TVMVP (version 1.0.5)

predict_portfolio: Predict Optimal Portfolio Weights Using Time-Varying Covariance Estimation

Description

This function estimates optimal portfolio weights using a time-varying covariance matrix derived from Local Principal Component Analysis (Local PCA). The procedure is available either as a stand-alone function or as a method in the `TVMVP` R6 class. It computes the following portfolios:

1. Global Minimum Variance Portfolio (MVP)

2. Maximum Sharpe Ratio Portfolio (if max_SR = TRUE)

3. Return-Constrained Minimum Variance Portfolio (if min_return is provided)

Usage

predict_portfolio(
  obj,
  horizon = 1,
  max_factors = 3,
  kernel_func = epanechnikov_kernel,
  min_return = NULL,
  max_SR = NULL,
  rf = NULL
)

Value

An object of class PortfolioPredictions (an R6 object) with:

summary

A data frame of evaluation metrics (expected return, risk, Sharpe ratio) for all computed portfolios.

MVP

A list containing the weights, expected return, risk, and Sharpe ratio for the Global Minimum Variance Portfolio.

max_SR

(Optional) A list with metrics for the Maximum Sharpe Ratio Portfolio.

MVPConstrained

(Optional) A list with metrics for the Return-Constrained Portfolio.

Arguments

obj

An object of class TVMVP with the data.

horizon

Integer. Investment horizon over which expected return and risk are computed. Default is 1.

max_factors

Integer. The number of latent factors to consider in the Local PCA model. Default is 3.

kernel_func

Function. Kernel used for weighting observations in Local PCA. Default is epanechnikov_kernel.

min_return

Optional numeric. If provided, the function computes a Return-Constrained Portfolio that targets this minimum return.

max_SR

Logical. If TRUE, the Maximum Sharpe Ratio Portfolio is also computed. Default is NULL.

rf

Numeric. Log risk-free rate. If NULL, defaults to 0.

Methods

The returned object includes:

• $print(): Nicely prints summary and portfolio access information.

• $getWeights(method = c("MVP", "max_SR", "MVPConstrained")): Retrieves the weights for the selected portfolio.

Details

Two usage styles:

#'

# R6 method interface
tv <- TVMVP$new()
tv$set_data(returns)
tv$determine_factors(max_m=5)
prediction <- tv$predict_portfolio(horizon = 1, min_return = 0.01, max_SR = TRUE)
#' # Function interface
prediction <- predict_portfolio(obj, horizon = 5, m = 2, min_return = 0.01, max_SR=TRUE)

The methods can then be used on prediction to retrieve the weights.

The function estimates a time-varying covariance matrix using Local PCA: $$\hat{\Sigma}_{r,t}=\hat{\Lambda}_t \hat{\Sigma}_F \hat{\Lambda}_t' + \tilde{\Sigma}_e$$ Where \(\hat{\Lambda}_t\) is the factor loadings at time t, \(\hat{\Sigma}_F\) is the factor covariance matrix, and \(\tilde{\Sigma}_e\) is regularized covariance matrix of the idiosyncratic errors.

It forecasts asset-level expected returns using a simple ARIMA model selection procedure and uses these in portfolio optimization. Optimization strategies include:

• Global minimum variance (analytical)

• Maximum Sharpe ratio (if max_SR = TRUE)

• Minimum variance with expected return constraint (if min_return is provided)

References

Lillrank, E. (2025). A Time-Varying Factor Approach to Covariance Estimation

Fan, Q., Wu, R., Yang, Y., & Zhong, W. (2024). Time-varying minimum variance portfolio. Journal of Econometrics, 239(2), 105339.

Examples

# \donttest{
set.seed(123)
returns <- matrix(rnorm(200 * 20, mean = 0, sd = 0.02), ncol = 20)

# Initialize object
tv <- TVMVP$new()
tv$set_data(returns)

# Optimize weights and predict returns
result <- predict_portfolio(
  tv,
  horizon = 5,
  m = 3,
  min_return = 0.02,
  max_SR = TRUE
)

# Print the portfolio performance summary
print(result)

# Access MVP weights
result$getWeights("MVP")

# Access Max Sharpe weights (if computed)
result$getWeights("max_SR")

# Or use R6 method interface
tv$determine_factors(max_m=5)
prediction <- tv$predict_portfolio(horizon = 1, min_return)
prediction
prediction$getWeights("MVPConstrained")
# }