A measure of the degree of linear association between a pair of random variables.

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28
votes
5answers
4k views

How do I graphically represent the evolution of a covariance matrix over time?

I am working with a set of covariance matrices evaluated at various points in time over some history. Each covariance matrix is $N\times N$ for $N$ financial time-series over $T$ periods. I would ...
26
votes
12answers
10k views

Why does the minimum variance portfolio provide good returns?

I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get ...
19
votes
4answers
6k views

What is the best way to “fix” a covariance matrix that is not positive semi-definite?

I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix). I am ...
18
votes
3answers
1k views

Tools in R for estimating time-varying copulas?

Are there libraries in R for estimating time-varying joint distributions via copulas? Hedibert Lopes has an excellent paper on the topic here. I know there is an existing packaged called copula but ...
12
votes
4answers
2k views

How do you evaluate a covariance forecast?

Suppose you have two sources of covariance forecasts on a fixed set of $n$ assets, method A and method B (you can think of them as black box forecasts, from two vendors, say), which are known to be ...
12
votes
2answers
1k views

Cleansing covariance matrices via Random matrix theory

I am exploring de-noising and cleansing of covariance matrices via Random Matrix Theory. RMT is a competitor to shrinkage methods of covariance estimation. There are various methods expressed usually ...
9
votes
1answer
416 views

How to estimate the covariance of an index with a basket of stocks?

What would be an ideal way to estimate the covariance of an index with a basket of stocks? For example, should I use one-tail ANOVA test or an individual stock & index F-test?
8
votes
4answers
513 views

Why shrink the covariance matrix?

I'm trying to understand why it's useful to shrink the covariance matrix for portfolio construction or in fact general. Think I missing something. I know if you have 5,000 stocks it's a lot of ...
8
votes
2answers
810 views

Analytical relationship between a covariance matrix and cross-sectional dispersion

Given an expected returns vector and a covariance matrix, one can perform a joint draw and measure the average cross-sectional variation as the standard deviation across returns for a particular joint ...
7
votes
3answers
296 views

age-sensitive correlation measurements in finances

When it comes to comparing returns or prices of instruments like stocks/ETFs, are there any well-established formulas, or ones in common use, that place stronger emphasis on recent correlations more ...
7
votes
2answers
185 views

Is there an optimal covariance one would want forecasts to have?

Often in a quant process, one will generate a time series of return forecasts and use them in some sort of optimization to generate a portfolio. Generally, there will be a covariance matrix of market ...
6
votes
1answer
519 views

What do eigenvalues/eigenvectors of the yield/forward rates covariance matrices mean?

I have 5 bonds (with maturities 1,2,3,4,5 years) which I calculated the yield curve for 10 days. I also calculated the forward rates from the yield rates. Now I've been told to calculate the ...
5
votes
1answer
536 views

Proof for non-positive semi-definite covariance matrix estimator

It is well known that the standard estimator of the covariance matrix can lose the property of being positive-semidefinite if the number of variables (e.g. number of stocks) exceeds the number of ...
5
votes
2answers
285 views

Most natural generalization of covariance/correlation to model dependence of extreme events

One of the most serious shortcomings of covariance/correlation are the assumptions of linearity and normality. What is the most natural generalization of these measures of dependence when you want to ...
5
votes
1answer
2k views

How to use Newey West covariance corrector?

I have implemented the following model: daily_vol(t+1) = A*daily_vol(t) + B*weekly_vol(t) + C*monthly_vol(t) + error where vol means volatility, and A, B, C are ...
5
votes
0answers
150 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 ...
5
votes
0answers
181 views

Stress testing covariance

Going one level beyond stressed scenarios, to parameters e.g. for a VaR measure: what are the most common approaches for stressing a covariance/correlation matrix, especially taking portfolio exposure ...
4
votes
0answers
245 views

Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
3
votes
2answers
771 views

Covariance for arbitrarily large portfolios

I am implementing a method in Java to calculate the variance, covariance, and value at risk for a portfolio, which should be flexible for use with any number of assets in a portfolio. I am struggling ...
3
votes
1answer
291 views

How to calculate tracking error given mismatches in available data

Apologies if this is an overly simple question. I have a series of stock returns, and I would like to estimate my portfolio's ex-ante tracking error versus the benchmark (S&P 500) given the ...
3
votes
1answer
99 views

How can I evaluate how poor a fit a parametric VaR result would be for a given holding?

I'm currently working on an application that, among other things, computes a one-day parametric VaR for security positions. I understand that the parametric method of computing VaR is a poor fit for ...
3
votes
3answers
551 views

portfolio diversification tester

Are there any online tools (optionally with developer API, to spare me the scraping) that given an existing portfolio, calculate how well a new candidate position would score to increase combined ...
3
votes
0answers
157 views

Should I use Resampling or Expectation Maximization to compute a robust covariance matrix?

I have several assets, each with different return histories. Some of the assets have 75 days of return history, others have 40 or so days. In calculating a robust covariance matrix, should I be using ...
2
votes
1answer
93 views

Correlation of asset to portfolio, given certain variables

Ultimately I'm trying to calculate stdev contribution, but I've hit a hurdle. What I have: 20x20 correlation matrix for various assets Standard deviations for each asset Returns for each asset ...
2
votes
1answer
253 views

Need overlapping sample autocorrelation correction for calculating asset return correlations

I want to measure the covariance structure of various asset returns based on varying investment periods. Campbell and Viceira (2005) do this, using known return predictors (i.e. dividend yield, ...
2
votes
1answer
81 views

To understand FOMC events and its impact on the market

Last month when FOMC meeting decision went out that fed would start to exit QE3, immediately we saw a deleveraging effect: SPY went down, GLD went down, and LQD (bond) went down, but US dollars went ...
2
votes
1answer
105 views

How to see the impact of one variable on a set of other variables?

Editing my question: I have decided to use multiple factor model to model my stress test. I am using factor shock method to implement the propagation of shocks. I am doing this according to a book ...
2
votes
1answer
188 views

Combining covariances?

Consider an economy with assets with return processes $A$, $B$, $C$, $D$. Consider a weighted index with return process $I=aA + bB + cC + dD$ where $a,b,c,d$ are coefficients, and $a+b+c+d = 1$. ...
2
votes
1answer
64 views

Why does my posterior mean differs from Idzorek's results?

I have implemented two different expressions (Idzorek p.6, Walters p.51) of a posterior mean return calculation within a Black-Litterman framework. My results are the same, irrespective of the ...
2
votes
0answers
147 views

Good criteria to sort state-space $\beta_{t}$ according to Kalman filter output

Let the usual state-space linear model (without constant term for the sake of simplicity): $y_{t}=\beta_{t} X_{t}+\epsilon_{t}$ If we use Gaussian Kalman filter to estimate $\beta_{t}$ we get ...
1
vote
3answers
333 views

Calculate correlation between two sub portfolios and the combined portfolio

I have two sub portfolios (lets call them portfolio a & portfolio b - a portfolio is just a vector of weights that sum to 1) that combine to create a total portfolio. I also have a 2 x 2 ...
1
vote
3answers
213 views

Handling Missing values in stocks returns when estimating the co variance matrix

What is the best way to handle missing values when stocks did not exist for the entire historical period?.
1
vote
1answer
336 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 - ...
1
vote
1answer
119 views

How to score a portfolio's diversity based on security returns?

What is the best way to score a portfolio's diversity based on it's returns covariance matrix? I know that if my portfolio has two securities and their returns' correlation coefficient is -1 that is ...
1
vote
3answers
2k views

Annualized Covariance

I have two time series. One with monthly returns on an asset and one with monthly returns on a benchmark index. I have calculated the covariance using the ...
1
vote
1answer
165 views

ex ante tracking error correlation between funds

I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold ...