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The professional management of an investment portfolio of various securities (shares, bonds and other securities) in order to meet specified investment goals. The process includes the specification of investment objectives and constraints, choice of asset mix, formulation of portfolio strategy, selection of securities, execution, revision, and evaluation.

The error in your numerical example is in the LHS: without rebalancing, after period 1, the weights of the assets are not 50% each, but 46% and 54%. So the portfolio return in period 2 is not 50%, but …
answered Jun 19 '18 by Enrico Schumann
Have you checked the performance of the particular stocks? library("quantmod") library("PMwR") cmp <- "AAPL" aapl <- getSymbols(Symbols = cmp, auto.assign = FALSE)\$AAPL.Adjusted cmp <- "FB" fb <- g …
answered Mar 5 '19 by Enrico Schumann
As commented by Alex C, the R package PMwR, which I maintain, may offer some useful functionality. A small example: I create a journal of three trades. (Note that a journal here is simply a collection …
answered Mar 5 '18 by Enrico Schumann
It is described in the PMwR manual. An example: I make up a trivial price series. library("PMwR") prices <- 1:5 The signal function instructs the algorithm to buy a random quantity at each timesta …
answered Nov 29 '18 by Enrico Schumann
Since you want to evaluate the results over time, you will need to value open positions between trades. Essentially, create an equity curve for each single-instrument trade; then sum these equity curv …
answered Jul 25 '18 by Enrico Schumann
You could try a heuristic approach. The problem can be split into two nested optimisations: i) in the inner optimisation, given a set of selected assets, compute mean--variance efficient weights; ii) …
answered Mar 16 '17 by Enrico Schumann
Portfolio beta is a function of market vol, portfolio vol and correlation between market and portfolio; so correlation is indeed the only free variable. (But if you have complete control over the port …
answered Jan 9 '20 by Enrico Schumann
Regularisation means that you impose structure on your problem; structure that could not be recognised from the data sample alone. In the context of mean-variance optimisation, regularisation is most …
answered Mar 4 '19 by Enrico Schumann
These problems arise when you compute arithmetic return contributions: in a given month, you want the sum of the funds' contributions to equal the portfolio return. The sum of these single-month contr …
answered Oct 20 '17 by Enrico Schumann
You need to factor borrowing costs into the scenarios (and the currently low interest rates help, so you may want to check with higher rates as well). Since you compute VaR from the scenarios, this w …
answered Feb 7 '19 by Enrico Schumann
It's normal that it takes very long to come close to the efficient frontier with random portfolios. How close you come how fast will be strongly influenced by how you sample the portfolios. In your co …
answered Feb 18 '21 by Enrico Schumann
It would have been helpful had you provided links to those papers. But in general, you need to distinguish between the optimisation model, and the numerical technique used to solve the model. Suppos …
answered Aug 11 '19 by Enrico Schumann