Questions tagged [covariance]

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

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432 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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422 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 ...
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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 ...
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108 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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209 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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275 views

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 ...
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53 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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211 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 ...
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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 $P_{t}$, ...
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1answer
150 views

Covariance - Negative Portfolio

How do you calculate the one day standard deviation (in dollars) for a portfolio that is short $30,000? How do you calculate the weightings to use? I already have the necessary covariance matrix.
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106 views

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 ...
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52 views

covariance matrix in the CAPM model

I'm running a simulation for a 5 asset portfolio, calculating the optimal weights of each asset both with the statistical model (i.e. single index) and with the CAPM. my question is: how do you ...
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31 views

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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53 views

One day standard deviation of a portfolio (long/short, different scalars)

I am attempting to calculate the expected one-day standard deviation of a portfolio in dollars. In other words, I am looking for the following: "I expect my portfolio to move _______ dollars on ...
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39 views

Covariance time frequency

I have rolling 3-year returns for an asset and a benchmark. I want to compare the covariance of the asset and benchmark, should I use the covariance of the rolling 3-year returns or the covariance ...
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90 views

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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265 views

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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171 views

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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45 views

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 (...
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885 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 ...
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244 views

modeling regime switching for Correlation matrix

I am trying to estimate covariance in multiple time series. However, I want to do this using a regime-switching framework. So, I start with fitting a GARCH(1,1) model and then de-volatalize the series....
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43 views

Ranking assets by covariance vs correlation

After every change in portfolio (i.e. every trade), I need to calculate a price for each asset in my portfolio. But the calculator is slow. So I want to order the sequence of price updates, from the ...
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27 views

Covariance of Individual Return and Portfolio Return

Hi guys, Is it possible to get the covariance between the individual return and portfolio return given the correlation matrix, volatility matrix, weights matrix and return matrix? I know how to get ...
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53 views

Can I build an efficient frontier using matrix algebra?

If i have a vector of expected returns $A$, a covariance matrix $C$ and a vector of the corresponding weights $W$ for each investment, is it possible to generate the efficient frontier with vector ...
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24 views

Decomposition of Contribution to Variance

$C$ is a $N\times N$ covariance matrix of stock returns. Assuming $w$ is a vector of positions in each asset, the total variance of the portfolio is $$w^TCw$$ The contribution to total variance of the ...
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1answer
38 views

Decomposing Co-variance of Two Assets Terminal Prices into Forward measures

Let $X_T,Y_T$ be the terminal values of two price processes following Continuous Gaussian Motion (I.E.) let us assume no jumps. Further assume the correct forwards/futures price is given by $F^X_{t,T} ...
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56 views

Trading Bands for Tactical Asset Allocation

I am currently working through Portfolio Construction and Risk Budgeting, 4th edition, by Dr. Bernd Scherer. In chapter 12.6 the following methodology to construct trading bands around a tactical ...
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37 views

Mean-Variance Optimization - Appropriate to use covariance of daily returns if strategy involves fixed hold of 3 months?

I'm implementing the strategy outlined Quantitative Momentum (Gray & Vogel), which basically involves investing each quarter in a set of "high-quality momentum stocks" for a fixed 3-month hold ...
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30 views

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 ...