# Questions tagged [covariance]

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

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### Covariance of the product of log normal process and normal procces

I tried to compute the following covariance : $$Cov(e^{\int_{t}^{T}W^1_sds},\int_{t}^{t+1}W^2_sds)$$ where $W^1_t$ and $W^2_t$ are Brownian motions such that $dW_t^1dW_t^2=\rho dt$ My idea was to ...
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### Using the MMULT TRANSPOSE Formula for Ex-Ante Tracking Error

I understand that the most widely used ex-ante tracking error expression is $\sqrt{w^TSw}$. This is very similar to the calculation of Portfolio Variance and/or Standard Deviation. The conceptual ...
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### Covariance of ARCH(2) model

I am having problems solving the following exercise: The solution is the following: I understand we are calculating E(r^2t) and E(r^2tr^2t-1) because they are part of the covariance formula, and ...
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### Find k of n assets that "minimize" the correlation matrix

I'm trying to find an efficient way to select $k$ from $n$ risky assets that are the least correlated with each other. I know that I can perform a brute-force search of all $k$-sized combinations of ...
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### Association between a random variable and Radon-Nikodym derivative

Suppose that $X$ is a random variable and $\frac{d\mathbb{Q}}{d\mathbb{P}}$ is the Radon-Nikodym derivative. The quantity under consideration is as follows: \begin{equation} Cov(X, \frac{d\mathbb{Q}}{...
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### Show that $\text{Cov}[X_r,X_s]=\text{Cov}[X_{r+h},X_{s+h}]$ for $X_t=a+bZ_t+cZ_{t-2}.$

Problem: Let $\{Zt\}$ be a sequence of independent normal random variables, each with mean $0$ and variance $\sigma^2$, and let $a$, $b$, and $c$ be constants. Is $X_t=a+bZ_t+cZ_{t-2}$ a (weakly) ...
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### Is it possible to apply PCA to a time-series of covariances?

I understand that Principal Component Analysis (PCA) can be applied for cross-sectional as well as for time-series data. Nevertheless, I am trying to figure out if there is anything wrong with ...
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### Calculating covariance from three variances

I have been asked to look to refactor some code. There is a line shown below: $\text{implied covariance} = -\frac{(\text{var}_1 - \text{var}_2 - \text{var}_3)} {2}$, where $\text{var}_1$ is the ...
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### Is there a differentiable formulation of Prado's HRP algo?

I get the sense the algo is just a graph representation the dependency structure. Am wondering if there is anything written on learning the weights by optimizing some parameters rather than a forward ...
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### Estimate covariance matrix using prices

We generally estimate the covariance matrix of assets using their returns instead of prices. Why is that the case? I can think of two possible reasons and would appreciate comments/feedback regarding ...
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### Is a more robust Covariance estimation possible?

I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...