Objective functions

Intermediate Portfolio Analysis in R

Ross Bennett

Instructor

Objective functions

Objective functions compute the objective value. In PortfolioAnalytics, objective functions can be any valid R function.

Common portfolio risk measures
- standard deviation, expected shortfall, value at risk, component contribution to risk, maximum drawdown, Sharpe Ratio
Common benchmark relative performance measures
- information ratio, tracking error, excess return, maximum relative drawdown

Custom objective functions

User defined functions as objective functions

Argument naming:
- R for asset returns
- weights for the portfolio weights
- mu, sigma, m3, m4 for the moments
Returns a single value

# Annualized sharpe ratio
sr_annualized <- function(R, weights, sigma, scale, rfr){

    # Geometric annualized return
    r <- Return.annualized(Return.portfolio(R, weights), scale = scale)
    # Annual excess return
    re <- r - rfr

    # Annualized portfolio standard deviation
    pasd <- sqrt(as.numeric(t(weights) %*% 
                 sigma %*% weights)) * sqrt(scale)

    return(re / pasd)
}

data(edhec)
asset_returns <- edhec[,1:4]

# Setup spec and add constraints
port_spec <- portfolio.spec(assets = colnames(asset_returns))
port_spec <- add.constraint(portfolio = port_spec, 
                            type = "full_investment")
port_spec <- add.constraint(portfolio = port_spec, 
                            type = "long_only")

# Add custom objective function
port_spec <- add.objective(portfolio = port_spec, 
                           type = "return", name = "sr_annualized",
                           arguments = list(scale = 12, rfr = 0.02))

Let's practice!

Intermediate Portfolio Analysis in R