findSig {CLA}

Find sigma(W) and W, given mu(W) and CLA result

Description

Find \sigma(W) and W, given \mu(W) and CLA result.

Usage

findSig(Mu0, result, covar, equal.tol)

Arguments

Mu0

numeric vector of \mu(W) values.

result

a list with components MS_weight and weights_set as resulting from CLA().

covar

the same n \times n covariance matrix (of asset returns) as the argument of CLA().

equal.tol

numeric tolerance to be used in all.equal(.., tolerance = equal.tol) in the check to see if the \mu of two neighbouring turning points are equal.

Value

a list with components

Sig

numeric vector of same length, say M, as Mu0.

weight

numeric n \times M matrix of weights.

References

Master thesis, p.33

See Also

findMu, CLA, MS.

Examples

data(muS.sp500)
## Full data taking too much time for example: Subset of n=21:
if(getRversion() >= "3.6") .Rk <- RNGversion("3.5.0") # for back compatibility & warning
set.seed(2018)
iS <- sample.int(length(muS.sp500$mu), 21)
if(getRversion() >= "3.6") do.call(RNGkind, as.list(.Rk)) # revert
cov21 <- muS.sp500$covar[iS, iS]
CLsp.21 <- CLA(muS.sp500$mu[iS], covar=cov21, lB=0, uB = 1/2)
CLsp.21 # 14 turning points
summary(tpM <- CLsp.21$MS_weights[,"Mu"])
str(m0 <- c(min(tpM),seq(0.00205, 0.00525, by = 0.00005), max(tpM)))
sig. <- findSig(m0, result=CLsp.21, covar=cov21)
str(sig.)
stopifnot(dim(sig.$weight) == c(21, length(m0)))
plot(sig.$Sig, m0, xlab=quote(sigma), ylab = quote(mu),
     type = "o", cex = 1/4)
points(CLsp.21$MS_weights, col = "tomato", cex = 1.5)
title("Efficient Frontier from CLA()")
mtext("findSig() to interpolate between turning points", side=3)