...
 
Commits (3)
......@@ -210,7 +210,9 @@ MS_plot <- function(ms, type = "o",
}
## FIXME:
## FIXME: --> see also in ../man/plot.CLA.Rd
## -----
## 0) Use findMu() and findSig() to draw the lines *between*
## 1) Learn from Tobias Setz to plot the lower part of the feasible region
## 2) Better title, using 'call'
## 3) mark some critical points particularly
......@@ -221,7 +223,7 @@ plot.CLA <- function(x, type = "o", main = "Efficient Frontier",
ylab = expression(mu(w)),
col = adjustcolor("blue", alpha.f = 0.5),
pch = 16, ...) {
stopifnot(is.matrix(ms <- x$MSweights))
stopifnot(is.matrix(ms <- x$MS_weights))
plot(ms[,"Sig"], ms[,"Mu"], type=type, pch=pch, col=col,
xlab=xlab, ylab=ylab, main=main, ...)
}
##-*- org -*--> Emacs .. [Tab] key + [Org] menu; C-c C-o to follow links
* Before release of package
* ASAP (no longer "Before release of package")
** check arguments e.g., lB <= uB, sum upper Bounds >= 1
** TODO References -->
*** 1) Master thesis: I'd like the thesis to be on our web page
*** 2) References from the thesis, including the "buried" python-paper with *WRONG* algo
** TODO References --> (partly done)
*** DONE 1) References from the thesis, including the "buried" python-paper with *WRONG* algo
*** TODO 2) Master thesis: I'd like the thesis to be on our web page
** DONE CLA() should return a (S3) class, "CLA" w/ print() and plot() methods
** TODO findMu() and findSig() regression check examples *before* changing R/findSigMu.R
** TODO Improve plot() method, using hyperbolic interpolation see R/CLA.R man/plot.CLA.Rd
** TODO A. Norring's Masters thesis has a small 12-asset example (from a published source).
We should add that as a minimally small data set to use in examples,
e.g. plot(). His thesis is in ~/Betreute-Arbeiten/YanhaoShi/Previous_Work/
* With more time, also, e.g., for a short R Journal paper
** SparseMatrix plot of the weights
\name{CLA}
\alias{CLA}
\title{Critical Line Algorithm}
\title{Critical Line Algorithm for mean-variance optimal portfolio}
\description{
The Critical Line Algorithm was first proposed by Markowitz to solve
the mean-variance optimal portfolio problem.
The Critical Line Algorithm was first proposed by Markowitz(1987) to
solve the mean-variance optimal portfolio problem.
... TODO: write more; give references (below) ...
We solve the problem with \dQuote{box} constraints, i.e., allow to
specify lower and upper bounds (via \code{lB} and \code{uB}) for each
asset weight.
Here we provide a pure \R{} implementation, quite fine tuned and
debugged compared to earlier ones.
}
\usage{
CLA(mu, covar, lB, uB, tol.lambda = 1e-07, give.MS = TRUE, keep.names = TRUE)
CLA(mu, covar, lB, uB, tol.lambda = 1e-07,
give.MS = TRUE, keep.names = TRUE)
}
\arguments{
\item{mu}{numeric vector of length \code{n} containing the expected
......@@ -24,28 +30,68 @@ CLA(mu, covar, lB, uB, tol.lambda = 1e-07, give.MS = TRUE, keep.names = TRUE)
\item{keep.names}{\code{\link{logical}} indicating if the
\code{weights_set} matrix should keep the (asset) \code{names(mu)}.}
}
%% \details{
%% }
\details{
The current implementation of the CLA is based (via Norring's)
on Bailey et al.(2013). We have found buglets in that implementation
which lead them to introduce their \dQuote{purge} routines
(\code{purgeNumErr}, \code{purgeExcess}),% in Y. Shi's masters' thesis
which are no longer necessary.
Even though this is a pure \R implementation, the algorithm is quite fast
also when the number of assets \eqn{n} is large (1000s), though that
depends quite a bit on the exact problem.
}
\value{
a \code{\link{list}} with components
\item{weights_set}{ ...}
an object of \code{\link{class}} \code{"CLA"} which is a
\code{\link{list}} with components
\item{free_indices}{ ... }
\item{gammas}{ ... }
\item{lambdas}{ .... }
\item{weights_set}{a \eqn{n \times m}{n * m} matrix of asset weights,
corresponding to the \eqn{m} steps that the CLA has completed or the
\eqn{m} \dQuote{turning points} it has computed.}
\item{free_indices}{a \code{\link{list}} of length \code{m}, the
\eqn{k}-th component with the indices in \eqn{\{1,\dots,n\}} of
those assets whose weights were not at the boundary afater ... }
\item{gammas}{numeric vector of length \eqn{m} of the values
\eqn{\gamma_k}{gamma[k]} for CLA step \eqn{k}, \eqn{k=1,\dots,n}.}
\item{lambdas}{numeric vector of length \eqn{m} of the Lagrange parameters
\eqn{\lambda_k}{lambda[k]} for CLA step \eqn{k}, \eqn{k=1,\dots,n}.}
\item{MS_weights}{the \eqn{\mu(W)} and \eqn{\sigma(W)} corresponding
to the asset weights \code{weights_set}, i.e., simply the same as
\code{MS(weights_set = weights_set, mu = mu, covar = covar)}.}
\code{\link{MS}(weights_set = weights_set, mu = mu, covar = covar)}.}
}
\references{
TODO
Markowitz, H. (1952)
Portfolio selection, \emph{The Journal of Finance} \bold{7}, 77--91;
\doi{10.2307/2975974}.
Markowitz, H. M. (1987, 1st ed.) and
Markowitz, H. M. and Todd, P. G. (2000)
\emph{Mean-Variance Analysis in Portfolio Choice and Capital Markets};
chapters 7 and 13.
%% Markowitz, H., Todd, P., Xu, G. and Yamane, Y. (1993)
%% Computation of mean-semivariance efficient sets by the Critical Line Algorithm,
%% \emph{Annals of Operations Research} \bold{45}(1): 307--317;
%% \doi{10.1007/BF02282055}.
Niedermayer, A. and Niedermayer, D. (2010)
Applying markowitz’s critical line algorithm, in J. B. Guerard (ed.),
Handbook of Portfolio Construction, Springer; chapter 12, 383--400;
\doi{10.1007/978-0-387-77439-8_12}.
Bailey, D. H. and López de Prado, M. (2013)
An open-source implementation of the critical-line algorithm for portfolio
optimization, \emph{Algorithms} \bold{6}(1), 169--196;
\doi{10.3390/a6010169},
}
\author{Alexander Norring did the very first version. Current
implementation: Yanhao Shi and Martin Maechler}
%% \note{
%% }
\author{Alexander Norring did the very first version (unpublished master
thesis). Current implementation: Yanhao Shi and Martin Maechler
}
\seealso{
\code{\link{MS}}.
\code{\link{MS}};
for plotting \code{CLA} results: \code{\link{plot.CLA}}.
}
\examples{
data(muS.sp500)
......@@ -56,11 +102,12 @@ iS <- sample.int(length(muS.sp500$mu), 24)
CLsp.24 <- CLA(muS.sp500$mu[iS], muS.sp500$covar[iS, iS], lB=0, uB=1/10)
CLsp.24 # using the print() method for class "CLA"
plot(CLsp.24)
if(require(Matrix)) { ## visualize how weights change "along turning points"
show(image(Matrix(CLsp.24$weights_set, sparse=TRUE),
main = "CLA(muS.sp500 <random_sample(size=24)>) $ weights_set",
xlab = "turning point", ylab = "asset number"))
}
}
%\keyword{ ~kwd1 }% use one of RShowDoc("KEYWORDS")
......@@ -18,8 +18,12 @@ MS(weights_set, mu, covar)
\item{covar}{covariance matrix of (log) returns (identical to
\emph{argument} of \code{\link{CLA}()}).}
}
%% \details{
%% }
\details{
These are trivially computable from the \code{\link{CLA}()}'s result.
To correctly \emph{interpolate} this, \dQuote{hyperbolic}
interpolation is needed, provided by the \code{\link{findSig}} and
\code{\link{findMu}} functions.% say more, here or there
}
\value{
a \code{\link{list}} with components
\item{Sig}{numeric vector of length \eqn{m} of standard deviations,
......
\name{plot.CLA}
\alias{plot.CLA}
\title{Plotting CLA() results including Efficient Frontier}
\description{
A partly experimental \code{\link{plot}()} method for
\code{\link{CLA}()} objects.
It draws the efficient frontier in the \eqn{\mu_w,\sigma_w} aka (mean,
std.dev.) plane.
Currently, this is quite rudimentary.\cr
Future improvements would allow
- to add the/some single asset points,
- to correctly (`hyperbolically') interpolate between turning points
- add text about the number of (unique) critical points
- add option \code{add = FALSE} which when TRUE would use
\code{\link{lines}} instead \code{plot}.
}
\usage{%% --> ../R/CLA.R
\method{plot}{CLA}(x, type = "o", main = "Efficient Frontier",
xlab = expression(sigma(w)),
ylab = expression(mu(w)),
col = adjustcolor("blue", alpha.f = 0.5),
pch = 16, \dots)
}
\arguments{
\item{x}{a named \code{\link{list}} as resulting from \code{\link{CLA}()}.}
\item{type}{the \code{\link{lines}}/\code{\link{points}} types used
for the efficient frontier. This will become more sophisticated,
i.e., \emph{may change non-compatibly!!}}
\item{main}{main \code{\link{title}}.}
\item{xlab, ylab}{x- and y- axis labels, passed to \code{\link{plot.default}}.}
\item{col, pch}{color and point type, passed to
\code{\link{plot.default}}, but with differing defaults in this method.}
\item{\dots}{potentially further arguments passed to
\code{\link{plot}}, i.e., \code{\link{plot.default}}.}
}
%% \details{
%% }
%% \value{
%% }
\author{Martin Maechler.}
\seealso{
\code{\link{CLA}}, \code{\link{plot.default}}.
}
\examples{
## TODO %% Add A. Norring's small 12-asset example see --> ../TODO
## ---- one example is in help(CLA)
}
\keyword{hplot}