1d:T7b1,# Plot the Bayesian efficient frontier \insertCite bauder21HDShOP and the provided portfolios. The plotted Bayesian efficient frontier is provided by \insertCite @Eq. (8) in @bauder21;textualHDShOP. 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 $\rm w^\prime \bar x$. ```r 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. ## Returns a ggplot object ## Examples ```r 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 ``` ## References \insertAllCited1e:T49a,M7.49933 0.25C3.49635 0.25 0.25 3.49593 0.25 7.50024C0.25 10.70

plot_frontier function