7 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....
  • 2,894
6 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 ...
  • 2,400
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 ...
5 votes
Accepted

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 ...
  • 2,770
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 $t_0$, $t_1$, ...
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 ...
  • 9,167
4 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 ...
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 ...
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}}....
  • 836
2 votes
Accepted

How to infer correlation?

You have the risk factor $F$ and the asset that it is correlated to $r_m$. You can calculate the variances of each of these, say $\sigma^2_F$ and $\sigma^2_m$. If you do not care about the ...
  • 13.3k
2 votes
Accepted

PCA on term structure of interest rates

If you look at changes of the points on the yield curve, then you probably find something stationary - right? Applying PCA on the covariance of these changes makes sense. E.g. you will find out that ...
  • 13.3k
2 votes

Does the correlation of matrices have explanatory power when building a pattern recognition model?

There is a vast literature on modelling time-series with periodcities. Rob Hyndman is one of the leading reseaerchers in this area. He has published the R package ...
  • 13.3k
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 ...
  • 301
2 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 $\mathbf{u}$,...
  • 8,099
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{...
  • 5,913
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
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 ...
  • 2,825
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 ...
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 ...
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 ...
  • 5,913
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 $V=C+D$. ...
  • 8,099
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 ...
  • 8,099
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 ...
  • 2,120
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 ...
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 ...
  • 1,487
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 $n$ ...
  • 13.3k
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

How to calculate ex Ante Tracking Error

Here are the steps:- 1.First you need to calculate the historical return series for your portfolio from the historical return series for each fund by adding the returns for each fund on a daily basis ...
  • 321
1 vote

Isolating single assets standard deviation in a portfolio accounting for correlation

If I understand correctly what you are after is the marginal volatility contribution of a single asset to the portfolio. This is given by $$ \sigma(X_j;X) = \sigma(X_j)\ \rho(X_j, X) $$ See here for ...
  • 4,247

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