Description Usage Arguments Details Value References

Computes Value-at-Risk and related measures for a portfolio of assets.

The functions are:

`pfolioVaR` | computes Value-at-Risk for a portfolio of assets, |

`pfolioCVaRplus` | computes Value-at-Risk+ for a portfolio of assets, |

`pfolioCVaR` | computes Conditional Value-at-Risk for a PF of assets, |

`lambdaCVaR` | computes CVaR's atomic split value lambda, |

`pfolioCVaRoptim` | computes Conditional VaR from mean-CVaR optimization, |

`pfolioMaxLoss` | computes Maximum Loss for a portfolio of assets, |

`pfolioReturn` | computes return values of a portfolio, |

`pfolioTargetReturn` | computes the target return of a portfolio, |

`pfolioTargetRisk` | computes the target risk of a portfolio, |

`pfolioHist` | plots a histogram of the returns of a portfolio. |

1 2 3 4 5 6 7 8 9 10 11 | ```
pfolioVaR(x, weights = NULL, alpha = 0.05)
pfolioCVaRplus(x, weights = NULL, alpha = 0.05)
pfolioCVaR(x, weights = NULL, alpha = 0.05)
lambdaCVaR(n, alpha = 0.05)
pfolioCVaRoptim(x, weights = NULL, alpha = 0.05)
pfolioMaxLoss(x, weights = NULL)
pfolioReturn(x, weights = NULL, geometric = FALSE)
pfolioTargetReturn(x, weights = NULL)
pfolioTargetRisk(x, weights = NULL)
pfolioHist(x, weights = NULL, alpha = 0.05, range = NULL, details = TRUE, ...)
``` |

`x` |
a 'timeSeries' object, data frame or any other rectangular
object which can be expressed as a matrix. The first
dimension is the number of observations, we call it |

`weights` |
usually a numeric vector which has the length of the number of
assets. The weights measures the normalized weights of the
individual assets. By default |

`geometric` |
a logical flag, should geometric returns be used, by default FALSE |

`alpha` |
a numeric value, the confidence interval, by default 0.05. |

`details` |
a logical value, should details be printed? |

`n` |
the number of observation from which the CVaR's atomic split
value |

`range` |
a numeric vector of two elements limiting the plot range of
the histogram. This is quite useful if one likes to compare
several plots on the same scale. If |

`...` |
optional arguments to be passet to the function |

The percentile measures of loss (or reward) are defined in the
following way: Let *f(x ,y)* be a loss functions depending
upon a decision vector *x = (x_1, ..., x_n )* and a random
vector *y = (y_1, ..., y_m)*, then

*pfolioVaR* is the alpha-percentile of the loss distribution, a
smallest value such that the probability that losses exceed or
are equal to this value is greater or equal to alpha.

*pfolioCVaRplus* or "CVaR+" or the "upper CVaR" are the expected
losses strictly exceeding VaR. This is also also called "Mean
Excess Loss" and "Expected Shortfall".

*pfolioCVaR* is a weighted average of VaR and CVaRplus defined as
*CVaR = lambda*VaR + (1-lambda)* CVaRplus, for
*0 <= lambda <= 1*.

Note, CVaR is convex, but VaR and CVaRplus may be non-convex. The
following inequalities are valid: *VaR <= CVaR <= CVaRplus*.

`pfolioVaR`

returns the value of risk, VaR, for a portfolio of assets, a
numeric value.

`pfolioCVaRplus`

returns the conditional value of risk plus, CVaRplus, for a
portfolio of assets, a numeric value.

`pfolioCVaR`

returns the conditional value of risk, CVaR, for a portfolio
of assets, a numeric value.

`lambdaCVaR`

returns CVaR's atomic split value `lambda`

, a numeric value.

`pfolioMaxLoss`

returns the maximum loss value of the portfolio, a numeric value.

`pfolioReturn`

returns the total portfolio return computed from the set of
assets `x`

, a numeric vector.

`pfolioTargetReturn`

returns the total return or target return computed from the set of
assets `x`

and weights `weights`

, a numeric value.

`pfolioTargetRisk`

returns the total risk (Sigma) or target risk computed from the set
of assets `x`

and `weights`

via the formual
`sqrt(weights %*% cov(x) %*% weights)`

, a numeric value.

`pfolioHist`

plots a histogram of portfolio returns and adds the values
for the VaR (blue), for the CVaRplus (red), and for the
maximum loss (green) to the histogram plot. The function
invisibly returns a list with the following elements: VaR,
VaRplus, maxLoss, mean, and sd. If `details`

is `TRUE`

,
then the result is printed.

Uryasev S. (2000);
*Conditional Value-at-Risk (CVaR): Algorithms and Applications*,
Risk Management and Financial Engineering Lab, University of Florida

Wuertz, D., Chalabi, Y., Chen W., Ellis A. (2009);
*Portfolio Optimization with R/Rmetrics*,
Rmetrics eBook, Rmetrics Association and Finance Online, Zurich.

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