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):
- 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:
$$X \sim N(\mu_1, \sigma_1^2)$$
$$Y \sim N(\mu_2, \...
- 2,118
11
votes
Accepted
What is the total correlation between assets in a portfolio?
This is indeed an interesting question.
According to this website, a paper by Goldman Sachs [Tierens and Anadu (2004)] proposes three alternative methods for estimating average stock correlations:
...
- 26.9k
10
votes
Accepted
Two correlated brownian motions
First you need to correct the formula to:
$$
W_t^2 = \rho W_t^1 + \sqrt{1-\rho^2} Z_t,
$$
where $Z_t$ is a BM independent of $W_t^1$
If you calculate the variance and the covariance, then you see ...
- 13.3k
9
votes
Accepted
Correlation between stock prices given correlation between returns
We can obtain a closed-form expression for price correlation given (log) return correlation when the two stocks follow geometric Brownian motion:
$$S_1(t) = S_1(0)e^{(\mu_1- \frac{1}{2} \sigma_1^2)t}...
- 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}...
- 473
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 ...
- 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 ...
- 4,217
7
votes
Accepted
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 ...
- 7,101
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....
- 2,874
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 ...
- 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 ...
- 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 (...
- 8,037
6
votes
Accepted
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, ...
- 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 ...
- 13.3k
5
votes
Accepted
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 $\forall t > 0$
$$ X_t = X_0 ...
- 13.8k
5
votes
Why isn't it appropriate to use correlation between prices in a pairs trade strategy?
You could, and it doesn't hurt for you to test this yourself. Some of my best work has come from drawing the opposite conclusion to conventional wisdom or stylized "facts" in publications.
That said, ...
- 5,052
5
votes
Accepted
5
votes
Accepted
How to annualize the correlation matrix?
No, because correlation is a unitless quantity. As you use volatilities to do the scaling, the $\sqrt{252}$ factor should already be taken into account in them.
If you take a correlation of 1 between ...
- 2,350
4
votes
How do I find the most diversified portfolio, or least correlated subset, of stocks?
If you only need to pick 5 out of 10 and want equal weights then just enumerate all 252 possibilities (as pointed out above) and compute the portfolio volatility
$(\textbf{1}'K^{(i)}\textbf{1})^{1/2}...
- 537
4
votes
Accepted
Regime Switching for Dynamic Correlations
The clearest and most intuitive article I have seen so far is
Kritzman et al., Regime Shifts: Implications for Dynamic Strategies in FAJ (May / June 2012)
It not only shows how you can use HMM for ...
- 26.9k
4
votes
Accepted
What is Base- vs. Implied Correlation of a CDO tranche?
An implied correlation $\rho_i(k_1,k_2)$ is a correlation that matches the $(k_1,k_2)$ tranche price $P_{k_1}^{k_2}$ (usually computed under a gaussian or student t copula)
$$
C(k_1,k_2,\rho_i(k_1,...
- 14.4k
4
votes
Accepted
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 ...
- 7,652
4
votes
Accepted
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$$*$...
- 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 ...
- 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.
- 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....
- 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, ...
- 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 ...
- 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.),...
- 2,926
Only top scored, non community-wiki answers of a minimum length are eligible