# portfOptim: Portfolio optimization for an index model In RcmdrPlugin.RiskDemo: R Commander Plug-in for Risk Demonstration

 portfOptim R Documentation

## Portfolio optimization for an index model

### Description

Finds an optimal portfolio for long-term investments and plots a return distribution.

### Usage

``````portfOptim(i, symbol, yield, vol, beta,
indexVol = 0.2, nStocks = 7, total = 1, balanceInt = 1,
C = 0.05, riskProportion = 1, riskfreeRate = 0, sim = FALSE)
``````

### Arguments

 `i` vector of the indices of the included risky investments `symbol` character vector of the symbols of the risky investments `yield` vector of expected yields (in euros) `vol` vector of volatilities `beta` vector of betas `indexVol` portfolio index volatility `nStocks` number of stocks in the portfolio `total` total sum invested (in euros) `balanceInt` balancing interval of the portfolio (in years) `C` expected portfolio return (in euros) `riskProportion` proportion of risky investments `riskfreeRate` risk-free interest rate `sim` is the return distribution simulated and plotted (logical value)?

### Details

The arguments vol, beta, indexVol, riskProportion and riskfreeRate are given in decimals. The portfolio is optimized by minimizing the variance of the portfolio yield for a given expected yield. The returns are assumed to be log-normally distributed. The covariance matrix is computed using the single index model and the properties of the log-normal distribution.

### Value

 `portfolio` numeric vector of allocations to each stock (in euros) `returnExpectation` expected value of the return distribution (in euros) `returnDeviation` standard deviation of the return distribution (in euros) `VaR` 0.5%,1%,5%,10% and 50% percentiles of the return distribution (in euros)

### Note

This function is usually called by drawFigure.

### Author(s)

Arto Luoma <arto.luoma@wippies.com>

### References

Bodie, Kane, and Marcus (2014) Investments, 10th Global Edition, McGraw-Hill Education, (see Section 7.4 The Markowitz Portfolio Optimization Model and Section 8.2 The Single-Index Model).

`drawFigure`
``````data(stockData, package="RcmdrPlugin.RiskDemo")