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

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2
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2answers
845 views

ex ante tracking error correlation between funds

I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold ...
2
votes
0answers
28 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 ...
3
votes
1answer
74 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 ...
2
votes
0answers
22 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 ...
0
votes
0answers
12 views

shrinkage intensity via tawny

I'm attempting to generate a shrunked covariance matrix using the tawny package according to the Ledoit-Wolf method. However, I'm getting an odd result for the shrinkage factor using ...
1
vote
0answers
35 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: ...
2
votes
1answer
87 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 ...
9
votes
0answers
223 views

Covariance estimation: shrinkage, random matrix theory, what else?

Shrinkage was much en-vogue before random matrix theory (RMT) took everybody's attention in covariance matrix estimation, however the latter also showed its limits. A plethora of other estimators has ...
0
votes
1answer
34 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: $$ ...
1
vote
0answers
52 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 ...
0
votes
1answer
68 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 ...
1
vote
1answer
29 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 ...
6
votes
2answers
217 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) ...
32
votes
12answers
16k 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 ...
20
votes
3answers
2k 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 ...
3
votes
0answers
53 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 ...
1
vote
0answers
26 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 ...
0
votes
2answers
98 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 ...
2
votes
0answers
38 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 ...
1
vote
2answers
240 views

Semi-variance/Downside Risk, what about the rest of the covariance matrix?

I just bumped into a rather interesting article from wikipedia : http://en.wikipedia.org/wiki/Downside_risk where they define the semi-variance also called Downside risk, which bascially only ...
5
votes
1answer
152 views

Beta between stock and option

In Black Scholes model I would like to compute $$ \beta_K = \frac{\mathrm{cov}(C_{K,T},S_T)}{\mathrm{cov}(S_T,S_T)} = \frac{\mathrm{cov}((S_T - K)^+,S_T)}{\mathrm{cov}(S_T,S_T)} $$ with respect to say ...
1
vote
0answers
154 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 ...
3
votes
2answers
135 views

How to get Multivariate Betas from an Estimated EWMA co variance Matrix?

I have a portfolio of 4 assets. I also have returns for 3 indices. I want to get the multivariate betas for these 4 assets-based on these assets. I only have the 7 x 7 covariance matrix estimated by a ...
1
vote
2answers
96 views

Garch for covariance matrix?

I have seen plenty of literature about GARCH on estimation volatility. how about covariance? There are plenty of risk models depending on the covariance matrix. I guess we can assume the correlation ...
1
vote
0answers
110 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 ...
3
votes
1answer
169 views

Markowitz Mean-Variance Implied Returns

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 ...
0
votes
1answer
1k views

Can the Minimum Variance Hedge ratio be greater than 1?

The Minimum Variance Hedge ratio is defined as: $h = \rho * \frac{\sigma_S}{\sigma_F}$ For correlation $\rho$ and $\sigma_S , \sigma_F$ for S.D. of changes in asset and future prices accordingly. ...
4
votes
1answer
489 views

Regime Switching for Dynamic Correlations

I would like to implement a Regime Switching for Dynamic Correlations in an out-of-sample analysis using MATLAB. After looking at the literature on the subject, they all refer to an article by Denis ...
1
vote
1answer
75 views

How can I forecast future correlation?

There are some standard models for forecasting volatility (e.g., GARCH) and for forecasting returns (e.g., factor models). What kind of standard models exist for forecasting future correlation between ...
3
votes
1answer
550 views

Covariance matrix and Cholesky decomposition

I am simulating a spread option with stochastic volatility using Monte Carlo simulation. I have the positive-definite covariance matrix $$ \rho = \left( \begin{array}{cccc} 1 & \rho_{1,2} & ...
2
votes
1answer
264 views

How to see the impact of one variable on a set of other variables?

Editing my question: I have decided to use multiple factor model to model my stress test. I am using factor shock method to implement the propagation of shocks. I am doing this according to a book ...
2
votes
3answers
939 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?.
2
votes
1answer
128 views

Correlation of asset to portfolio, given certain variables

Ultimately I'm trying to calculate stdev contribution, but I've hit a hurdle. What I have: 20x20 correlation matrix for various assets Standard deviations for each asset Returns for each asset ...
9
votes
4answers
1k views

Why shrink the covariance matrix?

I'm trying to understand why it's useful to shrink the covariance matrix for portfolio construction or in fact general. Think I missing something. I know if you have 5,000 stocks it's a lot of ...
1
vote
3answers
2k views

Calculate correlation between two sub portfolios and the combined portfolio

I have two sub portfolios (lets call them portfolio a & portfolio b - a portfolio is just a vector of weights that sum to 1) that combine to create a total portfolio. I also have a 2 x 2 ...
23
votes
4answers
9k views

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 ...
14
votes
2answers
2k 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 ...
2
votes
1answer
131 views

Why does my posterior mean differs from Idzorek's results?

I have implemented two different expressions (Idzorek p.6, Walters p.51) of a posterior mean return calculation within a Black-Litterman framework. My results are the same, irrespective of the ...
1
vote
1answer
154 views

How to score a portfolio's diversity based on security returns?

What is the best way to score a portfolio's diversity based on it's returns covariance matrix? I know that if my portfolio has two securities and their returns' correlation coefficient is -1 that is ...
2
votes
1answer
596 views

Need overlapping sample autocorrelation correction for calculating asset return correlations

I want to measure the covariance structure of various asset returns based on varying investment periods. Campbell and Viceira (2005) do this, using known return predictors (i.e. dividend yield, ...
3
votes
0answers
172 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 ...
1
vote
1answer
484 views

VaR Calculation - Covariance matrix is not positive semidefinite

This is a basic question. I have three assets, equally weighted, and all the mutual covariances are -1. Then, the covariance matrix looks like - ...
2
votes
0answers
197 views

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

Let the usual state-space linear model (without constant term for the sake of simplicity): $y_{t}=\beta_{t} X_{t}+\epsilon_{t}$ If we use Gaussian Kalman filter to estimate $\beta_{t}$ we get ...
2
votes
1answer
102 views

To understand FOMC events and its impact on the market

Last month when FOMC meeting decision went out that fed would start to exit QE3, immediately we saw a deleveraging effect: SPY went down, GLD went down, and LQD (bond) went down, but US dollars went ...
6
votes
0answers
229 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 ...
3
votes
1answer
507 views

How to calculate tracking error given mismatches in available data

Apologies if this is an overly simple question. I have a series of stock returns, and I would like to estimate my portfolio's ex-ante tracking error versus the benchmark (S&P 500) given the ...
3
votes
1answer
117 views

How can I evaluate how poor a fit a parametric VaR result would be for a given holding?

I'm currently working on an application that, among other things, computes a one-day parametric VaR for security positions. I understand that the parametric method of computing VaR is a poor fit for ...
5
votes
1answer
3k views

How to use Newey West covariance corrector?

I have implemented the following model: daily_vol(t+1) = A*daily_vol(t) + B*weekly_vol(t) + C*monthly_vol(t) + error where vol means volatility, and A, B, C are ...
3
votes
3answers
663 views

portfolio diversification tester

Are there any online tools (optionally with developer API, to spare me the scraping) that given an existing portfolio, calculate how well a new candidate position would score to increase combined ...