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Random Matrix Theory in Risk Management [duplicate]

How can we apply Random Matrix Theory(RMT) in Risk Management for estimation risk of portfolio consisting of correlated assets?
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42 views

Semi-variance/Downside Risk, what about the rest of the covariance matrix?

I just bumped into a rather interesting article from wikipedia : http://en.wikipedia.org/wiki/Downside_risk where they define the semi-variance also called Downside risk, which bascially only ...
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Bayes Stein Porfolio Implementation

From this paper from Jorion. Has anyone implemented this? How is the Covariance matrix estimated? It needs to estimate also the conditional distribution of the returns? Best
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2answers
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Black-Litterman: Why should the views be independent of each other?

This question relates to this question. In the Black-Litterman framework views of inverstors on the market are modelled. These views have a covariance-matrix $\Omega$. I always found it quite ...
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2answers
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How to get Multivariate Betas from an Estimated EWMA co variance Matrix?

I have a portfolio of 4 assets. I also have returns for 3 indices. I want to get the multivariate betas for these 4 assets-based on these assets. I only have the 7 x 7 covariance matrix estimated by a ...
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1answer
140 views

Practical implementation of Libor Market Model

I am trying to implement a project about the BGM model, suggested in the book "The Concepts and Practice of mathematical finance" by Mark Joshi. My question is related to the forward volatility ...
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1answer
162 views

short-sale constraint with nonpositive-definite matrix in portfolio optimization

I need help about portfolio optimization in R. I have inverted matrix and I want to use it as an input in portfolio optimization. It was non-positive definite before I have handled it. In portfolio ...
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1answer
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PCA on term structure of interest rates

Interest rate time series seems to be non-stationary whenever test is performed But covariance or correlation matrix is derived from term structure time series which are non stationary and later PCA ...
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1answer
92 views

“Adding” risk-free asset to covariance matrix after the fact

Given a covariance matrix that was calculated from the returns of a number of risky assets. Is there a way to "add" a risk-free asset to the covariance matrix without calculating its covariance with ...
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1answer
199 views

Portfolio Optimization - n risky assets

I'm currently implementing a CAPM model in Excel: A portfolio of n risky assets when n=6 (in this case) A riskless borrowing rate of 8% and riskless lending rate of 3% I'm given the expected return ...
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1answer
681 views

Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples

Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why? Thanks in advance.
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299 views

Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
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249 views

Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$ w^T \Sigma w + w^T c \rightarrow Min $$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{R}^N$ and ...
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4answers
376 views

Large (5K-10K) non positive definite (particularly near singular) covariance matrices and treatments for Cholesky decomposition

I have a very large covariance matrix (around 10000x10000) of returns, which is constructed using a sample size of 1000 for 10000 variables. My goal is to perform a (good-looking) Cholesky ...
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1answer
375 views

VaR Calculation - Covariance matrix is not positive semidefinite

This is a basic question. I have three assets, equally weighted, and all the mutual covariances are -1. Then, the covariance matrix looks like - ...
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159 views

Covariance estimation

Shrinkage was much en-vogue before RMT took everybody's attention, however the latter also showed its limits. A plethora of other estimators has been presented, but I could not yet spot a golden ...