The covariance tag has no wiki summary.
23
votes
5answers
2k 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 ...
21
votes
9answers
6k 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 ...
17
votes
2answers
712 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 ...
14
votes
3answers
3k 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 ...
11
votes
1answer
687 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 ...
10
votes
4answers
1k 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 ...
9
votes
1answer
343 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
2answers
578 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
2answers
164 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
181 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 ...
6
votes
3answers
259 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 ...
5
votes
1answer
393 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 ...
4
votes
2answers
199 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 ...
4
votes
1answer
252 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 ...
4
votes
0answers
155 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
610 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
73 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
70 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
430 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
85 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 ...
2
votes
1answer
101 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 $a+b+c+d = 1$.
...
1
vote
3answers
477 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 ...
