# Tag Info

Accepted

### 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 (...
• 11.6k

### Current industry standard for (active/passive) portfolio optimizations

I am a professor of finance who has spent his life working in the capital markets in operations, sales, compliance, and research. I would love to tell you about the existence of industry standards, ...
• 4,319
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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 ...
• 7,004
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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 ...
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• 6,084
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### Creating a Covariance Matrix

here is how to get covariance matrix from correlations:
Accepted

### Why does portfolio optimization require a positive-definite covariance matrix?

To supplement the other answer, yes there are optimization reasons for the covariance matrix being symmetric positive definite (SPD). All positive definite matrices are invertible and its inverse is ...
• 760
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### Which portfolio is more "diversified": the $\frac{1}{N}$, the MDP or the max decorrelation?

First of all, I am not sure what you mean by the ratio in your second point. However, I will try to give you a partial answer at least. There is a very comprehensive overview of these by EDHEC, page 4....
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### Portfolio Optimization and Global Minimum Variance Portfolio (GMV)

1) To be honest, any horizon is problematic in this respect. Simple sampling statistics 101 will tell you that the standard error around any estimate of true mean returns is the root time * variance. ...
• 5,101
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### Can a capital market line have a negative slope?

Two separate cases were identified by R.C. Merton in 1972: In the economically more relevant case, where $r_f < b/c$, efficient portfolios are combinations of a long position in [the tangency] ...
• 11.6k
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### Portfolio Optimization sum of weights constraint with short selling

In the early days of Portfolio Theory there were different views about short positions. Some authors modeled short positions as negative and required all weights to add up to 1 (first equation), ...
• 11.6k

### Why does portfolio optimization require a positive-definite covariance matrix?

Positive definite matrix $A$ is defined as $x^TAx > 0$ for all vectors $x$. Since a term $w^T\Sigma w$ in Markowitz (and other models as well) expresses variance in returns, it is a measure of ...

### Contribution of an asset's variance to portfolio variance

In this answer, I am assuming that you want to keep correlations constant. To begin with, note that the $N\times N$ covariance matrix $\Sigma$ with element $\Sigma_{i,j}=Cov(x_i,x_j)$ can be written ...
• 7,035
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### Why isn't the asset with minimum variance given a 100% portfolio weight?

Diversification is key. The clear cut answer is diversification. A weighted combination of assets will more often than not show a lower return variance than even the asset with the lowest variance ...
• 7,035

### What's the point of resampling?

The "estimation problem" in Portfolio Optimization is a serious one. The parameters (returns and covariances) are known very imprecisely. For example the covariance between stocks and bonds ...
• 11.6k
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### Maximum Certainty Equivalent Portfolio with Transaction Costs

Seems like a small mistake in the last equation. It should read \$\Delta^* = A^{-1} \left[\mu-\gamma \Sigma \omega_c - \frac{1}{\iota'A^{-1}\iota} \iota' A^{-1}(\mu-\gamma \Sigma \omega_c )\iota\...
• 116