# R/PCDaR.R In FRAPO: Financial Risk Modelling and Portfolio Optimisation with R

```PCDaR <- function(PriceData, alpha = 0.95, bound = 0.05, softBudget = FALSE, ...){
if(is.null(dim(PriceData))){
stop("Argument for 'PriceData' must be rectangular.\n")
}
if(any(is.na(PriceData))){
stop("NA-values contained in object for 'PriceData'.\n")
}
if(alpha <= 0 || alpha >= 1){
stop("Argument for 'alpha' must be in the interval (0, 1).\n")
}
if(bound <= 0 || bound >= 1){
stop("Argument for 'bound' must be in the interval (0, 1).\n")
}
call <- match.call()
RC <- as.matrix(returnseries(PriceData, method = "discrete", percentage = FALSE, compound = TRUE))
rownames(RC) <- NULL
N <- ncol(RC)
J <- nrow(RC)
w <- rep(0, N) ## weights
u <- rep(0, J) ## high-watermark
v <- rep(0, J) ## draw downs (above threshold)
z <- 0         ## thresh
x <- c(w, u, v, z)
## Defining objective (end-wealth)
obj <- c(as.numeric(RC[J, ]), rep(0, J), rep(0, J), 0)
## a1: constraint that weights are positive
a1 <- cbind(diag(N), matrix(0, nrow = N, ncol = 2 * J + 1))
d1 <- rep(">=", N)
b1 <- rep(0, N)
## a2: budget constraint
a2 <- c(rep(1, N), rep(0, 2 * J + 1))
ifelse(softBudget, d2 <- "<=", d2 <- "==")
b2 <- 1
## a3: draw-down constraint (1) assigning summands to v
a3 <- cbind(RC, -1 * diag(J), diag(J), matrix(1, ncol = 1, nrow = J))
d3 <- rep(">=", J)
b3 <- rep(0, J)
## a4: Unequality such draw downs above thresh are positive
a4 <- cbind(matrix(0, ncol = N, nrow = J),
matrix(0, ncol = J, nrow = J),
diag(J),
matrix(0, ncol = 1, nrow = J))
d4 <- rep(">=", J)
b4 <- rep(0, J)
## a5: defining average drawdowns above threshold
a5 <- c(rep(0, N), rep(0, J), (1/J)*(1/(1-alpha)) * rep(1, J), 1)
d5 <- "<="
b5 <- bound
## a6: draw-down constraint (2)
a6 <- cbind(-1 * RC, diag(J), matrix(0, nrow = J, ncol = J + 1))
d6 <- rep(">=", J)
b6 <- rep(0, J)
## a7: draw-down constraint (3)
D1 <- -1.0 * diag(J)
udiag <- embed(1:J, 2)[, c(2, 1)]
D1[udiag] <- 1
a7 <- cbind(matrix(0, ncol = N, nrow = J),
D1,
matrix(0, nrow = J, ncol = J + 1))
a7 <- a7[-J, ]
d7 <- rep(">=", J - 1)
b7 <- rep(0, J - 1)
## a8: draw-down constraint (4)
a8 <- c(rep(0, N), 1, rep(0, J-1), rep(0, J), 0)
d8 <- "=="
b8 <- 0
## Combining restrictions
Amat <- rbind(a1, a2, a3, a4, a5, a6, a7, a8)
Dvec <- c(d1, d2, d3, d4, d5, d6, d7, d8)
Bvec <- c(b1, b2, b3, b4, b5, b6, b7, b8)
## Solving LP
opt <- Rglpk_solve_LP(obj = obj, mat = Amat, dir = Dvec, rhs = Bvec,
max = TRUE, ...)
if(opt\$status != 0){
}
## Creating object PortMdd, inherits from PortSol
weights <- opt\$solution[1:N]
names(weights) <- colnames(PriceData)
equity <- matrix(apply(RC, 1, function(x) sum(x * weights)), ncol = 1)
rownames(equity) <- rownames(PriceData)
uvals <- opt\$solution[(N + 1):(N + J)]
dd <- as.timeSeries(uvals - equity)
colnames(dd) <- "DrawDowns"
z <- opt\$solution[N + J + J + 1]
CDaR <- mean(dd[dd >= z, 1])
obj <- new("PortCdd", weights = weights, opt = opt, type = "conditional draw-down at Risk", call = call, CDaR = CDaR, thresh = z, DrawDown = dd)
return(obj)
}
```

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FRAPO documentation built on May 2, 2019, 6:33 a.m.