目標函式

R 中級投資組合分析

Ross Bennett

Instructor

目標函式

目標函式會計算目標值。在 PortfolioAnalytics 中，目標函式可以是任何有效的 R 函式。

常見的投資組合風險衡量
- 標準差、期望短缺（ES）、在險價值（VaR）、風險成分貢獻、最大回落、Sharpe 比率
常見的相對基準績效衡量
- 資訊比率、追蹤誤差、超額報酬、最大相對回落

自訂目標函式

使用者自訂函式作為目標函式

參數命名：
- R：資產報酬
- weights：投資組合權重
- mu、sigma、m3、m4：各階動差
回傳單一數值

# 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))

一起來練習吧！

R 中級投資組合分析