# Tag Info

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### Why does the Markowitz mean-variance model require the assumption of normality?

it doesn't require normality. What it requires is that the investor's decisions are determined by mean and variance. A normal distribution is determined by mean and variance, so if you assume joint ...
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### What is the total correlation between assets in a portfolio?

This is indeed an interesting question. According to this website, a paper by Goldman Sachs [Tierens and Anadu (2004)] proposes three alternative methods for estimating average stock correlations: ...
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### Is there a way using matrix algebra to add portfolios to a covariance matrix of assets?

If your two assets are denoted by random variables $X_1$, $X_2$, with 2x2 covariance matrix $\mathbf{Q}$ and the portfolios: $$Z_1 = w_{11} X_1 + w_{12} X_2$$ $$Z_2 = w_{21} X_1 + w_{22} X_2$$ ...

### What is the total correlation between assets in a portfolio?

I just want to add to vonjd's answer some info on the comparison of the 3 methods. This is too big for a comment so I'm posting as a separate answer but please upvote his answer, not mine. Do the ...
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### Inverse Covariance Matrix Transformation from CAPM

This is the result of the Sherman-Morrison inversion for the sum of an invertible matrix and an outer product. You will find this (and many other helpful methods) in the Matrix Cookbook. Specifically, ...

### Estimate covariance matrix using prices

If you assume that a financial asset price has a change that is a wiener process then you can view the future value of that asset as the initial value plus the sum of the independent daily changes (...
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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 ...
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### Portfolio Optimisation/Covariance Estimation on a large scale

Broadly speaking, as you probably already know, there are 2 approaches to estimating large covariance matrices: 1) Shrinkage Methods like Ledoit-Wolf that try to reduce the noise in a large matrix (N ...
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### Transform raw forecasts into orthogonal forecasts

I do not have access to this book but I suppose the decomposition is the cholesky decomposition (if you use R, simply generate it with chol(cov(g)) where g is a ...

### Generating a random covariance matrix with variances in range

A useful decomposition is, in R's matrix notation, V = S %*% C %*% S, in which S is a matrix with the standard deviations on the ...