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3

One way to this is the following (you can code all these constraints if you use the right software, I am doing such things using mathematica) You define $w_{i,j}$ which is the weight of asset $j$ in subportfolio $i$, furthermore you define $w =(w_j)_{j=1}^{\text{no of assets}}$ the total weight of the portfolio in asset $j$. the objects for the ...


3

The problem as you formulate it above already allows for short-selling. You just have to add the constraint: $$ \theta_i \ge l $$ where $l$ is the lower bound. This is equivalent to $$ -\theta_i \le -l $$ which if often the way linear constraints are formulated. Any solver that is able to work with box-constaints can solve this.


3

There is one minor mistake: If you compute sum(mean.var) you'll obtain $-1$ instead of $1$. So it should be mean.var<-xt/sum(xt) in order to ensure that the weights sum up to one. The remainder is correct. Incorporating a risk aversion parameter into the framework requires the solution to the minVar problem (See for example here). Therefore, dividing ...


1

@Richard I assume your $V$ stands for variance so that your formula is correct. The question was about standard deviation, though, and there the square root needs to be taken.


0

The first part of the question is correct. The second is wrong: If you model daily log returns: $$ r_t = \log(P_t)-\log(P_{t-1} $$ then your yearly return $r_y$ is just $$ \sum_{t=0}^{250} r_t, $$ assuming $250$ days. Then $$ E[r_y] = 250 E[r_t], $$ and $$ V[r_y] = 250 V[r_t] $$ if we assume that returns are uncorrelated. In the case of arithmetic ...


3

It depends on the distribution of the returns. If you assume that it's roughly normally distributed, then you have a ~68% chance for a return in the range of 1 standard deviation, ~95% chance for 2 standard deviations, and so on.



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