# Tag Info

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### Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

Markowitz's concepts attracted a great deal of interest from theorists (and still do), but never had much application in practice. The results from practical application were always disappointing (...
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### cvxpy portfolio optimization with risk budgeting

The underlying problem: your ACTR constraints aren't convex The $i$th constraint on your risk contribution can be written: $$w_i \sum_j \sigma_{ij} w_j \leq c_i s$$ And this isn't a convex ...
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### Random Portfolios vs Efficient Frontier

You seem to have two distinct problems: How to generate random portfolios How optimal portfolios are structured Ad 1) A straightforward way to simulate the weights of random portfolios is to use ...

### Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

There has been a split in the community ever since Mandelbrot published his paper "On the Variation of Certain Speculative Prices." See: Mandelbrot, B. (1963). The variation of certain speculative ...

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### What's the importance of duality theory in portfolio optimization?

That's a pretty heavy question for this forum, and its answer is worthy of a semester-long discussion in a university course. The short answer is that (for convex optimization) the dual problem can ...
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### Portfolio with lots of subportfolios

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 ...

### What are some useful approximations to the Black-Scholes formula?

To answer the question by Robert about existing approximations for the Black-Scholes formula in the non-ATM case: yes there exists a simple and fast converging series representation for the Black-...

### Proof that linear returns aggregate across securities

I think you are simply confusing percentage weights and number of assets. In your definition the initial percentage weight of the $m$ assets in the portfolio are given by $w_i^{t - 1}$ and they sum ...
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### Derivation of the efficient frontier set (markowitz problem)

To solve this constraint minimization problem, first form the Lagrangian Function \begin{align} L(w,\lambda_1,\lambda_2)=w'\Sigma w + \lambda_1(w'\boldsymbol{\mu}-m) + \lambda_2 (w'\boldsymbol{1}-1). \...
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### Question on Rockafellar's Paper for optimisation of CVaR

On 1, I suspect that is a typo and that the second formula should sum to r. On 2, that is applying well-known techniques in how to handle piece-wise linear functions in an optimizer. For instance, ...
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### Optimisation with strong correlated Assets

This answer will try and outline all the different possibilities I came across over the last couple of years, including drawbacks. But first, let me outline the problem a little. To appreciate the ...
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