Finance, 7(1), 77–91.

Tam, A. (2021). "Lagrangians and Portfolio Optimization." https://www.adrian.idv.hk/2021-06-22-kkt/.

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Rolling Optimizations to Maximize Mean

Description

A function for computing rolling optimizations to maximize mean.

Usage

roll_max_mean(mu, total = 1, lower = 0, upper = 1)

Arguments

mu	matrix. Rows are means and columns are variables.
total	numeric. Sum of the weights.
lower	numeric. Lower bound of the weights.
upper	numeric. Upper bound of the weights.

Value

An object of the same class and dimension as mu with the rolling optimizations to maximize mean.

Examples

if (requireNamespace("roll", quietly = TRUE)) {

n_vars <- 3
n_obs <- 15
x <- matrix(rnorm(n_obs * n_vars), nrow = n_obs, ncol = n_vars)

mu <- roll::roll_mean(x, 5)

# rolling optimizations to maximize mean
roll_max_mean(mu)

}

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Rolling Optimizations to Maximize Utility

Description

A function for computing rolling optimizations to maximize utility.

Usage

roll_max_utility(mu, sigma, lambda = 1, total = 1, lower = 0,
  upper = 1)

Arguments

mu	matrix. Rows are means and columns are variables.
sigma	cube. Slices are covariance matrices.
lambda	numeric. Risk aversion parameter.
total	numeric. Sum of the weights.
lower	numeric. Lower bound of the weights.
upper	numeric. Upper bound of the weights.

Value

An object of the same class and dimension as mu with the rolling optimizations to maximize utility.

Examples

if (requireNamespace("roll", quietly = TRUE)) {

n_vars <- 3
n_obs <- 15
x <- matrix(rnorm(n_obs * n_vars), nrow = n_obs, ncol = n_vars)

mu <- roll::roll_mean(x, 5)
sigma <- roll::roll_cov(x, width = 5)

# rolling optimizations to maximize utility
roll_max_utility(mu, sigma, lambda = 1)

}

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Rolling Optimizations to Minimize Residual Sum of Squares

Description

A function for computing rolling optimizations to minimize residual sum of squares.

Usage

roll_min_rss(xx, xy, total = 1, lower = 0, upper = 1)

Arguments

xx	cube. Slices are crossproducts of x and x.
xy	cube. Slices are crossproducts of x and y.
total	numeric. Sum of the weights.
lower	numeric. Lower bound of the weights.
upper	numeric. Upper bound of the weights.

Value

An object of the same class and dimension as x with the rolling optimizations to minimize residual sum of squares.

Examples

if (requireNamespace("roll", quietly = TRUE)) {

n_vars <- 3
n_obs <- 15
x <- matrix(rnorm(n_obs * n_vars), nrow = n_obs, ncol = n_vars)
y <- rnorm(n_obs)

xx <- roll::roll_crossprod(x, x, 5)
xy <- roll::roll_crossprod(x, y, 5)

# rolling optimizations to minimize residual sum of squares
roll_min_rss(xx, xy)

}

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Rolling Optimizations to Minimize Variance

Description

A function for computing rolling optimizations to minimize variance.

Usage

roll_min_var(sigma, total = 1, lower = 0, upper = 1)

Arguments

sigma	cube. Slices are covariance matrices.
total	numeric. Sum of the weights.
lower	numeric. Lower bound of the weights.
upper	numeric. Upper bound of the weights.

Value

An object of the same class and dimension as mu with the rolling optimizations to minimize variance.

Examples

if (requireNamespace("roll", quietly = TRUE)) {

n_vars <- 3
n_obs <- 15
x <- matrix(rnorm(n_obs * n_vars), nrow = n_obs, ncol = n_vars)

sigma <- roll::roll_cov(x, width = 5)

# rolling optimizations to minimize variance
roll_min_var(sigma)

}

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