portfOptim | R Documentation |

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

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

`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)? |

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.

`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) |

This function is usually called by drawFigure.

Arto Luoma <arto.luoma@wippies.com>

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")
with(stockData,portfOptim(i=1:5,symbol=rownames(stockData),
yield=divYield/100,vol=vol/100,beta=beta/100,total=100, sim=TRUE))
```

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