8
votes
Accepted
Which portfolio is more "diversified": the $\frac{1}{N}$, the MDP or the max decorrelation?
First of all, I am not sure what you mean by the ratio in your second point. However, I will try to give you a partial answer at least.
There is a very comprehensive overview of these by EDHEC, page 4....
- 2,915
7
votes
Accepted
How to annualize the correlation matrix?
No, because correlation is a unitless quantity. As you use volatilities to do the scaling, the $\sqrt{252}$ factor should already be taken into account in them.
If you take a correlation of 1 between ...
- 2,570
5
votes
Accepted
Correlation between brownian motions and Cholesky decomposition
I assume, the first equation is about creating 2 correlated standard normal random variables. Then $X_1 = Z_1$ and $X_2 = \rho Z_1 + \sqrt{1- \rho^2}Z_2 $ are correlated with correlation $\rho$. One ...
- 166
5
votes
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Double objective in portfolio optimization
There is nothing wrong mathematically (nor ethically) with this objective function. However, this objective is weird in a couple of ways.
First, there is no weighting on these which implies you prefer ...
- 2,880
5
votes
How to calculate ex Ante Tracking Error
For ex-ante tracking error, you need a forecast covariance matrix $C$. Then the quantity you require is $\sqrt{w^{T}Cw}$, where $w$ is a vector of excess weights relative to the benchmark. You can ...
- 440
4
votes
Accepted
Average Correlation
He is forced to use some tricks because Excel can only take average of a rectangular area, but he wants the avg of upper non-diagonal elements of the matrix only. So he subtracts $\frac{1}{n}$ (the ...
- 9,332
4
votes
Accepted
Correlation Matrix - NaN Values
Your biggest problem is with computing the pairwise correlations of returns.
Suppose for simplicity that you have 2 assets A and B. For asset A, you have closing prices for all 3 days $t_0$, $t_1$, ...
- 12k
3
votes
Accepted
N asset covariance matrix vs N-1 asset covariance matrix
The M-V framework is a minimisation problem of the form:
$$\min_\mathbf{x_n} f(\mathbf{x_n}, \mathbf{u})$$
where $\mathbf{x_n^*}$ solves the $N$ assets weights subject to fixed parameters $\mathbf{u}$,...
- 9,215
3
votes
Accepted
How to properly calculate the average across multiple correlations?
The problem with sample correlation estimator defined as:
$$r_{sample} =\frac{\sum\left(X_i - \bar{X}\right)\left(Y_i - \bar{Y}\right)}{\sqrt{\sum\left(X_i-\bar{X}\right)^2\left(Y_i-\bar{Y}\right)^2}}....
- 866
3
votes
Accepted
Didier Sornette's Strategy to Exploit Return Correlations
I do not understand why t is zero in B(t,t) and 1,2,3,4 in B(i,t). And why did you interprete the value B(i,t) as the inverse of C, but not B(t,t)?
I think B(i,t) is the first column of I. An inverse ...
- 81
3
votes
Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples
I think Cholesky on correlation matrix is better because it makes code apply more generally in case we don't have full rank.
For example, suppose we want to simulate three correlated normals with ...
- 31
2
votes
Accepted
Averaging Correlation Matrices based on different Periodicity
I don't know how common this is, but I've seen it done. Many risk model vendors (Northfield, Axioma) allow the blending of different risk models with different periodicity (e.g. a shorter horizon risk ...
- 321
1
vote
Select top $n$ most correlated assets in universe
Given the question text, my reply would be:
Compute the correlation between all (or just a random subset, if 600^2 computations is too much) pairs of stocks.
Sort the pairs, and choose stocks from ...
- 123
1
vote
Accepted
Sub-portfolio correlation
It was my code :/
VBA is brutal for this work, but my company only lets me use VBA at the moment.
1
vote
Odd Result from Computing Correlation Matrix from Kalman Filter Posteriori Covariance Estimate
Let your linear system be defined by the latent multivariate state variable $x_t$, progressing in an AR(1) fashion, and let your observation at time step $t$ be linear in the latent state:
$$
\begin{...
- 6,435
1
vote
Should portfolios have zero or negative correlation between assets?
While the close vote might be reasonable, there is mathematical arguments that show there is a limit to how negatively correlated a set of assets can be. It is even a classic quant interview question: ...
- 717
1
vote
Accepted
Which is more ill-conditioned, the asset correlation matrix or covariance matrix?
After having tried this with randomly generated vectors, I am consistently seeing the correlation matrix of randomly generated numbers, regardless of which distribution they are sampled from, are ...
- 2,980
1
vote
Which is more ill-conditioned, the asset correlation matrix or covariance matrix?
Yes, you can compare matrix condition numbers if evaluating them for the same problem, for example taking the matrix's inverse. For L2:
For the additional mathematical characterization of ...
- 750
1
vote
Accepted
Computing covariance matrix with historical data
I don’t see how just calculation of Portfolio variance would need an invertible var-covar matrix, I mean you don’t even have to use the matrix notation to calculate it. It may be so that lower time ...
- 958
1
vote
Accepted
How to stress test a correlation matrix
As the correlation matrix will most probably become non-positive-semi-definite with such an ad hoc manipulation, you may try one of the following:
Still run that algorithm and check that the ...
- 6,435
1
vote
Accepted
Correlations between different baskets of assets
Just looking at the basic properties of RVs in terms of correlation and covariance:
Suppose 4 assets; $A,B,C,D$ with $\rho_{X,Y}$ known $\forall X,Y \in \{A,B,C,D\}$.
Let, $U=A+B$, and $V=C+D$.
...
- 9,215
1
vote
Parametric VaR assumption question
Parametric simply means that a set of parameters govern the nature of the (joint) probability distribution of assets, some of those parameters being the correlations. It is not true in general to ...
- 9,215
1
vote
How to do QE scheme for n correlated assets?
I am not familiar with the QE scheme, but I think your question is more general: You want to do a multi-variate diffusion, for $n$ correlated processes.
You have your instantaneous correlations ...
- 2,200
1
vote
generating a correlated RV which has the same correlation to existing samples
As other answers have pointed out, you cannot in general impose any arbitrary correlation structure on your samples. But you can try to rearrange your new sample in such a way that you get as close as ...
- 3,186
1
vote
Accepted
generating a correlated RV which has the same correlation to existing samples
As Richard says, this is really hard to do in a general setting. But if we make extra assumptions about the distribution of the variables, it might be doable.
Assume for instance that your variables ...
- 1,507
1
vote
generating a correlated RV which has the same correlation to existing samples
I think it is hard to add a random variable $X$ with a predefined correaltion to a whole sample $(X_1, \ldots, X_n)$ because this would mean that you have to define relations to each of the $n$ ...
- 13.6k
1
vote
Didier Sornette's Strategy to Exploit Return Correlations
Why you don't just do a least square regression ?
It is likely not stable no ?
- 11
1
vote
Stock Correlation Matrix, Multiple Currencies
What You can do is to just calculate the daily returns, Mean Returns and Excess Returns for each asset, Generate a Variance-Covariance Matrix and multiply it by the Standard Deviation Matrix to ...
- 111
1
vote
ex ante tracking error correlation between funds
Correlation is not an asset allocation measure and thus should have nothing to do with the weights in the portfolio. What you want to do is to figure out the correlation between the two portfolios ...
- 11
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