Questions tagged [covariance]
A measure of the degree of linear association between a pair of random variables.
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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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6answers
218 views
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 ...
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1answer
63 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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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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1answer
135 views
Questions about beta, correlation, and covariance
Currently, I calculate beta, correlation, and covariance measures using daily log normal returns of Security A and Benchmark A. What would it mean if I were to use daily log normal excess returns in ...
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0answers
33 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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1answer
56 views
Covariance matrix from GJR-GARCH?
I am implementing a AR(1)-GJR-GARCH(1,1) model to some asset returns, and I would need to have a covariance matrix but I struggle to see how I can compute one from the model I used?
I know I can have ...
2
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1answer
106 views
Why the weight vector of 'global minimum variance' the 'eigenvector' with the minimum eigenvalue?
Question
Why is it the case that the weight vector of the global minimum variance portfolio the eigenvector of the covariance matrix with the smallest eigenvalue?
Question with more details
I ...
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2answers
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Widely accepted methods for coming up with the co-variance matrix of assets?
Question
What are the widely accepted ways for coming up with co-variance matrix of assets
after the Markowitz's modern portfolio theory?
Question explained in more detail
After Modern portfolio ...
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1answer
55 views
Generate scenarios of multiple related parameters
Assume I have three industry datasets: interest rates, inflation and unemployment. Data contains information of last ten years and it's monthly.
Now, I would like to create N possible scenarios of ...
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0answers
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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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34 views
Cross-Sectional Multi-Index Model
I'm unsure how to find the covariance matrix in part (b) and what the residual deviations are. Any tips on how to tackle this?
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2answers
157 views
Prove ρ(X,Z) = ρ
The covariance of two random variables $X$ and $Y$ is defined by:
$$\mathrm{Cov}(X,Y）= \operatorname{E}(X-\operatorname{E}(X))(Y-\operatorname{E}(Y))=\operatorname{E}(XY)-\operatorname{E}(X)\...
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1answer
92 views
Co-variance of Portfolio A with Portfolio B
I'm trying to calculate the correlation between two separate portfolios.
I've used A*COV(AB)*B to calculate the co-variance of each portfolio where:
A = Array ...
3
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0answers
93 views
Is Ledoit-Wolf Shrinkage with a Constant Correlation Prior Reasonable for a Stock/Bond Mix?
I've been looking into Ledoit-Wolf shrinkage but I've found the papers concentrate on large numbers of assets that tend to all be highly correlated. Often a universe of large cap stocks.
I'm ...
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1answer
90 views
Covariance and Beta: can anyone explain this calculation?
Let us consider a simple equity portfolio that has exposures to only two factors:
0.5 exposure to value and 0.8 exposure to momentum. Let us assume that the volatilities of the two factors are 3% for ...
2
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1answer
271 views
How to calculate the covariance between two stochastic integrals?
How to calculate the covariance between the integral of a Brownian motion at different times:
$$\text{Cov}\left(\int^{t_1}_0\sigma(t)dW_t,\int^{t_2}_0\sigma(t)dW_t\right)\ ?$$
I know the answer is:
$$\...
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1answer
216 views
target market correlation for long / short equity portfolio
Given a long / short equity portfolio, I want to have some net long market exposure.
My portfolio volatility is fixed to a target, so I don't think it makes sense to target market beta. I think I ...
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1answer
82 views
What are the units of the variance of returns?
I am a little confused about the units of the variance of returns. One way to compute that would be to look at the units of returns-
$$r=\frac{1}{\Delta t}\ln\frac{P(t+\Delta t)}{P(t)}=\text{...
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2answers
341 views
Filtering smallest eigenvalues
In Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors [1], which introduces minimum torsion bets, Meucci gives an example involving the computation of covariance matrices on ...
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3answers
695 views
Negative variance?
Using the formula w*Cov*t(w) I can generate a negative portfolio variance. What are the implications of a negative variance? Should I just assume it's zero? A negative variance is troublesome ...
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1answer
163 views
Variance covariance matrix - number of periods required
Hi I am reviewing the example of Barra risk model in the following document page 23 there is the statement:
"Estimating a covariance matrix for, say, 3,000 stocks requires data
for at least 3,...
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3answers
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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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1answer
133 views
Finding a minimum variance portfolio when using a regulariser?
I am aware that the minimum variance portfolio of a market with $n$ securities can be shown to be:
\begin{equation}
w^* = (1^T_n\Sigma^{-1}1_n)^{-1}\Sigma^{-1}1_n, \\ s.t. \ \ 1^T_nw = 1
\end{...
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1answer
26 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 ...
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0answers
181 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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1answer
122 views
Interest rate risk using copulas
In order to simulate an interest rate yield curve, can I just estimate a covariance matrix of historical key rate data, simulate with a normal copula, spline my simulated key rates, then price my ...
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1answer
350 views
Correlation of asset X with a portfolio of asset Y and Z [closed]
I have three assets and a covariance matrix.
How do I calculate the correlation of asset X with a portfolio that includes assets Y and Z?
For example, assume I want to calculate the correlation of ...
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1answer
318 views
How can I use a more efficient volatility estimator to improve the co-variance matrix?
Using mean-variance, I need to estimate a co-variance matrix $\Sigma$ to obtain the best weights in my portfolio.
However, there are other ways to compute the volatility $\sigma$ than historical ...
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2answers
112 views
Explanations regarding Minimum Variance Portfolio
I am sorry in advance if this question seems a bit stupid but during my class my lecturer said that:
"The traditional estimator of the variance-covariance matrix is the sample covariance. However ...
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0answers
85 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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1answer
4k views
Using CAPM to find correlation of two assets with each other
I stumpled upon an exercise in an investments book:
The data below describe a three-stock financial market that satisfies
the single-index model.
...
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1answer
728 views
How to efficiently get covariance matrices from a rolling window in Matlab?
I'am trying to produce a rolling window to estimate a covariance matrix using a for-loop. I have my returns under the variable returns_sec and I have 260 ...
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1answer
278 views
Variance of a straddle (Black Scholes)
I am trying to determine the variance of the payout of a straddle. For puts and calls individually:
Var[P] = E[P^2] - E[P]^2
Var[C] = E[C^2] - E[C]^2
where:
$$
E[...
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2answers
301 views
Are two stochastic processes independent if the Wiener processes inside are uncorrelated
Assume there are two stochastic processes:
$dx_t = \alpha_1(x_t,t)dt + \beta_1(x_t,t)dW^1_t$
and $dy_t = \alpha_2(y_t,t)dt + \beta_2(y_t,t)dW^2_t$.
Does $dW^1_t\times{dW^2_t} = 0$ imply that $\...
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0answers
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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 ...
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1answer
1k views
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(-...
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1answer
294 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 ...
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0answers
231 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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1answer
144 views
Correlation -1 and standard deviation [closed]
My book says that for a portfolio of two stocks:
$\sigma_p = \sqrt{w_A^2 \sigma_A^2 + (1-w_A)^2 \sigma_B^2 + 2 w_A (1 - w_A) \rho_{AB} \sigma_A \sigma_B}$
Elsewhere it says that if the correlation ...
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1answer
74 views
how to find the weights in a portfolio? [closed]
Compute the weights in a portfolio consisting of two kinds of stocks if the expected return on the portfolio is to be $E(K_v)=10\%$, given the following information on the returns on stock 1 and 2:
$$
...
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1answer
943 views
Variance covariance matrix for a portfolio containing bonds also with other asset classes
What should we take for a bond or a zero coupon bond in order to make a variance covariance matrix?
For example:-
Equities - we take the market price
Cash - we take the spot rates
Bonds - Do we take ...
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1answer
247 views
Calculate control variate for monte carlo simulation
For an exercise I need to calculate $\mathbb{E}[X]$ with a Monte Carlo simulation. I need to use control variate $Y$ with $\text{Var}(Y)=2$ and $\text{Cov}(X,Y)=1$.
I am asked to give the optimale ...
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0answers
166 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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2answers
459 views
What is the preferred GARCH method in practice?
My advance apologies, if this question is too naive or basic. Please be patient with my first experiences with SE; ask for clarification, if needed.
I recognize there are many (often-criticized) ...
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3answers
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How to estimate variance-covariance matrix of assets with different length of historical data? [duplicate]
Consider you have 4 assets A, B, C and D, where
Asset <...
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0answers
259 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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0answers
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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 (...
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0answers
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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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3answers
1k views
Ledoit-Wolf Shrinkage estimator not giving positive definite covariance matrix
I used ten year daily data for 407 stocks and computed the daily and monthly covariance matrices. Since I have more variables than observations for the monthly matrix, I wasn't surprised to find the ...
