14 votes
Accepted

Estimate Beta of CAPM from Implied Volatility?

Yes it is a better way. Just take a look to figure 3, from Buss and Vilkov (2012, RFS):
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  • 6,820
11 votes

Two correlated brownian motions

Here is the general approach you can follow to generate two correlated random variables. Let's suppose, X and Y are two random variable, such that: $$X \sim N(\mu_1, \sigma_1^2)$$ $$Y \sim N(\mu_2, \...
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  • 2,118
11 votes
Accepted

What is the total correlation between assets in a portfolio?

This is indeed an interesting question. According to this website, a paper by Goldman Sachs [Tierens and Anadu (2004)] proposes three alternative methods for estimating average stock correlations: ...
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  • 26.9k
10 votes
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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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  • 13.3k
9 votes
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Correlation between stock prices given correlation between returns

We can obtain a closed-form expression for price correlation given (log) return correlation when the two stocks follow geometric Brownian motion: $$S_1(t) = S_1(0)e^{(\mu_1- \frac{1}{2} \sigma_1^2)t}...
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  • 3,250
8 votes

Calculate correlation between two sub portfolios and the combined portfolio

To clarify notation, you have an universe of $n=2000 \space$ stocks and two portfolio vectors $\mathbf{a},\mathbf{b}\in\mathbb{R}^{n}$ with $\left\|\mathbf{a}\right\|_{1}=\left\|\mathbf{b}\right\|_{1}...
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8 votes

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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  • 741
7 votes

What is the preferred GARCH method in practice?

I personally use the simple Garch(1,1) for volatility filtering in the risk management area. In fact in most cases I don't even estimate the parameters, I stick 0.94 for mean reversion, 0.04 for the ...
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  • 4,217
7 votes
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Correlation basket equities

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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7 votes
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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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  • 2,874
6 votes

Why do volatility and correlation increase in times of crisis?

Extra market volatility alone will cause correlations and stock volatilities to spike as you describe, even when overall market structure remains unchanged. There's a minor variation of the very ...
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  • 14.4k
6 votes
Accepted

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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  • 6,820
6 votes

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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  • 8,037
6 votes
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Simulating covariance matrices with nonzero correlation

What does 'simulate a covariance matrix' mean? If the question means, generate an arbitrary correlation matrix for 1000 stocks, then we can choose any symmetric matrix with all 1s down the diagonal, ...
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  • 2,826
5 votes

Correlation of asset to portfolio, given certain variables

If $\Sigma$ is the covariance matrix of all assets and $w$ is the column vector of weightings of the asset in a certain portfolio. Then $$ w^T \Sigma w = VAR $$ is the variance of the portfolio. The ...
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  • 13.3k
5 votes
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Correlation of a lognormal asset and a normal asset

Let $(X_t)_{t\geq 0}$ denote a Geometric Brownian Motion $$ \frac{dX_t}{X_t} = \mu_X dt + \sigma_X dW^X_t,\ \ \ X(0) = X_0$$ such that $X_t$ is lognormally distributed $\forall t > 0$ $$ X_t = X_0 ...
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  • 13.8k
5 votes

Why isn't it appropriate to use correlation between prices in a pairs trade strategy?

You could, and it doesn't hurt for you to test this yourself. Some of my best work has come from drawing the opposite conclusion to conventional wisdom or stylized "facts" in publications. That said, ...
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  • 5,052
5 votes
Accepted

Creating a Covariance Matrix

here is how to get covariance matrix from correlations:
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5 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 ...
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  • 2,350
4 votes

How do I find the most diversified portfolio, or least correlated subset, of stocks?

If you only need to pick 5 out of 10 and want equal weights then just enumerate all 252 possibilities (as pointed out above) and compute the portfolio volatility $(\textbf{1}'K^{(i)}\textbf{1})^{1/2}...
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  • 537
4 votes
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Regime Switching for Dynamic Correlations

The clearest and most intuitive article I have seen so far is Kritzman et al., Regime Shifts: Implications for Dynamic Strategies in FAJ (May / June 2012) It not only shows how you can use HMM for ...
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  • 26.9k
4 votes
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What is Base- vs. Implied Correlation of a CDO tranche?

An implied correlation $\rho_i(k_1,k_2)$ is a correlation that matches the $(k_1,k_2)$ tranche price $P_{k_1}^{k_2}$ (usually computed under a gaussian or student t copula) $$ C(k_1,k_2,\rho_i(k_1,...
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  • 14.4k
4 votes
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Garch for covariance matrix?

I think you're looking for multivariate GARCH models of which this is an overview paper. Multivariate GARCH models have one big drawback: they are pretty hard to estimate due to the number of ...
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  • 7,652
4 votes
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Estimating correlation using EWMA

The $\lambda$ value used in the original paper is arbitrary, but you can estimate that by assuming (in the simplest case) 2 assets and running the following model: $\sigma^2_{12,t+1}$ $=$ $\lambda$$*$...
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  • 2,438
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 ...
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  • 9,077
4 votes
Accepted

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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  • 193
4 votes

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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  • 3,735
4 votes

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, ...
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  • 9,077
4 votes
Accepted

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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  • 1,002
4 votes

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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