# 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 (...

### 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, ...
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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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### 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....

### 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. ...
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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] ...
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### 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 ...

### 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 ...
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### What are the quantitative requirements to distinguish between asset classes?

Defining asset classes from a quantitative perspective is an interesting question that is not really addressed "officially" as far as I know. Let's try to write some requirements you want ...

### 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 ...
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### Mean Variance Portfolio theory and real-world problem?

Mean-variance (MV) is a framework rather than a prescription. This framework allows one to make, discuss, and defend his investment decision. In practice, there are many ways to make adjustments to ...
Seems like a small mistake in the last equation. It should read $\Delta^* = A^{-1} \left[\mu-\gamma \Sigma \omega_c - \frac{1}{\iota'A^{-1}\iota} \iota' A^{-1}(\mu-\gamma \Sigma \omega_c )\iota\... 6 votes Accepted ### What's the importance of duality theory in portfolio optimization? That's a pretty heavy question for this forum, and its answer is worthy of a semester-long discussion in a university course. The short answer is that (for convex optimization) the dual problem can ... 6 votes Accepted ### How can I use a more efficient volatility estimator to improve the co-variance matrix? Let$s$be a$N\times1$vector of standard deviations and$C$be an$N\times N$correlation matrix. The covariance matrix is equal to $$\Sigma=\text{diag}(s) \ C \ \text{diag}(s)$$ where$\text{diag}...
Something to perhaps realize is that your two problems may not be as different as you think if $\lambda$ is an ad-hoc parameter. For any solution to your 2nd problem (where $\theta > 1$), there ...