# Questions tagged [covariance]

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

20 questions
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### Factor Models: uncorrelated errors don't impact covariances of assets

This question stems from time series factor models (e.g., CAPM, Fama-French, etc.), but is a broader idea. I am trying to comprehend how adding noise to a time series (e.g., error/residual from a ...
369 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 ...
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### 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 ...
201 views

### Using Kendall rank correlation to construct a covariance matrix?

I am wondering if it's mathematically 'correct' to employ a correlation matrix based on Kendall-correlation when constructing a covariance matrix? I.e., is it wrong to multiply standard deviations of ...
63 views

### Why are thousand-ish-factor vendor risk models not extremely overfit and inaccurate?

Many vendor risk models have many hundreds, or even thousands of factors (many of which are highly correlated with each other). Underlying all these risk models is some sort of covariance matrix in ...
70 views

### Is Ledoit-Wolf Shrinkage with a Constant Correlation Prior Reasonable for a Stock/Bond Mix?

I've been looking into Ledoit-Wolf shrinkage but I've found the papers concentrate on large numbers of assets that tend to all be highly correlated. Often a universe of large cap stocks. I'm ...
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### Finding mean vector and covariance matrix for annual returns given quarterly returns

I am currently trying to calculate a vector for the mean annual returns of 4 different asset classes along with their 4x4 covariance matrix in excel. However, I am having problems since the data I ...
206 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 ...
276 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 $P_{t}$, ...
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### target correlation for portfolio

Given a long / short equity portfolio, I want to have some net long exposure. My portfolio volatility is fixed to a target, so in trying to have a certain beta to the market, the only thing I can ...
147 views

### Parametric VaR of a portfolio of a stock and an option on that stock

I understand how to calculate the parametric VaR of a stock and an option separately. But I don't understand how one can calculate the VaR of a portfolio of a stock and an option on that stock using ...
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### Ledoit-Wolf, expected order of optimal shrinkage intensity

I have a question regarding the optimal shrinkage intensity derived in the Ledoit-Wolf method. Specifically, I'm referring to their version concerned with the target defined as the single index factor ...
47 views

### How to calculate the estimation error of portfolio variance using propagation results?

I am trying to find a conservative approximation for the propagated estimation error of a investment portfolio's variance (comprising two assets), given we know the estimation error for the variance ...
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### Deriving Cox, Ingersoll and Ross expression for the relationship between forwards and futures, how do they conclude a specific step?

I'm trying to derive a specific relationship about the relationship between forwards and futures from "The relationship between forward and futures prices", written 1981 by Cox, Ingersoll and Ross (...
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### Marchenko–Pastur, Student distribution and returns

I have a question regarding random matrix theory. I've been studying various papers and I found some confusing definitions of Marchenko-Pastur law. The most clear was the one on wiki: wiki-Pastur-...
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### Fourier transform covariance estimator

I am estimating realized variance and covariance by the estimator described in this paper, and relying on Fourier Transform. Now, as my data is one day of data in ultra high frequency, so that the ...
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### Portfolio Hedging under Uncertain Correlations

I have a portfolio ($w_0=1$) and two hedging assets ($w_1,w_2$) and a co-variance matrix for the three $\Sigma$. However the co-variance $\Sigma$ is only an estimate. For fairly well behaved assets (...
789 views

### How to calculate beta against a multi-asset benchmark

Lets say that I have a benchmark, $BM$ that consists of 3 assets- 30% asset $A$, 30% asset $B$ and 40% asset $C$. Now, lets further assume I am trying to construct a portfolio that uses $BM$ as its ...