plot_frontier {HDShOP}

Plot the Bayesian efficient frontier (Bauder et al. 2021) and the provided portfolios.

Description

The plotted Bayesian efficient frontier is provided by Eq. (8) in Bauder et al. (2021). It is the set of optimal portfolios obtained by employing the posterior predictive distribution on the asset returns. This efficient frontier can be used to assess the mean-variance efficiency of various estimators of the portfolio weights. The standard deviation of the portfolio return is plotted in the x-axis and the mean portfolio return in the y-axis. The portfolios with the weights \rm{w} are added to the plot by computing \sqrt{\rm{w}^\prime S w} and \rm w^\prime \bar x.

Usage

plot_frontier(x, weights.eff = rep(1/nrow(x), length = nrow(x)))

Arguments

x

a p by n matrix or a data frame of asset returns. Rows represent different assets, columns – observations.

weights.eff

matrix of portfolio weights. Each column contains p values of the weights for a given portfolio. Default: equally weighted portfolio.

Value

a ggplot object

References

Bauder D, Bodnar T, Parolya N, Schmid W (2021). “Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty.” Quantitative Finance, 21(2), 221–242.

Examples

p <- 150
n <- 300
gamma <- 10
mu <- seq(0.2,-0.2, length.out=p)
Sigma <- RandCovMtrx(p=p)

x <- t(MASS::mvrnorm(n=n , mu=mu, Sigma=Sigma))

EW_port <- rep(1/p, length=p)
MV_shr_port <- new_MV_portfolio_weights_BDOPS21(x=x, gamma=gamma,
                                                b=EW_port, beta=0.05)$weights
GMV_shr_port <- new_MV_portfolio_weights_BDOPS21(x=x, gamma=Inf, b=EW_port,
                                                 beta=0.05)$weights
MV_trad_port <- new_MV_portfolio_traditional(x=x, gamma=gamma)$weights
GMV_trad_port <- new_MV_portfolio_traditional(x=x, gamma=Inf)$weights

weights.eff <- cbind(EW_port, MV_shr_port, GMV_shr_port,
                     MV_trad_port, GMV_trad_port)
colnames(weights.eff) <- c("EW", "MV_shr", "GMV_shr", "MV_trad", "GMV_trad")


Fplot <- plot_frontier(x, weights.eff)
Fplot