Description Usage Arguments Details Value Author(s) See Also Examples
Computes the Sharpe ratio of the hedged Markowitz portfolio of some observed returns.
1 2 3 4 5 6 7 | as.del_sropt(X, G, drag = 0, ope = 1, epoch = "yr")
## Default S3 method:
as.del_sropt(X, G, drag = 0, ope = 1, epoch = "yr")
## S3 method for class 'xts'
as.del_sropt(X, G, drag = 0, ope = 1, epoch = "yr")
|
X |
matrix of returns, or |
G |
an g x q matrix of hedge constraints. A
garden variety application would have |
drag |
the 'drag' term, c0/R. defaults to 0. It is assumed
that |
ope |
the number of observations per 'epoch'. For convenience of
interpretation, The Sharpe ratio is typically quoted in 'annualized'
units for some epoch, that is, 'per square root epoch', though returns
are observed at a frequency of |
epoch |
the string representation of the 'epoch', defaulting to 'yr'. |
Suppose xi are n independent draws of a q-variate normal random variable with mean mu and covariance matrix Sigma. Let G be a g x q matrix of rank g. Let xbar be the (vector) sample mean, and S be the sample covariance matrix (using Bessel's correction). Let
zeta(w) = (w'xbar - c0)/sqrt(w'Sw)
be the (sample) Sharpe ratio of the portfolio w, subject to risk free rate c0.
Let w* be the solution to the portfolio optimization problem:
max {zeta(w) | 0 < w'Sw <= R^2, G S w = 0},
with maximum value z* = zeta(w*).
Note that if ope
and epoch
are not given, the
converter from xts
attempts to infer the observations per epoch,
assuming yearly epoch.
An object of class del_sropt
.
Steven E. Pav shabbychef@gmail.com
Other del_sropt:
del_sropt
,
is.del_sropt()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | nfac <- 5
nyr <- 10
ope <- 253
# simulations with no covariance structure.
# under the null:
set.seed(as.integer(charToRaw("be determinstic")))
Returns <- matrix(rnorm(ope*nyr*nfac,mean=0,sd=0.0125),ncol=nfac)
# hedge out the first one:
G <- matrix(diag(nfac)[1,],nrow=1)
asro <- as.del_sropt(Returns,G,drag=0,ope=ope)
print(asro)
G <- diag(nfac)[c(1:3),]
asro <- as.del_sropt(Returns,G,drag=0,ope=ope)
# compare to sropt on the remaining assets
# they should be close, but not exact.
asro.alt <- as.sropt(Returns[,4:nfac],drag=0,ope=ope)
# using real data.
if (require(xts)) {
data(stock_returns)
# hedge out SPY
G <- diag(dim(stock_returns)[2])[3,]
asro <- as.del_sropt(stock_returns,G=G)
}
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