# Tag Info

Accepted

### Two correlated brownian motions

First you need to correct the formula to: $$W_t^2 = \rho W_t^1 + \sqrt{1-\rho^2} Z_t,$$ where $Z_t$ is a BM independent of $W_t^1$ If you calculate the variance and the covariance, then you see ...
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### What is the total correlation between assets in a portfolio?

I just want to add to vonjd's answer some info on the comparison of the 3 methods. This is too big for a comment so I'm posting as a separate answer but please upvote his answer, not mine. Do the ...
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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 ...
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### 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....
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### What is the most stable, non-trivial dependence structure in finance?

It is hard to find a stable non-trivial dependence structure in financial data. Usually when such is found it is hard to rationalize. One of my favorite (although I am sure there are others) is the ...
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Accepted

Let us consider a basket $B$ with components $S_1,\dots,S_n$ : $$B(t) = \sum_{i=1}^nw_iS_i(t)$$ At time $t$, each component has standard deviation $\sigma_i$, $i \in \{1,\dots,n\}$, and pairwise ...
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### Creating a Covariance Matrix

here is how to get covariance matrix from correlations:

### Estimate covariance matrix using prices

If you assume that a financial asset price has a change that is a wiener process then you can view the future value of that asset as the initial value plus the sum of the independent daily changes (...
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• 353

### How to design a strategy whose PnL is proportion to correlation?

You are looking for a correlation swap. There is a PhD thesis on static replication. Sébastien Bossu. Static replication of European options and dynamic replication of correlation swaps. Business ...
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### Correlation between prices or returns?

There is a good explanation here. Summarizing, what we are computing with Pearson correlations are relations between deviations respect to the means, which is no meaningful using prices. So, you ...
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 ...
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### What is the covariance of two correlated Ornstein-Uhlenbeck processes?

Using https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process#Solution $$X^i_t = (X^i_0 + \int_0^t\sigma_i e^{a_i u} dB^i_u)e^{-a_it}$$ and  X^i_t-\mathbb{E}[X^i_t] = e^{-a_it} \int_0^...
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### Pearson correlation coefficient based on OHLC data

Given only OHLC information, with no timing information as when H and L occured in relation to one another, the covariance between any two assets is only defined for O and C since you know when these ...
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### Control for non-synchronous trading in correlations

I contacted one the authors of the original paper. He confirmed that the overlapping three day log returns are to be used on both stock and market returns.
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### Why isn't it appropriate to use correlation between prices in a pairs trade strategy?

If you are correlating prices that would imply that you are sizing positions based on the number of shares in each position. This can result in a book that is very biased in terms of dollars invested....
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### How to calculate implied correlation via observed market price (Margrabe option)

We know that $-1\le\rho_{imp}\le 1$ so perhaps the simplest approach is to try the possible values $\rho_{imp}=\{-1,-0.9,-0.8,\cdots,0.8,0.9,+1\}$, to calculate resulting $\sigma$ values, d± values, ...
• 9,372
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### Brownian Motions theorems

For the first part looks quite obvious, since independence implies that the covariance is zero and since the correlation is just the covariance divided by the product of the standard deviations, it ...
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### Calculating Correlation of Two portfolios?

You may be over-thinking it. It is a straightforward calculation using matrices, as easy as turning the crank of a sausage-making machine. The standard deviation matrix is ...
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### How to test ESG score as a factor against traditional factors

Preliminary/Warning: A correlation test is not an appropriate method for analyzing potential risk-factors! Let's (very precisely) recall, what a risk-factor is (see Bali/Engle/Murray (2016), p.173f.),...
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