# Questions tagged [covariance]

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

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### 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 ...
28k 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 ...
4k 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 ...
2k 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 ...
3k 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?.
8k 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 ...
3k 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 ...
2k views

### CAPM model as a regression

The CAPM model states that the returns of a stock are- $r_s=r_f+\beta (r_m-r_f)+\varepsilon_s$ The $\beta$ defined above is then calculated as $\frac{cov(r_s,r_m)}{var(r_m)}$. My question is ...
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### What is the covariance of two correlated Ornstein-Uhlenbeck processes?

What is the covariance of two correlated Ornstein-Uhlenbeck processes? I was trying correlation(1,2)*Var1^(1/2)*Var2^(1/2), but I am not sure! I took Var1=(sigma1^2/(2*speedofmeanreversion1))*(1-exp(-...
283 views

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

Let's assume the usual state-space linear model without constant term for simplicity: $y_{t}=\beta_{t} X_{t}+\epsilon_{t}$ If we apply Gaussian Kalman filter to estimate $\beta_{t}$ we get $P_{t}$, ...
768 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 ...
What is the closed form solution for the following inverse Markowitz problem? Given a mean-variance optimized fully invested portfolio $X$, a risk aversion parameter $\lambda$ and a var-covar ...