# Tag Info

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....
• 2,914
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### 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 ...
• 2,510
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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 ...
• 2,810

### 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
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### 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 ...
• 9,212
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### 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 $t_0$, $t_1$, ...
• 10.8k
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### 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 ...
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 ...
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### 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 ...
Accepted

• 6,175
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: ...
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 ...
• 8,207
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 ...
• 2,130
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 ...
• 2,956
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 ...
• 1,497
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 $n$ ...
• 13.4k
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 ?
1 vote
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### 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 ...
• 2,885
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
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### 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 ...
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 ...
• 6,175
1 vote
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### 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 $V=C+D$. ...
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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

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